We divide by 2 to get 3,000. We then multiply the numbers in the circles and add the result to 3,000:
3 × 7 = 21
3,000 + 21 = 3,021
Let’s try one more:
Add diagonally and multiply the result by the reference number (multiply by 100 and then divide by
2):
64 + 1 = 65
65 × 100 = 6,500
Then we halve the answer.
Half of 6,000 is 3,000. Half of 500 is 250. Our subtotal is 3,250.
Now multiply the numbers in the circles:
1 × 14 = 14
Add 14 to the subtotal to get 3,264.
Our problem now looks like this:
We could check that by casting out the nines:
Six and 4 in 64 add up to 10, which added again gives us 1.
Six times 1 does give us 6, so the answer is correct.
Test yourself
Here are some problems for you to do. See how many you can do in your head.
a) 45 × 45 =
b) 49 × 49 =
c) 47 × 43 =
d) 44 × 44 =
e) 51 × 57 =
f) 54 × 56 =
g) 51 × 68 =
h) 51 × 72 =