algebra 1 student edition

Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 1 Foundations for Algebra Exercise 1.9

Algebra 1 Common Core Answers Student Edition Grade 8 – 9

Chapter 1 Foundations for Algebra Exercise 1.9 1LC

Chapter 1 Foundations for Algebra Exercise 1.9 1RE

Chapter 1 Foundations for Algebra Exercise 1.9 2LC

Chapter 1 Foundations for Algebra Exercise 1.9 2RE

Chapter 1 Foundations for Algebra Exercise 1.9 3LC

Chapter 1 Foundations for Algebra Exercise 1.9 3RE

Chapter 1 Foundations for Algebra Exercise 1.9 4LC

Chapter 1 Foundations for Algebra Exercise 1.9 4RE

Chapter 1 Foundations for Algebra Exercise 1.9 5LC
The objective is to differentiate between inductive and deductive reasoning.
Inductive reasoning is the process of reaching a conclusion that starts with an observed pattern. It is based on the assumption that the observed pattern continues. So, the conclusion may not be always true in real world.
On the other side, deductive reasoning is the process of reaching a conclusion logically that starts with rules that are true. So, the conclusion must be true.

Chapter 1 Foundations for Algebra Exercise 1.9 6LC
The objective is to find the similarity and difference between writing an equation to represent a situation involving two variables and writing an equation to represent a situation involving only one variable.
One similarity is that each equation contains unknown value(s).
One difference is that one of them contains only a single variable and the other is a relation connecting two variables.

Chapter 1 Foundations for Algebra Exercise 1.9 7LC

Chapter 1 Foundations for Algebra Exercise 1.9 8E

Chapter 1 Foundations for Algebra Exercise 1.9 9E

Chapter 1 Foundations for Algebra Exercise 1.9 10E

Chapter 1 Foundations for Algebra Exercise 1.9 11E

Chapter 1 Foundations for Algebra Exercise 1.9 12E

Chapter 1 Foundations for Algebra Exercise 1.9 13E

Chapter 1 Foundations for Algebra Exercise 1.9 14E

Chapter 1 Foundations for Algebra Exercise 1.9 15E

Chapter 1 Foundations for Algebra Exercise 1.9 16E

Chapter 1 Foundations for Algebra Exercise 1.9 17E

Chapter 1 Foundations for Algebra Exercise 1.9 18E

Chapter 1 Foundations for Algebra Exercise 1.9 19E

Chapter 1 Foundations for Algebra Exercise 1.9 20E

Chapter 1 Foundations for Algebra Exercise 1.9 21E

Chapter 1 Foundations for Algebra Exercise 1.9 22E

Chapter 1 Foundations for Algebra Exercise 1.9 23E

Chapter 1 Foundations for Algebra Exercise 1.9 24E

Chapter 1 Foundations for Algebra Exercise 1.9 25E

Chapter 1 Foundations for Algebra Exercise 1.9 26E

Chapter 1 Foundations for Algebra Exercise 1.9 27E

Chapter 1 Foundations for Algebra Exercise 1.9 28E

Chapter 1 Foundations for Algebra Exercise 1.9 29E

Chapter 1 Foundations for Algebra Exercise 1.9 30E

Chapter 1 Foundations for Algebra Exercise 1.9 31E

Chapter 1 Foundations for Algebra Exercise 1.9 32E

Chapter 1 Foundations for Algebra Exercise 1.9 33E
Consider the pattern “Each packet contains 12 pencils”.
So, the number of pencils is affected by the number of packets. To find the total number of pencils in a number of packets, you need to multiply the number of packets and the number of pencils contained in each packet. For example, the total number of pencils in 5 packets is.
Two variables are required to represent the pattern using an equation, one that represent number of packets and another that represent number of pencils.
Let x represent number of packets and y represent number of pencils.
Since each packet contains 12 pencils, y is always 12 times x.
So, the equation that represents the pattern is, where x denoting number of packets y denoting number of pencils.

Chapter 1 Foundations for Algebra Exercise 1.9 34E
Consider the pattern “Temperature risesevery 45 min”.
Suppose that the starting temperature is.
The aim is to represent the pattern using a table, an equation, and a graph.
Note that,
So, if the number of hours increases by, the temperature will be increase by.
To represent the pattern using a table, draw two rows having a number of columns.
Label the first row “Hours (h)” and the second row “Temperatures”.
Put the valuesin the first row.

Two variables are required to represent the pattern using an equation, one that represents hours and another that represents temperatures in.
Let x represent hours and y represent temperature in.
Replace the labels in the table by the variables.

Looking at the above table, you can see that y is always 60 more thantimes x.
So, the equation that represents the relationship is, where x denoting number of hours and y denoting temperatures in.
After converting the fractions into decimals, the ordered pairsrepresented by the table are:
To represent the relationship using a graph, plot the ordered pairs on a coordinate plane and connect them by a straight line.
Extend the line on both sides and add arrow(s) to show that the line continues infinitely.

Chapter 1 Foundations for Algebra Exercise 1.9 35E
Consider the ordered pairs:
The aim is to represent the ordered pairs using a table, a graph, and an equation.
In an ordered pair, the first value is the x-coordinate and the second value is the y-coordinate.
For example, the x- and y-coordinates of the first ordered pairare 2 and -5.5 respectively.
To represent the ordered pairs using a table, draw two rows having a number of columns.
Label the first row “x” and the second row “y”.

