Using Mathematical Structure

Question 1

A baker has 7 trays, and each tray holds 13 cupcakes. She decides to find the total number of cupcakes by using the distributive property. Which choice shows the correct way to break the multiplication into two easy parts and gives the right total?

Accepted Answer

7 × 13 = 7 × (10 + 3) = 7 × 10 + 7 × 3 = 70 + 21 = 91

Answer

7 × 13 = 7 × 10 + 10 × 3 = 70 + 30 = 100

Answer

7 × 13 = 7 × 10 + 3 = 70 + 3 = 73

Answer

7 × 13 = (7 + 10) × 3 = 17 × 3 = 51

Question 2

Mia has the number 405. She wants to find 10 × 405 without using a calculator. Which explanation correctly shows why writing a zero at the end of 405 (making 4050) gives the right answer?

Accepted Answer

Multiplying by 10 moves each digit one place to the left, so the hundreds digit becomes thousands, the tens digit becomes hundreds, the units digit becomes tens, and the new units digit is 0.

Answer

Because adding a zero adds ten units, the new number is ten larger than the original.

Answer

You multiply each individual digit by 10 and then place those results side‑by‑side to get the product.

Answer

Since the original number already has a zero in the tens place, writing another zero simply keeps the value unchanged.

Question 3

When you multiply the number 346 by 10, the answer is 3460. Why does the digit 6 move to the tens place and a 0 appears at the end?

Accepted Answer

Each digit moves one place to the left because multiplying by 10 adds a zero in the units place, shifting the place values.

Answer

Multiplying by 10 adds 10 to the original number, so a 0 is added at the end.

Answer

Multiplying by 10 doubles each digit, and the extra digit becomes a 0.

Answer

Multiplying by 10 removes the ones digit and replaces it with a 0.

Try three questions

A baker has 7 trays, and each tray holds 13 cupcakes. She decides to find the total number of cupcakes by using the distributive property. Which choice shows the correct way to break the multiplication into two easy parts and gives the right total?

Mia has the number 405. She wants to find 10 × 405 without using a calculator. Which explanation correctly shows why writing a zero at the end of 405 (making 4050) gives the right answer?

When you multiply the number 346 by 10, the answer is 3460. Why does the digit 6 move to the tens place and a 0 appears at the end?

Keep going on this shelf