7 7 7 7 7 28
- × 4 means - + - + - + -, _i.e._, --; or
9 9 9 9 9 9
7 × 4
-----
9
Hence, to multiply a fraction by a whole number, simply multiply the
numerator by that number.
Since the multiplier thus becomes a factor of the numerator, we cancel
any common factors contained in the multiplier and the denominator; and
this may be done before we perform the actual multiplication:
EXAMPLE 2: Multiply 19/46 by 69.
19 19 × 69 19 × 3 57
-- × 69 = ------- + ------ (cancelling 23), = -- = 28-1/2 _Ans._
46 46 2 2
It follows that if the multiplier be itself a factor of the denominator,
we may, to multiply a fraction by a whole number, divide the denominator
by that number.
(ii) When the multiplier is a fraction.
EXAMPLE: In performing the operation 7 × 9, it is plain that we do to 7
what we do to a unit to obtain 9. Similarly, 3/5 × 4/11 may be looked
upon as doing to 3/5 what we do to the unit to obtain 4/11.
Now, to obtain 4/11 from the unit, we must divide the unit into 11 equal
parts and take 4 of them.
Therefore, to find the value of 3/5 × 4/11 we must divide 3/5 into 11
equal parts and take 4 of them.
But 3/5 = 33/55 = 3/55 × 11, so that, the eleventh part of 3/5 is 3/55;
and, if we take 4 of these parts, we get 3/55 × 4 or 12/55.
3 4 12
Thus, - × -- = --. Now 12 = 3 × 4, and 55 = 5 × 11.
5 11 55
Hence we have the following rule: To multiply two fractions together,
multiply the numerators for a new numerator and the denominators for a
new denominator.
As in Example 2 the work is shortened if we cancel common factors from
the numerators and denominators.
EXAMPLE: Multiply 22/91 by 13/77.
2
2̸2̸ × 1̸3̸ 2
The product = -------- = -- _Ans._
9̸1̸ × 7̸7̸ 49
7 7
Here, the 22 of the numerator and the 77 of the denominator contain a
common factor, 11. Therefore, we cross out the 22 and write 2 above it,
and cross out the 77 and write 7 under it. Similarly, we cancel the
factor 13 from 13 and 91. There is now 2 left for numerator and 7 × 7
for denominator.
To multiply more than two fractions together, we proceed in the same
way.
In multiplication of fractions, mixed numbers must first be expressed as
improper fractions.
EXAMPLE: Simplify 5-1/7 × 11/27 × 1-11/24.
3̸ 5
3̸6̸ 11 3̸5̸ 55 1
Given expression = -- × -- × -- = -- = 3-- _Ans._
7̸ 2̸7̸ 2̸4̸ 18 18
9 2