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Lesson 5: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication. — Practice Questions

  1. 1. To calculate $45 \times 23$, you can decompose $23$ into $20 + 3$. What is the partial product of $45 \times 20$? The answer is ___.

  2. 2. Which expression shows the correct way to find $53 \times 18$ using two partial products?

    • A. $(53 \times 10) + (53 \times 8)$
    • B. $(50 \times 10) + (3 \times 8)$
    • C. $(53 + 10) \times (53 + 8)$
    • D. $(53 \times 1) + (53 \times 8)$
  3. 3. To calculate $71 \times 34$, the partial products found by decomposing $34$ are $284$ and $2130$. What is the total product? The total product is ___.

  4. 4. When calculating $28 \times 45$ by finding the values of $28 \times 5$ and $28 \times 40$, what are the results of these two smaller multiplications called?

    • A. sums
    • B. quotients
    • C. partial products
    • D. factors
  5. 5. Use the partial products method to solve $47 \times 25$. First, decompose $25$ into $20 + 5$. The total product is ___.

  6. 6. To find $53 \times 38$, you can decompose $38$ into $30 + 8$. What is the partial product of $53 \times 30$? The answer is ___.

  7. 7. Which expression shows the correct way to find $47 \times 23$ by decomposing $23$ into its tens and ones?

    • A. $(47 \times 20) + (47 \times 3)$
    • B. $(40 \times 20) + (7 \times 3)$
    • C. $(47 \times 2) + (47 \times 3)$
    • D. $(40 \times 23) + (7 \times 23)$
  8. 8. To calculate $71 \times 14$, the partial products are found to be $710$ and $284$. What is the total product? The total is ___.

  9. 9. When multiplying $85 \times 16$, the number $16$ is split into $10$ and $6$. What do the calculations $85 \times 10$ and $85 \times 6$ represent in the area model method?

    • A. The final product
    • B. The partial products
    • C. The factors
    • D. The sums
  10. 10. Calculate $45 \times 31$ by decomposing $31$ into $30$ and $1$. Find the two partial products and add them to get the final answer. The final product is ___.