Chapter 1 Foundations for Algebra Exercise 1.9 36E

Chapter 1 Foundations for Algebra Exercise 1.9 37E

Chapter 1 Foundations for Algebra Exercise 1.9 38E

Chapter 1 Foundations for Algebra Exercise 1.9 39E

Chapter 1 Foundations for Algebra Exercise 1.9 40E

Chapter 1 Foundations for Algebra Exercise 1.9 41E

Chapter 1 Foundations for Algebra Exercise 1.9 42E

Chapter 1 Foundations for Algebra Exercise 1.9 43E

Chapter 1 Foundations for Algebra Exercise 1.9 44E

Chapter 1 Foundations for Algebra Exercise 1.9 45E

Chapter 1 Foundations for Algebra Exercise 1.9 46E

Chapter 1 Foundations for Algebra Exercise 1.9 47E

Chapter 1 Foundations for Algebra Exercise 1.9 48E

Chapter 1 Foundations for Algebra Exercise 1.9 49E

Chapter 1 Foundations for Algebra Exercise 1.9 50E

Chapter 1 Foundations for Algebra Exercise 1.9 51E

Chapter 1 Foundations for Algebra Exercise 1.9 52E

Chapter 1 Foundations for Algebra Exercise 1.9 53E

Chapter 1 Foundations for Algebra Exercise 1.9 54E

Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 1 Foundations for Algebra Exercise 1.8

Algebra 1 Common Core Answers Student Edition Grade 8 – 9

Chapter 1 Foundations for Algebra Exercise 1.8 1CB
The amount y (in ton) of waste placed in the landfill in x months is given by the equation
y = 560x
The aim is to find the number of months required to accumulate 11,200 t of waste in the landfill by making a table on a graphical calculator.
We need to find the value of x when y = 11,200.
On a T-83 Plus graphical calculator,





The value of x for which y = 11,200 is x = 20.
It will take 20 months to accumulate 11,200 t of waste in the landfill.

Chapter 1 Foundations for Algebra Exercise 1.8 1LC
Consider the equation
y + 1 = 8
The aim is to check whether y = -9 a solution of the equation y + 1 = 8.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
First substitutein the equation and then check whether it is true.

Chapter 1 Foundations for Algebra Exercise 1.8 2CB
The amount y (in dollars) of the customer’s purchase, if x is the amount (in dollars) of the purchase before the coupon is used, is given by the equation
y = x – 15
The aim is to find the original price of a shirt if a customer using the coupon pays $17.
We need to find the value of x when y = 17.
Prepare a table of values using a graphical calculator.
On a T-83 Plus graphical calculator,





The value of x for which y = 17 is x = 32.
Therefore, the original price of the shirt was $32.

Chapter 1 Foundations for Algebra Exercise 1.8 2LC
Consider the equation
x – 3 = 12
The aim is to find the solution of the equation using mental math.
The phrase that describes the equation is “a number minus 3 equals 12”.
Ask yourself “What number minus 3 is equal to 12?”
The answer is 15.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.

Chapter 1 Foundations for Algebra Exercise 1.8 3LC

Chapter 1 Foundations for Algebra Exercise 1.8 4LC

Chapter 1 Foundations for Algebra Exercise 1.8 5LC
An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.
The aim is to write an open equation containing one variable and division.
An example of an open equation containing one variable(x) and division is

Chapter 1 Foundations for Algebra Exercise 1.8 6LC

Chapter 1 Foundations for Algebra Exercise 1.8 7E
Consider the equation 85 + (-10) = 95
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation does not contain variable(s), it is not an open sentence.
Simplify each side of the equation and check whether they are equal.

Since the expressions on either side of the equal sign are not equal, the equation is false.

Chapter 1 Foundations for Algebra Exercise 1.8 8E
Consider the equation 225 ÷ t – 4 = 6.4
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation contains a variable, t, it is an open sentence.

Chapter 1 Foundations for Algebra Exercise 1.8 9E
Consider the equation 29 – 34 = -5
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation does not contain variable(s), it is not an open sentence.
Simplify each side of the equation and check whether they are equal.

Since the expressions on either side of the equal sign are equal, the equation is true.

Chapter 1 Foundations for Algebra Exercise 1.8 10E
Consider the equation -8(-2) – 7 = 14 – 5
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation does not contain variable(s), it is not an open sentence.
Simplify each side of the equation and check whether they are equal.

Since the expressions on either side of the equal sign are equal, the equation is true.

Chapter 1 Foundations for Algebra Exercise 1.8 11E
Consider the equation 4(-4) ÷ (-8)6 = -3 + 5(3)
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation does not contain variable(s), it is not an open sentence.
Simplify each side of the equation and check whether they are equal.

Since the expressions on either side of the equal sign are not equal, the equation is false.

Chapter 1 Foundations for Algebra Exercise 1.8 12E
Consider the equation 91 ÷ (-7) – 5 = 35 ÷ 7 + 3
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation does not contain variable(s), it is not an open sentence.
Simplify each side of the equation and check whether they are equal.

Since the expressions on either side of the equal sign are not equal, the equation is false.

Chapter 1 Foundations for Algebra Exercise 1.8 13E
Consider the equation 4a – 3b = 21
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation contains variables a and b, it is an open sentence.

Chapter 1 Foundations for Algebra Exercise 1.8 14E
Consider the equation 14 + 7 + (-1) = 21
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation does not contain variable(s), it is not an open sentence.
Simplify each side of the equation and check whether they are equal.

Since the expressions on either side of the equal sign are not equal, the equation is false.

Chapter 1 Foundations for Algebra Exercise 1.8 15E
Consider the equation 5x + 7 = 17
The aim is to test whether the equation is true, false, or open.
Remember that:

• An equation is true if the expressions on either side of the equal sign are equal.
• An equation is false if the expressions on either side of the equal sign are not equal.
• An equation is an open sentence if it contains one or more variables and may be true or false depending on the values of its variables.

Since the equation contains a variable, x, it is an open sentence.

Chapter 1 Foundations for Algebra Exercise 1.8 16E
Consider the equation 8x + 5 = 29
The aim is to check whether x = 3 a solution of the equation.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
First substitute x = 3 in the equation and then check whether it is true.

Chapter 1 Foundations for Algebra Exercise 1.8 17E
Consider the equation 5b + 1 = 16
The aim is to check whether b = -3 a solution of the equation.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
First substitute b = -3 in the equation and then check whether it is true.

Chapter 1 Foundations for Algebra Exercise 1.8 18E
Consider the equation 6 = 2n – 8
The aim is to check whether n = 7 a solution of the equation.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
First substitute n = 7 in the equation and then check whether it is true.

Chapter 1 Foundations for Algebra Exercise 1.8 19E
Consider the equation 2 = 10 – 4y
The aim is to check whether y = 2 a solution of the equation.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
First substitute y = 2 in the equation and then check whether it is true.

Chapter 1 Foundations for Algebra Exercise 1.8 20E
Consider the equation 9a – (-72) = 0
The aim is to check whether a = -8 a solution of the equation.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
First substitute a = -8 in the equation and then check whether it is true.

