DIVIDING BY A DECIMAL

For some real-world problems, we may need to divide a number by a decimal.

Let us see how a number can be divided by a decimal.

When we multiply both the dividend and the divisor like  

8 ÷ 4

by the same power of 10, the quotient does not change.

That is,

To divide a number by a decimal, first change the divisor to a whole number by multiplying it by a power of 10. Then multiply the dividend by the same power of 10.

For example,

In the above working, both the dividend and the divisor are multiplied by 10.

Example 1 :

Every smoothie sold contains 0.5 cup of raspberries. How many smoothies can be sold using 3.25 cups of raspberries ?

Solution :

To know the number of smoothies can be sold using 3.25 cups, we have to divide 3.25 by 0.5.

Because, every smoothie sold contains 0.5 cup of raspberries.

Let us divide 3.25 by 0.5.

The divisor 0.5 has one decimal place, so multiply both the dividend and the divisor by 10 so that the divisor is a whole number.

0.5 x 10 = 5

3.25 x 10 = 32.5

In the above long division, we have to move decimal point as given below.

Now, the above long division becomes as given below.

Hence, the number smoothies can be sold using 3.25 cups is 6.

Example 2 :

Anthony spent $11.52 for some pens that were on sale for $0.72 each. How many pens did Anthony buy ?

Solution :

To know the number of pens, we have to divide 11.52 by 0.72.

Because, each pen costs $0.72.

Let us divide 11.52 by 0.72.

The divisor 0.72 has two decimal places, so multiply both the dividend and the divisor by 100 so that the divisor is a whole number.

0.72 x 100 = 72

11.52 x 100 = 1152

In the above long division, we have to move decimal point as given below.

Now, the above long division becomes as given below.

Hence, Anthony bought 16 pens.

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