Steemkids lessons: Multiplication and division of decimals.

Multiplications of decimals

When multiplying a decimal by multiples of 10(100,1000,10000....) we move the decimal point to the right depending on the number of zero(s).

Example
Multiply the following:

• 1.34 × 10
• 14.657 × 100
• 6.05 × 1000

Solutions

a. 1.34 × 10
move the decimal point once to the right since there is only one zero.

b. 14.657 × 100
Move the decimal point twice to the right since there are two zeros.

C. 6.05 × 1000
Move the decimal point three times to the right since there are three zeros

Example 2
Simplify the following:

• 6.452 × 500
• 3.6 × 20
• 12.42 × 800

Solutions
a. 6.452 × 500

Step 1:split 500 into: 100 × 5

Step 2: multiply 6.452 by 100
6.452 × 100 = 645.2
Step 3: multiply the result by 5.
645.2 × 5 = 3226

b. 3.6 × 20
Step 1: split 20 into: 10 × 2

Step 2: multiply 3.6 by 10
3.6 × 10 = 36
Step 3: multiply result by 2.
36 × 2 = 72.

c. 12.42 × 800
*follow the same steps as in (a.) and (b.)
100 × 8
12.42 × 100 = 1242.0
12.42 × 8 = 9936.

Sample 3

Simplify the following
a. 2.32 × 15
b. 14.42 × 2.5
c. 32.45 × 62
Solutions
2.32 × 15
Step 1: Remove the decimal point and multiply as whole numbers.

Step 2: Put back the decimal point to indicate decimal place. Put the decimal point according to the number if decimal places in the question

The total number of decimal places in the question is two.
Therefore the answer should be in two decimal places.

3480 = 34.80.

(b.) 14.42 × 2.5
Step 1: remove the decimal point and multiply as whole numbers
Step 2: put back the decimal point according to the number of decimal places in the question.

Divisions of decimals

When dividing decimal numbers by multiples of 10, we move the decimal point to the left according to the number of zero(s).

Sample 1

Divide the following:
(a). 4.75 ÷ 10
(b). 8.62 ÷ 100
(c) 1.85 ÷ 1000

Solution

4.75 ÷ 10
*Move the decimal point once to the left since there is only one zero and replace zero at the start if there is no number left.

(b). 8.62 ÷ 100
8.62 ÷ 100 = 0.0862

(c).1.85 ÷ 1000 = 0.00185

Sample 2

Divide the following
(a).55.34 by 300
(b). 7.23 by 400

Solution

55.34 ÷ 300
Step 1: split 300 into: 100 × 3

Step 2: divide 55.34 by splitted 300.

(b). 7.23 ÷ 400
Step 1: Split 400 into: 100 × 4
Step 2: Divide 7.23 by splited 400.

Sample 3

Divide the following:
(a). 3.4 by 0.17
(b). 14.8 by 2.6

Solutions:

Step 1: change decimals to fractions. We learnt how to do so in our last class.

Step 2: Simplify the fractions. We have also learnt how to do this

(b). Follow the same method as in (a).

Assignment

1). Multiply the following

• 64.2 × 100
• 49.07 × 500
• 67.26 × 10
  6.987 × 7.24

2). Divide the following

• 48.65 ÷ 100
• 6.24 ÷ 1000
• 2.4 ÷ 0.6
• 6.7 ÷ 400

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