Chapter 1 Foundations for Algebra Exercise 1.8 21E

Chapter 1 Foundations for Algebra Exercise 1.8 22E

Chapter 1 Foundations for Algebra Exercise 1.8 23E

Chapter 1 Foundations for Algebra Exercise 1.8 24E

Chapter 1 Foundations for Algebra Exercise 1.8 25E

Chapter 1 Foundations for Algebra Exercise 1.8 26E

Chapter 1 Foundations for Algebra Exercise 1.8 27E
The athlete trains for 115 min each day.
In d days, the athlete will be trains for 115 × d = 115d min.
If the athlete trains for 690 min in d days, 115d must be equal to 690.
115d = 690
Therefore, the equation that relates the number of days d that the athlete spends training when the athlete trains for 690 min is 115d = 690.

Chapter 1 Foundations for Algebra Exercise 1.8 28E
The manager of the restaurant earns $2.25 more each hour than the host of the restaurant.
If the host of the restaurant earns the amount h (in dollars) each hour, the manager will earn the amount
(h + 2.25)(in dollars), which must be equal to $11.50.
h + 2.25 = 11.50
Therefore, the equation that relates the amount h that the host of the restaurant earns each hour when the manager earns $11.50 each hour is h + 2.25 = 11.50.

Chapter 1 Foundations for Algebra Exercise 1.8 29E
Consider the equation x – 3 = 10
The aim is to find the solution of the equation using mental math.
The phrase that describes the equation is “a number minus 3 equals 10”.
Ask yourself “What number minus 3 is equal to 10?”
The answer is 13.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
Let us check whether x = 13 a solution of the equation x – 3 = 10.
First substitute x = 13 in the equation and then check whether it is true.
x – 3 = 10
x – 3 = 10 Substitute x = 13
10 = 10 Simplify each side
The simplified equation 10 = 10 is true, because each side of the equal sign is 10.
So, x = 13 is a solution of the equation x – 3 = 10.
Therefore, the solution of the equation is x = 13.

Chapter 1 Foundations for Algebra Exercise 1.8 30E
Consider the equation 4 = 7 – y
The aim is to find the solution of the equation using mental math.
The phrase that describes the equation is “4 is equal to 7 minus a number”.
Ask yourself “What number when subtracted from 7 gives 4?”
The answer is 3.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.
Let us check whether y = 3 a solution of the equation 4 = 7 – y.

Chapter 1 Foundations for Algebra Exercise 1.8 31E
Consider the equation 18 + d = 24
The aim is to find the solution of the equation using mental math.
The phrase that describes the equation is “the sum of 18 and a number is 24”.
Ask yourself “What number when added to 18 gives 24?”
The answer is 6.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.

Chapter 1 Foundations for Algebra Exercise 1.8 32E

Chapter 1 Foundations for Algebra Exercise 1.8 33E

Chapter 1 Foundations for Algebra Exercise 1.8 34E

Chapter 1 Foundations for Algebra Exercise 1.8 35E

Chapter 1 Foundations for Algebra Exercise 1.8 36E
Consider the equation 20a = 100
The aim is to find the solution of the equation using mental math.
The phrase that describes the equation is “a number multiplied by 20 is 100”.
Ask yourself “What number when multiplied by 20 gives 100?”
The answer is 5.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.

Chapter 1 Foundations for Algebra Exercise 1.8 37E
Consider the equation 13c = 26
The aim is to find the solution of the equation using mental math.
The phrase that describes the equation is “a number multiplied by 13 is 26”.
Ask yourself “What number when multiplied by 13 gives 26?”
The answer is 2.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.

Chapter 1 Foundations for Algebra Exercise 1.8 38E

Chapter 1 Foundations for Algebra Exercise 1.8 39E

Chapter 1 Foundations for Algebra Exercise 1.8 40E

Chapter 1 Foundations for Algebra Exercise 1.8 41E

Chapter 1 Foundations for Algebra Exercise 1.8 42E

Chapter 1 Foundations for Algebra Exercise 1.8 43E

Chapter 1 Foundations for Algebra Exercise 1.8 44E

Chapter 1 Foundations for Algebra Exercise 1.8 45E

Chapter 1 Foundations for Algebra Exercise 1.8 46E

Chapter 1 Foundations for Algebra Exercise 1.8 47E

Chapter 1 Foundations for Algebra Exercise 1.8 48E

Chapter 1 Foundations for Algebra Exercise 1.8 49E

Chapter 1 Foundations for Algebra Exercise 1.8 50E

Chapter 1 Foundations for Algebra Exercise 1.8 51E
An expression is a mathematical relationship between numbers and variables.
For example, 3x + 5 is an expression.
On the other side, an equation shows that two expressions are equal.
For example, 2x + 1 = 5 is an equation.
An expression does not have a solution, however, can be simplified.

Chapter 1 Foundations for Algebra Exercise 1.8 52E
The number of peoples attend a basketball team’s championship game is 1254.
The number of identical benches in the gymnasium is 6.
The aim is to find the number of peoples to seat in each bench, which tells us that we will be dividing.
We need to divide 1254 peoples in 6 benches.
Divide 1254 by 6.
1254 ÷ 6 = 209
Therefore, 209 peoples are expected to seat in each bench.

Chapter 1 Foundations for Algebra Exercise 1.8 53E
Consider the equation x + 4 = -2
The aim is to find (or estimate) the solution of the equation.
Use mental math.
The phrase that describes the equation is “the sum of a number and 4 is -2”.
Ask yourself “What number when added to 4 gives -2?”
The answer is -6.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.

Chapter 1 Foundations for Algebra Exercise 1.8 54E

Chapter 1 Foundations for Algebra Exercise 1.8 55E

Chapter 1 Foundations for Algebra Exercise 1.8 56E
Consider the equation -3 + t = 19
The aim is to find (or estimate) the solution of the equation.
Use mental math.
The phrase that describes the equation is “the sum of -3 and a number is 19”.
Ask yourself “What number when added to -3 gives 19?”
The answer is 22.
Remember that a solution of an equation containing a variable is a value of the variable that makes the equation true.

