There is no difference between 8 and 8.0. The first number equals 8; the second number equals 8 too,
but it is accurate to one decimal place. The value doesn’t change.
We can use 8.0 and work out the problem as if it were 80, as we did above. We can now use a
reference number of 100. Let’s see what happens:
Now the problem is easy. Subtract diagonally.
79 − 20 = 59
Multiply 59 by the reference number (100) to get 5,900.
Multiply the numbers in the circles.
20 × 21 = 420
(To multiply by 20 we can multiply by 2 and then by 10.) Add the result to the subtotal.
5,900 + 420 = 6,320
The completed problem would look like this:Now, we have to place the decimal. How many digits are there after the decimal in the problem? One,
the 0 we provided. So we count one digit back in the answer.
632.0 Answer
We would normally write the answer as 632.
Let’s check this answer using estimation. Eight is close to 10 so we can round upwards.
10 × 79 = 790
The answer should be less than, but close to, 790. It certainly won’t be around 7,900 or 79. Our
answer of 632 fits so we can assume it is correct.
We can double-check by casting out nines.
Eight times 7 equals 56, which reduces to 11, then 2. Our answer is correct.
Let’s try another.
98 × 968 =
We write 98 as 98.0 and treat it as 980 during the calculation. Our problem now becomes 980 × 968.Our next step is:
968 − 20 = 948
Multiply by the reference number:
948 × 1,000 = 948,000
Now multiply 32 by 20. To multiply by 20 we multiply by 2 and by 10.
32 × 2 = 64
64 × 10 = 640