Multiplying Fraction by a Whole Number
We know that multiplication is repeated addition. So, multiplying a fraction by a whole number is equivalent to adding the fraction for the whole number of times.
For example:
3 x 14can be shown as
Algebraically this means, 3 x 14 = 1 4 + 14 + 1 4 = 1 + 1 + 14 = 34
Consider the product 5 x 23 .
This is equivalent to adding 23, 5 times. Since the repeated addition can be done by multiplication, this can be done by multiplying the numerator by 5.
That is 5 x 23 = 5×24 = 103
Another way of looking at it is by considering the whole number 5 as a fraction with denominator 1. To multiply two fractions, multiply the numerators and denominators separately and then write their products as the numerators and denominators respectively.
5 x 23 = 51 + 23 =5×21×3 = 103
Since the product is an improper fraction convert it into a mixed number. Divide 10 by 3. The quotient is 3 and the remainder is 1.
Thus, 103 = 313.
This can be clearly identified in the geometrical interpretation as shown:
Example:
Catherine is making a cake for which she needs to use a three-fourths cup of oil. If she decides to make three cakes, what would be the amount of oil required?
For three cakes, the amount of the oil used be 3 times of three-fourths cup of oil.
3 x 34 = 31 x 34 = 3×31×3 = 94
Convert the improper fraction into a mixed number.
9 ÷ 4 = Q 2 R 1
Thus, 94 = 21 4
Therefore, the new recipe would require 2 and a quarter cups of oil.
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Example: 5 x 62 3
First, convert 62 3 into an improper fraction.
623 = (6×3)+23 =203
So, 5 x 623 = 5 x 203 =51 x203= 1003
Now, convert 1003 into a mixed fraction.
120 ÷ 3= Q 33 R 1
Thus, 1003 = 3313