Chapter 1 Foundations for Algebra Exercise 1.8 57E

Chapter 1 Foundations for Algebra Exercise 1.8 58E

Chapter 1 Foundations for Algebra Exercise 1.8 59E

Chapter 1 Foundations for Algebra Exercise 1.8 60E

Chapter 1 Foundations for Algebra Exercise 1.8 61E

Chapter 1 Foundations for Algebra Exercise 1.8 62E
The drill advances at the rate of 67 m/h.
The aim is to find the time will it take the drill to reach a depth of 300 m, which tells us that we will be dividing 300 by 67.
Divide 300 by 67.
300 ÷ 67 = 4.5 (Rounded to first decimal place)
Therefore, the drill will take 4.5 hours to reach the depth of 300 m.
To model the situation, first identify the variables.
Here the variables are depth and time.
Let us suppose that the drill takes t hours to reach a depth of d meter.
Since the drill advances at the rate of 67 m/h, it will reach at the depth of (67t) meter in t hours.
So, we must have
d = 67t
Therefore, the equation that model the situation is
d = 67t,
Where d is the depth (in meter) reach by the drill in t hours.
To model the situation, we need the rate 67 m/h at which the drill advances through the ice sheet.

Chapter 1 Foundations for Algebra Exercise 1.8 63E

Chapter 1 Foundations for Algebra Exercise 1.8 64E

Chapter 1 Foundations for Algebra Exercise 1.8 65E
Consider the equation 15 = 4 + 2t
The solution of the equation is the value of t for which the value of the expression on the right side of the equal sign will be 15.
Since 2 is an even number, for any integer t, 2t will be even number.
Since the sum or difference of two even numbers is an even number and 4 is an even number, ( 4 + 2t)will be an even number for any integer t.
The number on the right side of the equal sign is 15, which is an odd number.
So, the equation can’t have an integer solution, the solution must be a fraction.
A fraction must lie in between two consecutive integers.
So, the solution of the equation is between two consecutive integers.

Chapter 1 Foundations for Algebra Exercise 1.8 66E
The construction crew needs to install 550 ft of curbing.
Yesterday the crew installed 272 ft of curbing.
Today the crew needs to install ( 550 – 272) = 278 ft of curbing, if it wants to finish the job.
The crew can install curbing at the rate of 32 ft/h.
To find the time the crew will take to install 278 ft of curbing at the rate 32 ft/h, we will be dividing.
We need to divide 278 by 32.
Divide 278 by 32.
278 ÷ 32 = 8.7 (Rounded to one decimal place)
The crew will take 8.7 hours to install 278 ft of curbing.

Chapter 1 Foundations for Algebra Exercise 1.8 67E

Chapter 1 Foundations for Algebra Exercise 1.8 68E

Chapter 1 Foundations for Algebra Exercise 1.8 69E

Chapter 1 Foundations for Algebra Exercise 1.8 70E

Chapter 1 Foundations for Algebra Exercise 1.8 71E

Chapter 1 Foundations for Algebra Exercise 1.8 72E

Chapter 1 Foundations for Algebra Exercise 1.8 73E

Chapter 1 Foundations for Algebra Exercise 1.8 74E

Chapter 1 Foundations for Algebra Exercise 1.8 75E

Chapter 1 Foundations for Algebra Exercise 1.8 76E

Chapter 1 Foundations for Algebra Exercise 1.8 77E

Chapter 1 Foundations for Algebra Exercise 1.8 78E

Chapter 1 Foundations for Algebra Exercise 1.8 79E

Chapter 1 Foundations for Algebra Exercise 1.8 80E

Chapter 1 Foundations for Algebra Exercise 1.8 81E

Chapter 1 Foundations for Algebra Exercise 1.8 82E

Chapter 1 Foundations for Algebra Exercise 1.8 83E

Chapter 1 Foundations for Algebra Exercise 1.8 84E

Chapter 1 Foundations for Algebra Exercise 1.8 85E

Chapter 1 Foundations for Algebra Exercise 1.8 86E

Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 1 Foundations for Algebra Exercise 1.7

Algebra 1 Common Core Answers Student Edition Grade 8 – 9

Chapter 1 Foundations for Algebra Exercise 1.7 1LC

Chapter 1 Foundations for Algebra Exercise 1.7 2LC

Chapter 1 Foundations for Algebra Exercise 1.7 3LC

Chapter 1 Foundations for Algebra Exercise 1.7 4LC
To tell whether the terms are like terms
3a and -5a
Since the 2 terms nave same variable, the 2 terms are like terms
Conclusion:- The 2 terms are like terms

Chapter 1 Foundations for Algebra Exercise 1.7 5LC

Chapter 1 Foundations for Algebra Exercise 1.7 6LC

Chapter 1 Foundations for Algebra Exercise 1.7 7LC

Chapter 1 Foundations for Algebra Exercise 1.7 8LC

Chapter 1 Foundations for Algebra Exercise 1.7 9E

Chapter 1 Foundations for Algebra Exercise 1.7 10E

Chapter 1 Foundations for Algebra Exercise 1.7 11E

Chapter 1 Foundations for Algebra Exercise 1.7 12E

Chapter 1 Foundations for Algebra Exercise 1.7 13E

Chapter 1 Foundations for Algebra Exercise 1.7 14E

Chapter 1 Foundations for Algebra Exercise 1.7 15E

Chapter 1 Foundations for Algebra Exercise 1.7 16E

Chapter 1 Foundations for Algebra Exercise 1.7 17E

Chapter 1 Foundations for Algebra Exercise 1.7 18E

Chapter 1 Foundations for Algebra Exercise 1.7 19E

Chapter 1 Foundations for Algebra Exercise 1.7 20E

Chapter 1 Foundations for Algebra Exercise 1.7 21E

Chapter 1 Foundations for Algebra Exercise 1.7 22E
To use the distributive property to simplify the expression
0(3.7x – 4.21) = 0 Product of any number and zero is zero
Conclusion:- 0(3.7x – 4.21) = 0

