How do you Multiply and Divide Decimals?

How do you Multiply and Divide Decimals?

Multiplication of Decimal Numbers

Multiplication of a decimal by 10, 100, 1000 etc.:

Method:
On multiplying a decimal number by 10, 100, 1000, … the decimal point is shifted to the right by one, two, three, … places respectively.
For example,
How do you Multiply and Divide Decimals 1

Multiplication of a decimal by a whole number:

Method :
Multiply the whole number by decimal (without the decimal point). Mark the decimal point in the product from right side to have as many decimals as there are in the given decimal.
For example, 12 × 3.82
First find the product of 12 and 382
(ignoring decimal) 382 × 12
How do you Multiply and Divide Decimals 2
Now, 3.82 × 12 = 45.84 (mark the point after two digits from right).

Multiplication of a decimal by a decimal:

Method :
1. Multiply the decimal numbers as of ordinary number (ignoring decimal points)
2. Mark the decimal point in the product after as many places (from the right) as the sum of the decimal places in the each number.
For example, 82.53 × 7.4
First find the product of 8253 and 74 (ignoring decimal point)
How do you Multiply and Divide Decimals 3
Now, 82.53 × 7.4 = 610.722 (mark the decimal point after (2 + 1 = 3) digits from right).

Multiplication of Decimal Numbers Problems with Solutions

1. Multiply : (i) 1.6 by 0.3 (ii) 8.03 by 2.9 (iii) 0.657 by 27
Solution:
How do you Multiply and Divide Decimals 4

2. Find the following products :
(i) 23.25 × 5 (ii) 2.325 × 25
Solution:
(i) 23.25 × 5
How do you Multiply and Divide Decimals 5
So, 23.25 × 5 = 116.25
Step 1 :
Multiply the multiplicand by the multiplier without bothering about the decimal point.
Step 2 :
Count the number of digits in the multiplicand after decimal point. It is 2 in this case. Count two digits from the unit place in the product and put a decimal point.
Therefore, 23.25 × 5 = 116.25

(ii) 2.325 × 25
How do you Multiply and Divide Decimals 6
So, 2.325 × 25 = 58.125
Step 1 :
Multiply the multiplicand by the multiplier without bothering about the decimal point.
Step 2 :
The multiplicand has 3 places of decimal. Count three digits from the unit place of the product and put the decimal point.
Therefore, 2.325 × 25 = 58.125

3. Multiply 6.7 × 4.25 × 12.3
Solution:
(i) 6.7 × 4.25 × 12.3 = (6.7 × 4.25) × 12.3
= 28.475 × 12.3 = 350.2425
How do you Multiply and Divide Decimals 7
Also we can make the grouping as
(ii) 6.7 × 4.25 × 12.3
= 6.7 × (4.25 × 12.3) = 6.7 × 52.275
= 350.2425
How do you Multiply and Divide Decimals 8
We find that
(6.7 × 4.25) × 12.3 = 6.7 × (4.25 × 12.3)
Hence,
To find the product of three decimal fractions, we can regroup them in any order, the result is the same in both cases. Thus, multiplication of decimals is associative.

4. Find (i) 10.05 × 1.05 (ii) 100.01 × 1.1
Solution:
(i) First multiply 1005 by 105
How do you Multiply and Divide Decimals 9
Sum of decimal places in the given decimal
= (2 + 2) = 4
So, product will contain 4 places of decimals from the right side.
10.05 × 1.05 = 10.5525
(ii) 100.01 × 1.1
How do you Multiply and Divide Decimals 10
First multiply 10001 by 11.
Sum of decimal places in the given decimals
= (2 + 1) = 3
So, product will contain 3 places of decimals from the right side.
100.01 × 1.1 = 110.011

Division of Decimal Numbers

Dividing a decimal by 10, 100, 1000 etc.:

Method:
On dividing a number by 10, 100, 1000, … the digits of the number and quotient are same but the decimal point in the quotient shifts to left by one, two, three, … places.
For example,
3.27 ÷ 10 = 0.327
3.27 ÷ 100 = 0.0327
3.27 ÷ 1000 = 0.00327

Dividing a decimal by a whole number:

Method:
(i) Divide the dividend considering it as a whole number.
(ii) When the division of whole-number part of the dividend is complete, mark the decimal point in the quotient and proceed with the division as in case of whole number.
For example,
How do you Multiply and Divide Decimals 11

Dividing a decimal by a decimal:

Method:
(i) Convert the divisor into a whole number by multiplying it by 10, 100, 1000, … etc, depending upon the number of decimal places in it. Also we multiply the dividend by the same multiplier.
(ii) Divide the new dividend by the whole number obtained above.
For example, 22.08 ÷ 1.5
How do you Multiply and Divide Decimals 12

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Division of Decimal Numbers Problems with Solutions

1. Find 15.225 ÷ 0.35
Solution:
How do you Multiply and Divide Decimals 13
Thus, we note that
15.225 ÷ 0.35 = 1522.5 ÷ 0.35 = 1522.5 ÷ 35
Thus if the decimal point is moved to two places towards right in the divisor then the decimal point is also moved to the right in dividend by same number of places.

2. Find 50.76 ÷ 9.4
Solution:
How do you Multiply and Divide Decimals 14
Hence, 50.76 ÷ 9.4 = 507.6 ÷ 94
Thus, we note that we can make the divisor as a whole number by shifting the decimal point to right by as many places as the number of the decimal places in the divisor. This way, the divisor is changed into a whole number.

3. Divide (i) 15.225 by 0.35 (ii) 50.76 ÷ 9.4
Solution:
How do you Multiply and Divide Decimals 15

4. Find the quotient of 0.06688 ÷ 0.038
Solution:
Make the divisor a whole number by shifting the decimal point in dividend to the right by three places, How do you Multiply and Divide Decimals 16

5. Find 0.024 ÷ 0.6
Solution:
How do you Multiply and Divide Decimals 17

5. Find 64 ÷ 0.08
Solution:
How do you Multiply and Divide Decimals 18
[Shift the decimal points two places to the right in both the numbers]

Dividing of a whole number by a decimal:
For example,
How do you Multiply and Divide Decimals 19

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