Final answer:
Thomas is using the compensation strategy for multiplication, making a more complex problem simpler by adjusting one number, conducting the easier operation, and then compensating at the end to get the correct answer.
Step-by-step explanation:
Thomas is using a mental math strategy known as compensation to calculate 9 × 7. This strategy involves adjusting one of the numbers in the multiplication to make the calculation easier and then compensating for that adjustment at the end. In Thomas's case, he knows that multiplying by 10 is simpler, so he multiplies 7 by 10 to get 70. He then subtracts one multiple of 7 from this result to get back to 9 × 7. So his calculation is essentially 70 (7 × 10) minus 7, which equals 63.
When approaching more complex problems, such as finding the cube of a number like (74)³, a similar strategy of breaking down the number into easier to manage parts can be quite helpful. The number 74 can be expressed as 7 x 7 x 7 x 7, and to find its cube, you would need to multiply this expression by itself three times.
In another example, if asked to compute 24 x 14 in your head, as mentioned by Daniel Kahneman in his book Thinking Fast and Slow, a similar strategy can be applied. One could round 14 up to 15, multiply it by 24 to get 360, and then subtract 24 to compensate for the initial rounding up. The final answer then is 336.