Chapter 1 Foundations for Algebra Exercise 1.7 23E

Chapter 1 Foundations for Algebra Exercise 1.7 24E

Chapter 1 Foundations for Algebra Exercise 1.7 25E

Chapter 1 Foundations for Algebra Exercise 1.7 26E

Chapter 1 Foundations for Algebra Exercise 1.7 27E

Chapter 1 Foundations for Algebra Exercise 1.7 28E

Chapter 1 Foundations for Algebra Exercise 1.7 29E

Chapter 1 Foundations for Algebra Exercise 1.7 30E

Chapter 1 Foundations for Algebra Exercise 1.7 31E

Chapter 1 Foundations for Algebra Exercise 1.7 32E

Chapter 1 Foundations for Algebra Exercise 1.7 33E

Chapter 1 Foundations for Algebra Exercise 1.7 34E

Chapter 1 Foundations for Algebra Exercise 1.7 35E

Chapter 1 Foundations for Algebra Exercise 1.7 36E

Chapter 1 Foundations for Algebra Exercise 1.7 37E

Chapter 1 Foundations for Algebra Exercise 1.7 38E

Chapter 1 Foundations for Algebra Exercise 1.7 39E

Chapter 1 Foundations for Algebra Exercise 1.7 40E

Chapter 1 Foundations for Algebra Exercise 1.7 41E

Chapter 1 Foundations for Algebra Exercise 1.7 42E

Chapter 1 Foundations for Algebra Exercise 1.7 43E

Chapter 1 Foundations for Algebra Exercise 1.7 44E

Chapter 1 Foundations for Algebra Exercise 1.7 45E

Chapter 1 Foundations for Algebra Exercise 1.7 46E

Chapter 1 Foundations for Algebra Exercise 1.7 47E

Chapter 1 Foundations for Algebra Exercise 1.7 48E

Chapter 1 Foundations for Algebra Exercise 1.7 49E

Chapter 1 Foundations for Algebra Exercise 1.7 50E

Chapter 1 Foundations for Algebra Exercise 1.7 51E

Chapter 1 Foundations for Algebra Exercise 1.7 52E

Chapter 1 Foundations for Algebra Exercise 1.7 53E

Chapter 1 Foundations for Algebra Exercise 1.7 54E

Chapter 1 Foundations for Algebra Exercise 1.7 55E

Chapter 1 Foundations for Algebra Exercise 1.7 56E

Chapter 1 Foundations for Algebra Exercise 1.7 57E

Chapter 1 Foundations for Algebra Exercise 1.7 58E

Chapter 1 Foundations for Algebra Exercise 1.7 59E

Chapter 1 Foundations for Algebra Exercise 1.7 60E

Chapter 1 Foundations for Algebra Exercise 1.7 61E

Chapter 1 Foundations for Algebra Exercise 1.7 62E

Chapter 1 Foundations for Algebra Exercise 1.7 63E

Chapter 1 Foundations for Algebra Exercise 1.7 64E

Chapter 1 Foundations for Algebra Exercise 1.7 65E

Chapter 1 Foundations for Algebra Exercise 1.7 66E

Chapter 1 Foundations for Algebra Exercise 1.7 67E

Chapter 1 Foundations for Algebra Exercise 1.7 68E

Chapter 1 Foundations for Algebra Exercise 1.7 69E

Chapter 1 Foundations for Algebra Exercise 1.7 70E

Chapter 1 Foundations for Algebra Exercise 1.7 71E

Chapter 1 Foundations for Algebra Exercise 1.7 72E

Chapter 1 Foundations for Algebra Exercise 1.7 73E

Chapter 1 Foundations for Algebra Exercise 1.7 74E
To find the gallons of water that will be saved in 8-minute shower
Consider water-saving shower head
For 1 minute 2.5 gallons of water is used
For 8 minutes 8 × 2.5 = 20.0 gallons of water is used
Consider regular shower head
For 1 minute 7 gallons of water is used
For 8 minutes 8 × 7 = 56 gallons of water is used
The amount of water saved is 56 – 20 = 36 gallons
To find the expression(addition or subtraction)we use to represent water saved each minute
The expression we use to represent water saved each minute is subtraction.
To tell how we can use distributive property to find the total amount of water saved.

Chapter 1 Foundations for Algebra Exercise 1.7 75E

Chapter 1 Foundations for Algebra Exercise 1.7 76E

Chapter 1 Foundations for Algebra Exercise 1.7 77E

Chapter 1 Foundations for Algebra Exercise 1.7 78E

Chapter 1 Foundations for Algebra Exercise 1.7 79E

Chapter 1 Foundations for Algebra Exercise 1.7 80E

Chapter 1 Foundations for Algebra Exercise 1.7 81E

Chapter 1 Foundations for Algebra Exercise 1.7 82E
Consider the diagram provided in textbook.
Since, a pairs out of 3 pairs are wrap around the blue bar therefore remaining pairs are wrap around the orange bar.
Hence, the expression which represents the total score is calculated as follows,
= 20a + 10(3 – a)
= 20a + 30 – 10a
= 10a + 30
Therefore from the provided option in textbook, option (A) is correct.

Chapter 1 Foundations for Algebra Exercise 1.7 83E

Chapter 1 Foundations for Algebra Exercise 1.7 84E

Chapter 1 Foundations for Algebra Exercise 1.7 85E

Chapter 1 Foundations for Algebra Exercise 1.7 86E

Chapter 1 Foundations for Algebra Exercise 1.7 87E

Chapter 1 Foundations for Algebra Exercise 1.7 88E

Chapter 1 Foundations for Algebra Exercise 1.7 89E

Chapter 1 Foundations for Algebra Exercise 1.7 90E

Chapter 1 Foundations for Algebra Exercise 1.7 91E

Chapter 1 Foundations for Algebra Exercise 1.7 92E

Chapter 1 Foundations for Algebra Exercise 1.7 93E

Chapter 1 Foundations for Algebra Exercise 1.7 94E

Chapter 1 Foundations for Algebra Exercise 1.7 95E

Chapter 1 Foundations for Algebra Exercise 1.7 96E

Chapter 1 Foundations for Algebra Exercise 1.7 97E

Chapter 1 Foundations for Algebra Exercise 1.7 98E
To write a word or a phrase tor the algebraic expression
x-10
The phrase is 10 less than a number x
conclusion:- 10 less than a number x

Chapter 1 Foundations for Algebra Exercise 1.7 99E
To write a word or a phrase tor the algebraic expression
5x—18
The phrase is 18 less than the product otfive and x
Conclusion:- The phrase is 18 less than the product Of five and x

Chapter 1 Foundations for Algebra Exercise 1.7 100E

Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 1 Foundations for Algebra Exercise 1.6

