Multiplication Using Two Reference Numbers 97
(100 ÷ 2) 96 × 48 = 4,600
–4
–2
- 8
–2
4,608 Answer
Th at worked out well, but what would happen if we multiplied 97
by 48? Th en we have to halve an odd number. Let’s see:
(100 ÷ 2) 97 × 48 = 4,650
–3
–2 - 6
-^3 / 2
4,656 Answer
–1^1 / 2
In this case we have to divide the 3 below the 97 by the 2 in the
parentheses. Th ree divided by 2 is ⁄ or 1½. Subtracting 1½ from
48 gives an answer of 46½. Th en we have to multiply 46½ by 100.
Forty-six by 100 is 4,600, plus half of 100 gives us another 50. So,
46½ times 100 is 4,650.
Th en we multiply 3 by 2 for an answer of 6; add this to 4,650 for
our answer of 4,656.
Let us check this answer by casting out the nines:
97 × 48 = 4,656
7 12 12
3 3
We check by multiplying 7 by 3 to get 21, which reduces to 3, the
same as our answer. Our answer is correct.
What if we multiply 97 by 23? We could use 100 and 25 (100 ÷ 4)
as reference numbers.