# Division of Decimal Fractions by Multiples

This topic would deal with division of decimals by multiples. That means we need to divide decimal fractions by multiples of 10 like 10, 20, 30. 40, 50……etc. Or division by multiples of 100 that is 100, 200, 300, 400, 500,…. and likewise. In case of division by the multiple of 1000 the division would be like 1000, 2000, 3000 and so on. We will learn about each of them.

For example:

346.8 ÷ 30

Solution:

346.8 ÷ 30

= 346.8/30

This can also be written as

= 346.8/(3 × 10)

We can also write it as;

= (346.8/3) × (1/10)

Now we will divide 346.8 by 3 first

= 115.6

Now, 115.6 × (1/10)

Now since it is actually division by 10 the decimal point will move 1 place to the left. Hence the decimal will be placed after 11. That means

= 11.56

Here are few more examples to illustrate the division of decimal fractions by multiples

1. 8582.32 ÷ 400

Solution:

8582.32 ÷ 400

= 8582.32/400

= 8582.32/ (4 × 100)

= (8582.32/4) × (1/100)

Now we will divide 8582.32 by 4 first

= 2145.58

Now, 2145.58 × (1/100)

=it is actually division by 100 the decimal point will move 2 places to the left. Hence the decimal will be placed after 1. That means

= 21.4558

2. 28984.25 ÷ 5000

Solution:

28984.25 ÷ 5000

= 28984.25/5000

= 28984.25 / (5 × 1000)

= 28984.25/5 × (1/1000)

So, first divide 28984.25 by 5

= 5796.25

Therefore, now 5796.25 × (1/1000)

That is actually 5796.25 divided by 1000. As there are three zeros in thousand hence the decimal point will move three places to the left. That is

= 5.79625

3. 771.84 ÷ 600

Solution:

771.84 ÷ 600

= 771.84/600

= 771.84 / (6× 100)

= 771.84/6 × (1/100)

Hence we need to first divide 771.84 by 6

= 128.64

Now we actually need to divide 128.64 by 100 and hence the decimal point will move 2 places to the left as there are 2 zeros in 100. That is

= 1.2864

4. 96.35 ÷ 50

Solution:

96.35 ÷ 50

= 96.35/50

= 96.35/ (5 × 10)

= 96.35/5 × (1/10)

Now we will first divide 96.35 by 5

= 19.27

Now we need to divide 19.27 by 10. The decimal point will move one place to the left. That is the answer will be

= 1.927

5. 170.46 ÷ 300

Solution:

170.46 ÷ 300

= 170.46/300

= 170.46/ (3 × 100)

= 170.46/3 × (1/100)

Hence first we need to divide 170.46 by 3

= 56.82

Now we need to actually divide 56.82 by 100. There are 2 zeros in 100 hence the decimal point will move 2 places to the left. That is the answer will be

= 0.5682

In this way we can solve these divisions by multiples by first dividing the decimal with whole number and then with the answer by 10, 100 or 1000 as asked in the question