Algebra 1 Common Core Answers Student Edition Grade 8 – 9

Chapter 1 Foundations for Algebra Exercise 1.6 1CB

Chapter 1 Foundations for Algebra Exercise 1.6 1LC

Chapter 1 Foundations for Algebra Exercise 1.6 2CB

Chapter 1 Foundations for Algebra Exercise 1.6 2LC

Chapter 1 Foundations for Algebra Exercise 1.6 3CB

Chapter 1 Foundations for Algebra Exercise 1.6 3LC

Chapter 1 Foundations for Algebra Exercise 1.6 4CB

Chapter 1 Foundations for Algebra Exercise 1.6 4LC

Chapter 1 Foundations for Algebra Exercise 1.6 5CB

Chapter 1 Foundations for Algebra Exercise 1.6 5LC

Chapter 1 Foundations for Algebra Exercise 1.6 6CB

Chapter 1 Foundations for Algebra Exercise 1.6 6LC
To use a number line to explain why -15 ÷ 3 = -5
A number line to explain why -15 ÷ 3 = -5

From the above number line we get to know that -15 divided into 3 parts gives -5.

Chapter 1 Foundations for Algebra Exercise 1.6 7CB

Chapter 1 Foundations for Algebra Exercise 1.6 7LC

Chapter 1 Foundations for Algebra Exercise 1.6 8CB

Chapter 1 Foundations for Algebra Exercise 1.6 8E

Chapter 1 Foundations for Algebra Exercise 1.6 9CB

Chapter 1 Foundations for Algebra Exercise 1.6 9E

Chapter 1 Foundations for Algebra Exercise 1.6 10CB

Chapter 1 Foundations for Algebra Exercise 1.6 10E

Chapter 1 Foundations for Algebra Exercise 1.6 11CB

Chapter 1 Foundations for Algebra Exercise 1.6 11E

Chapter 1 Foundations for Algebra Exercise 1.6 12CB

Chapter 1 Foundations for Algebra Exercise 1.6 12E

Chapter 1 Foundations for Algebra Exercise 1.6 13CB

Chapter 1 Foundations for Algebra Exercise 1.6 13E

Chapter 1 Foundations for Algebra Exercise 1.6 14CB

Chapter 1 Foundations for Algebra Exercise 1.6 14E

Chapter 1 Foundations for Algebra Exercise 1.6 15CB

Chapter 1 Foundations for Algebra Exercise 1.6 15E

Chapter 1 Foundations for Algebra Exercise 1.6 16CB

Chapter 1 Foundations for Algebra Exercise 1.6 16E

Chapter 1 Foundations for Algebra Exercise 1.6 17CB

Chapter 1 Foundations for Algebra Exercise 1.6 17E

Chapter 1 Foundations for Algebra Exercise 1.6 18CB

Chapter 1 Foundations for Algebra Exercise 1.6 18E

Chapter 1 Foundations for Algebra Exercise 1.6 19E

Chapter 1 Foundations for Algebra Exercise 1.6 20E

Chapter 1 Foundations for Algebra Exercise 1.6 21E

Chapter 1 Foundations for Algebra Exercise 1.6 22E

Chapter 1 Foundations for Algebra Exercise 1.6 23E

Chapter 1 Foundations for Algebra Exercise 1.6 24E

Chapter 1 Foundations for Algebra Exercise 1.6 25E

Chapter 1 Foundations for Algebra Exercise 1.6 26E

Chapter 1 Foundations for Algebra Exercise 1.6 27E

Chapter 1 Foundations for Algebra Exercise 1.6 28E

Chapter 1 Foundations for Algebra Exercise 1.6 29E

Chapter 1 Foundations for Algebra Exercise 1.6 30E

Chapter 1 Foundations for Algebra Exercise 1.6 31E

Chapter 1 Foundations for Algebra Exercise 1.6 32E

Chapter 1 Foundations for Algebra Exercise 1.6 33E

Chapter 1 Foundations for Algebra Exercise 1.6 34E

Chapter 1 Foundations for Algebra Exercise 1.6 35E

Chapter 1 Foundations for Algebra Exercise 1.6 36E

Chapter 1 Foundations for Algebra Exercise 1.6 37E

Chapter 1 Foundations for Algebra Exercise 1.6 38E

Chapter 1 Foundations for Algebra Exercise 1.6 39E

Chapter 1 Foundations for Algebra Exercise 1.6 40E

Chapter 1 Foundations for Algebra Exercise 1.6 41E

Chapter 1 Foundations for Algebra Exercise 1.6 42E

Chapter 1 Foundations for Algebra Exercise 1.6 43E

Chapter 1 Foundations for Algebra Exercise 1.6 44E

Chapter 1 Foundations for Algebra Exercise 1.6 45E

Chapter 1 Foundations for Algebra Exercise 1.6 46E

Chapter 1 Foundations for Algebra Exercise 1.6 47E

Chapter 1 Foundations for Algebra Exercise 1.6 48E

Chapter 1 Foundations for Algebra Exercise 1.6 49E

Chapter 1 Foundations for Algebra Exercise 1.6 50E

Chapter 1 Foundations for Algebra Exercise 1.6 51E

Chapter 1 Foundations for Algebra Exercise 1.6 52E

Chapter 1 Foundations for Algebra Exercise 1.6 53E

Chapter 1 Foundations for Algebra Exercise 1.6 54E

Chapter 1 Foundations for Algebra Exercise 1.6 55E

Chapter 1 Foundations for Algebra Exercise 1.6 56E

Chapter 1 Foundations for Algebra Exercise 1.6 57E

Chapter 1 Foundations for Algebra Exercise 1.6 58E

Chapter 1 Foundations for Algebra Exercise 1.6 59E

Chapter 1 Foundations for Algebra Exercise 1.6 60E

Chapter 1 Foundations for Algebra Exercise 1.6 61E

Chapter 1 Foundations for Algebra Exercise 1.6 62E

Chapter 1 Foundations for Algebra Exercise 1.6 63E

Chapter 1 Foundations for Algebra Exercise 1.6 64E

Chapter 1 Foundations for Algebra Exercise 1.6 65E

Chapter 1 Foundations for Algebra Exercise 1.6 66E

Chapter 1 Foundations for Algebra Exercise 1.6 67E
To determine whether each statement is always, sometimes or never true
Statement:-The quotient of a nonzero number and its opposite is -1
This is always true
Consider an example-3. Its opposite is 3.Quotient when the 2 are divided is -1
Conclusion:-
The given statement is always true.

