79 × 4 means 79 + 79 + 79 + 79, i.e., 289 or 7 × 49
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.
1946 × 69 = 19 × 6946 = 19 × 32 (cancelling 23), = 572 = 2812 Ans.
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.