Question

Carl wants to find the product 30×56 . Which of the following best explains how he can find the product mentally?

A.He knows that 30÷5 is 6. He then multiplies 6 by 6 to get 36.
B.He knows that 30×66 is 30. He then subtracts 1 from 30 to get 29.
C.He knows that 3×6=18. He then adds 18 and 5 to get 23.
D.He knows that 30×16 is 5. He then multiplies 5 by 5 to get 25.

Answer 1

To find the product of 30 and 56 mentally, Carl can multiply 3 by 5 and then by 10 to account for the place value, and then add that to the product of 6 and 30. This process results in 150 plus 180, equalling 1680.

Step-by-step explanation:

Carl wants to find the product 30×56. To perform this calculation mentally, he can use a strategy that involves breaking the numbers down into more manageable parts. Step one is to multiply the tens place of both numbers; that is, 3 (from 30) by 5 (from 56).

This results in 15. In step two, he needs to multiply this result by 10, giving 150, because the original 30 had an implicit one-zero after the 3.

The final step involves multiplying the 6 in 56 by the 30. Since we know 3×6 equals 18, and again 30 is three with a zero, it is 180 when multiplied by 6. Adding the results of the steps together, 150+180, gives the correct product of 1680. None of the provided options A, B, C, and D correctly demonstrates this process for mental multiplication.