Chapter 1 Foundations for Algebra Exercise 1.6 68E
To determine whether each statement is always, sometimes or never true
Statement:-If the product of 2 fractions is negative, then their quotient is positive.
This is never true because the product of 2 fractions is negative, then their quotient is negative( both multiplication and division rules are same)
Conclusion:-
The given statement is never true.

Chapter 1 Foundations for Algebra Exercise 1.6 69E
To find the greatest integer n for which (-n)³ is positive and the value of the expression has a 2 in the ones place
The greatest integer for n for which (-n)³ is positive and the value of the expression has a 2 in the ones place is -8.
The value of the expression has a 2 in the ones place if it is the cube of 8 or numbers ending with 8. (-n)³ is positive only if n is negative.Such greatest integer which has 8 in ones place and n is negative is -8.

Chapter 1 Foundations for Algebra Exercise 1.6 70E

Chapter 1 Foundations for Algebra Exercise 1.6 71E

Chapter 1 Foundations for Algebra Exercise 1.6 72E

Chapter 1 Foundations for Algebra Exercise 1.6 73E
To find the difference
46-16
To find difference of 2 numbers, we subtract the 2 numbers and keep the greater number sign
46 -16 =30
Conclusion:- 46 -16 =30

Chapter 1 Foundations for Algebra Exercise 1.6 74E
To find the difference
34 – 44
To find difference of 2 numbers, we subtract the 2 numbers and keep the greater number sign
34 – 44 = -10
Conclusion:- 34 – 44 = -10

Chapter 1 Foundations for Algebra Exercise 1.6 75E
To find the difference
-37 – (-27)
Product of 2 negative sign is positive
-37 – (-27) = -37 + 27
To find difference of 2 numbers, we subtract the 2 numbers and keep the greater number sign
= -10
Conclusion:- -37 – (-27) = -10

Chapter 1 Foundations for Algebra Exercise 1.6 76E
To name the property that the statement illustrates
– x + 0 = – x
Zero is the additive identity
The property that the statement illustrates is additive identity
Conclusion:- The property that the statement illustrates is additive identity.

Chapter 1 Foundations for Algebra Exercise 1.6 77E
To name the property that the statement illustrates
13(-11) = -11(13)
The property that the statement illustrates is commutative property of multiplication
Its general form is a . b = b . a
Conclusion:-
The property that the statement illustrates is commutative property of multiplication

Chapter 1 Foundations for Algebra Exercise 1.6 78E
To name the property that the statement illustrates
-5 . (m . 8) = (-5 . m) . 8
The property that the statement illustrates is associative property of multiplication
Its general form is a .(b . c) = (a . b) . c
Conclusion:-
The property that the statement illustrates is associative property of multiplication

Algebra 1 Common Core Answers Student Edition Grade 8 – 9 Chapter 1 Foundations for Algebra Exercise 1.5

Algebra 1 Common Core Answers Student Edition Grade 8 – 9

Chapter 1 Foundations for Algebra Exercise 1.5 1CB
Consider the following description is always, sometimes, or never true about the member of group:
Takes an algebra class
Therefore, takes an algebra class is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 1LC

Chapter 1 Foundations for Algebra Exercise 1.5 2CB
Consider the following description is always, sometimes, or never true about the member of group:
Lives in your state
Therefore, lives in your state is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 2LC

Chapter 1 Foundations for Algebra Exercise 1.5 3CB
Consider the following description is always, sometimes, or never true about the member of group:
Plays a musical instrument
Therefore, Plays a musical instrument is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 3LC

Chapter 1 Foundations for Algebra Exercise 1.5 4CB
Consider the following description is always, sometimes, or never true about the member of group:
is less than 25 years old
Therefore, is less than 25 years old is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 4LC

Chapter 1 Foundations for Algebra Exercise 1.5 5CB
Consider the following description is always, sometimes, or never true about the member of group:
Speaks more than one language
Therefore, speaks more than one language is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 5LC

Chapter 1 Foundations for Algebra Exercise 1.5 6CB
Consider the following description is always, sometimes, or never true about the member of group:
Is taller than 5m
Therefore, is taller than 5m is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 6LC

Chapter 1 Foundations for Algebra Exercise 1.5 7CB
Consider the following description is always, sometimes, or never true about the member of group:
Has a sibling
Therefore, has a sibling is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 7LC

Chapter 1 Foundations for Algebra Exercise 1.5 8CB
Consider the following description is always, sometimes, or never true about the member of group:
Plays basketball
Therefore, Plays basketball is sometimes true.

Chapter 1 Foundations for Algebra Exercise 1.5 8LC

Chapter 1 Foundations for Algebra Exercise 1.5 9CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Greater than 2
Cards number 3,6,10 and 13 are greater than 2.
Therefore, a group member will have always a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 9LC
Result is wrong.
If the number is positive then the opposite of the number is negative.
If the number is negative then the opposite number is positive.
The positive of a is.
The positive of is a.
Hence, the opposite of a number is not always negative.

Chapter 1 Foundations for Algebra Exercise 1.5 10CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Greater than 25
Cards number 3,6,10 and 13 are all less than 25.
Therefore, a group member will have never a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 10E

Chapter 1 Foundations for Algebra Exercise 1.5 11CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Even
In card number 3,6,10 and 13,
Card number 6 and 10 are even.
Therefore, a group member will have sometimes a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 11E

Chapter 1 Foundations for Algebra Exercise 1.5 12CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Irrational number
An irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals.
Card number 3,6,10 and 13 are not irrational number.
Therefore, a group member will have never a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 12E

Chapter 1 Foundations for Algebra Exercise 1.5 13CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Prime number
A prime number (or a prime) is a natural number greater than that has no positive divisors other than and itself.
In card number 3,6,10 and 13.
Number 3 and 13 are prime number.
Therefore, a group member will have sometimes a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 13E

Chapter 1 Foundations for Algebra Exercise 1.5 14CB

Chapter 1 Foundations for Algebra Exercise 1.5 14E

Chapter 1 Foundations for Algebra Exercise 1.5 15CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Divisible by 2
See the card number 3,6,10 and 13.
Number 6 and 10 are divisible by 2.
Therefore, a group member will have sometimes a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 15E

Chapter 1 Foundations for Algebra Exercise 1.5 16CB
Suppose each member of group takes one of the four cards as provided in textbook.
Consider the description as shown below:
Less than 10
See the card number 3,6,10 and 13.
Number 3 and 6 are less than 10
Therefore, a group member will have sometimes a number that fit the description.

