## ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 9 Algebra Ex 9.3

Question 1.

Form four expressions with numbers 7, 5 and 8 (no variables) using operations of addition, subtraction or multiplication with the condition that every number should be used but not more than once.

Solution:

The possible expressions are:

5 × 7 + 8, 5 × 8 – 7

(5 + 8) – 7, 8 × (5 + 7)

Question 2.

Which out of following are expressions with numbers only?

(i) 2y + 3

(ii) (7 × 20) – 82

(iii) 5 × (21 – 7) + 9 x 2

(iv) 5 -11 n

(v) (5 × 4) – 45 + p

(vi) 3 × (11 + 7) – 24 + 3

Solution:

(iii) 5 × (21 – 7) + 9 × 2,

(vi) 3 × (11 + 7) – 24 ÷ 3 are expressions with numbers only.

Question 3.

Identify the operations (addition, subtraction, multiplication, division) in forming the following expressions and tell how the expressions have been formed:

(i) x + 5

(ii) y – 7

(iii) 3z

(iv) \(\frac{p}{5}\)

(v) 2x + 17

(vi) 3y – 5

(vii) \(-7 m+\frac{2}{3}\)

(viii) \(\frac{x}{3}-15\)

Solution:

(i) x + 5

Addition on → 5 added to x.

(ii) y – 7

Subtraction → 7 subtracted from y.

(iii) 3z

Multiplication → z multiplied by 3.

(iv) \(\frac{p}{5}\)

Division → p divided by 5.

(v) 2x + 17

Multiplication and addition → First x mutliplied by 2 and then 17 added to the product.

(vi) 3y – 5

Multiplication and subtraction → First y multiplied by 3 and then 5 subtracted from the product.

(vii) \(-7 m+\frac{2}{3}\)

Multiplication and addition → First m multiplied by -7 and then \(\frac{2}{3}\) added to the product.

(viii) \(\frac{x}{3}-15\)

Division and subtraction → First x divided by 3 and then 15 subtracted from the quotient.

Question 4.

Write expression for the following:

(i) 7 added to p

(ii) p subtracted from 7

(iii) p multiplied by 7

(iv) p divided by 7

(v) 7 divided by p

(vi) 7 subtracted from -m

(vii) p multiplied by -5

(viii) -p divided by 5

Solution:

(i) p + 7

(ii) 7 – p

(iii) 7p

(iv) \(\frac{p}{7}\)

(v) \(\frac{7}{p}\)

(vi) -m – 7

(vii) -5p

(viii) \(\frac{-p}{5}\)

Question 5.

Write expression for the following:

(i) 11 added to 2 m

(ii) 11 subtracted from 2 m

(iii) 3 added to 5 times y

(iv) 3 subtracted from 5 times y

(v) y is multiplied by -8 and then 5 is added to the result

(vi) y is multiplied by 5 and then the result is subtracted from 16.

Solution:

(i) 2m + 11

(ii) 2m – 11

(iii) 5y + 3

(iv) 5y – 3

(v) -8y + 5

(vi) 16 – 5y

Question 6.

Write the following in mathematical form using signs and symbols:

(i) 6 more than thrice a number x.

(ii) 7 taken away from y.

(iii) 3 less than quotient of x by y.

Solution:

(i) 3x + 6

(ii) \(\frac{x}{y}-3\)

(iii) y – 7

Question 7.

Form six expressions using t and 4. Use not more than one number operation and every expression must have t in it.

Solution:

t + 4, t – 4, 4 – t, 4t, \(\frac{t}{4}, \frac{4}{t}\)

Question 8.

Form expressions using y, 2 and 7. Use only two different number operations and every expression must have y in it.

Solution:

2y + 7, 2y- 1, 7y + 2, 7y – 2, \(\frac{y}{2}+7, \frac{y}{2}\) – 7, …..

Question 9.

A student scored x marks in English but the teacher deducted 5 marks for bad handwriting. What was the student’s final score in English?

Solution:

Marks in English = x

Deducted = 5

Final score = x – 5

Question 10.

Raju’s father’s age is 2 years more than 3 times Raju’s age. If Raju’s present age is y years, then what is his father’s age?

Solution:

(3y + 2) years

Question 11.

Mohini is x years old. Express the following in algebraic form:

(i) three times Mohini’s age next year.

(ii) four times Mohini’s age 3 years ago.

(iii) the present age of Mohini’s uncle, if his uncle is 5 times as old as Mohini will be two years from now.

(iv) the present age of Mohini’s cousin, if her cousin is two years less than one-third of Mohini’s age five years ago.

Solution:

(i) 3(x + 1) years

(ii) 4(x – 3) years

(iii) 5(x + 2) years

(iv) \(\left[\frac{1}{3}(x-5)-2\right]\) years

Question 12.

A cuboidal box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.

Solution:

Length of the box = 5h cm

Breadth of the box = (5h – 10) cm

Question 13.

A bus travels at v km per hour. It is going from Delhi to Jaipur. After the bus has travelled 5 hours, Jaipur is still 20 km away. What is the distance from Delhi to Jaipur?

Solution:

Speed of the bus = v km/hr

Distance travelled in 5 hours = 5v km

∴ Total distance = (5v + 20) km

Question 14.

Change the following statements using expressions into statements in ordinary language:

(i) A notebook cost ₹ p. A book costs ₹ 3p.

(ii) The cost of rice per kg is ₹ p. The cost of oil per litre is ₹5p.

(iii) The speed of a truck is v km per hour. The speed of a bus is (v + 10) km per hour.

(iv) Tony’s box contains 8 times the marbles he puts on the table.

(v) The total number of students in the school is 20 times that of our class.

(vi) Raju is x years old. His uncle is 4x years old and his aunt is (4x – 3) years old.

(vii) In arrangement of dots there are r rows. Each row contains 5 dots.

Solution:

(i) The cost of a book is 3 times the cost of a note book.

(ii) The cost of oil per litre is 5 times the cost of rice per kg.

(iii) The speed of a bus is 10 km per hour more than the speed of a truck.

(iv) Tony puts q marbles on the table. He has 8q marbles in his box.

(v) Our class has n students. The school has 20 n students.

(vi) Raju’s uncle is 4 times older than Raju and his aunt is 3 years younger than his uncle.

(vii) The total number of dots is 5 times the number of rows.