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Multiplication of Fractions

Multiplication of a Fraction by a Whole Number

3
Ruhi’s mother bought 12 apples. She used of total apples to make an apple pie cake for Ruhi’s
4
birthday party. How many apples did she use to make an apple pie cake?

To know about the number of apples used to make the apple pie cake. Let us divide 12 apples into
groups of 3 apples each, that are in 4 groups, then separate 3 groups of them to find how many
apples are used to make an apple pie cake.

×
3 312 36
So, × 12 = = = 9 apples
4 4 4
Thus, to multiply a fraction with a whole number, multiply the whole number to the numerator of
the fractions and keep the denominator same and then simplify the resultant fraction, if necessary.
Let us take another example to understand the
multiplication of fractions by a whole number. + + =

We know that multiplication is the process of repeated 1 1 1 3
1 + + =
addition. Suppose, we have to add a fraction three 4 4 4 4
1 1 1 4
times. It means + + .
4 4 4

1 1
We can also write it as × 3timesor × 3
4 4

1 3 13 3 Quick Check
×
= × = =
4 1 41 4 1. Find 5 × 1 using the
×
Example 5: Multiply the following: 2
7 1 2 process of repeated
(a) × 72 (b) 1 × 2 (c) 54 3× addition.
8 3 9 2. Find the following:

×
7 772 504 4 3
Solution: (a) × 72 = = = 63 (a) 1 × 7 (b) × 27
8 8 8 9 9
1 4 42 8 2
×
(b) 1 ×= ×= = = 2
2
2
3 3 3 3 3
2 29 54 29
×
(c) 54 3 = 54 × = =× 174
×
629 =
9 9 9
35 Fractions and Decimals