Chapter 1 Foundations for Algebra Exercise 1.5 16E

Chapter 1 Foundations for Algebra Exercise 1.5 17CB

Chapter 1 Foundations for Algebra Exercise 1.5 17E

Chapter 1 Foundations for Algebra Exercise 1.5 18CB

Chapter 1 Foundations for Algebra Exercise 1.5 18E

Chapter 1 Foundations for Algebra Exercise 1.5 19CB

Chapter 1 Foundations for Algebra Exercise 1.5 19E

Chapter 1 Foundations for Algebra Exercise 1.5 20CB

Chapter 1 Foundations for Algebra Exercise 1.5 20E

Chapter 1 Foundations for Algebra Exercise 1.5 21CB

Chapter 1 Foundations for Algebra Exercise 1.5 21E

Chapter 1 Foundations for Algebra Exercise 1.5 22CB

Chapter 1 Foundations for Algebra Exercise 1.5 22E

Chapter 1 Foundations for Algebra Exercise 1.5 23CB

Chapter 1 Foundations for Algebra Exercise 1.5 23E

Chapter 1 Foundations for Algebra Exercise 1.5 24CB

Chapter 1 Foundations for Algebra Exercise 1.5 24E

Chapter 1 Foundations for Algebra Exercise 1.5 25E

Chapter 1 Foundations for Algebra Exercise 1.5 26E

Chapter 1 Foundations for Algebra Exercise 1.5 27E

Chapter 1 Foundations for Algebra Exercise 1.5 28E

Chapter 1 Foundations for Algebra Exercise 1.5 29E

Chapter 1 Foundations for Algebra Exercise 1.5 30E

Chapter 1 Foundations for Algebra Exercise 1.5 31E

Chapter 1 Foundations for Algebra Exercise 1.5 32E

Chapter 1 Foundations for Algebra Exercise 1.5 33E

Chapter 1 Foundations for Algebra Exercise 1.5 34E

Chapter 1 Foundations for Algebra Exercise 1.5 35E

Chapter 1 Foundations for Algebra Exercise 1.5 36E

Chapter 1 Foundations for Algebra Exercise 1.5 37E

Chapter 1 Foundations for Algebra Exercise 1.5 38E

Chapter 1 Foundations for Algebra Exercise 1.5 39E

Chapter 1 Foundations for Algebra Exercise 1.5 40E

Chapter 1 Foundations for Algebra Exercise 1.5 41E

Chapter 1 Foundations for Algebra Exercise 1.5 42E

Chapter 1 Foundations for Algebra Exercise 1.5 43E

Chapter 1 Foundations for Algebra Exercise 1.5 44E

Chapter 1 Foundations for Algebra Exercise 1.5 45E

Chapter 1 Foundations for Algebra Exercise 1.5 46E

Chapter 1 Foundations for Algebra Exercise 1.5 47E

Chapter 1 Foundations for Algebra Exercise 1.5 48E

Chapter 1 Foundations for Algebra Exercise 1.5 49E

Chapter 1 Foundations for Algebra Exercise 1.5 50E

Chapter 1 Foundations for Algebra Exercise 1.5 51E

Chapter 1 Foundations for Algebra Exercise 1.5 52E

Chapter 1 Foundations for Algebra Exercise 1.5 53E
Consider the sum,
-225+318
According to the rule for addition, subtract the absolute values of the addends when adding two numbers with opposite signs. The resultant has the same sign of the higher absolute value.
In the sum of -225+318, the higher absolute value has positive sign, so the resultant must have positive sign.
Therefore, the value of the expression -225+318 is positive.

Chapter 1 Foundations for Algebra Exercise 1.5 54E

Chapter 1 Foundations for Algebra Exercise 1.5 55E

Chapter 1 Foundations for Algebra Exercise 1.5 56E

Chapter 1 Foundations for Algebra Exercise 1.5 57E

Chapter 1 Foundations for Algebra Exercise 1.5 58E

Chapter 1 Foundations for Algebra Exercise 1.5 59E

Chapter 1 Foundations for Algebra Exercise 1.5 60E

Chapter 1 Foundations for Algebra Exercise 1.5 61E

Chapter 1 Foundations for Algebra Exercise 1.5 62E

Chapter 1 Foundations for Algebra Exercise 1.5 63E

Chapter 1 Foundations for Algebra Exercise 1.5 64E

Chapter 1 Foundations for Algebra Exercise 1.5 65E

Chapter 1 Foundations for Algebra Exercise 1.5 66E

Chapter 1 Foundations for Algebra Exercise 1.5 67E

Chapter 1 Foundations for Algebra Exercise 1.5 68E

Chapter 1 Foundations for Algebra Exercise 1.5 69E

Chapter 1 Foundations for Algebra Exercise 1.5 70E

Chapter 1 Foundations for Algebra Exercise 1.5 71E

Chapter 1 Foundations for Algebra Exercise 1.5 72E

Chapter 1 Foundations for Algebra Exercise 1.5 73E

Chapter 1 Foundations for Algebra Exercise 1.5 74E

Chapter 1 Foundations for Algebra Exercise 1.5 75E

Chapter 1 Foundations for Algebra Exercise 1.5 76E

Chapter 1 Foundations for Algebra Exercise 1.5 77E

Chapter 1 Foundations for Algebra Exercise 1.5 78E

Chapter 1 Foundations for Algebra Exercise 1.5 79E

Chapter 1 Foundations for Algebra Exercise 1.5 80E

Chapter 1 Foundations for Algebra Exercise 1.5 81E
Consider the number:
82.0371
In the decimal form 82.0371 is terminating decimal.
The number 82.0371 belongs to the set of rational numbers because it is terminated.
Therefore, the number 82.0371 belongs to the set of all rational numbers.

Chapter 1 Foundations for Algebra Exercise 1.5 82E

Chapter 1 Foundations for Algebra Exercise 1.5 83E

Chapter 1 Foundations for Algebra Exercise 1.5 84E

Chapter 1 Foundations for Algebra Exercise 1.5 85E