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Lesson 2: Modeling Multiplication with Area Models and Partial Products — Practice Questions

  1. 1. To multiply $48 \times 152$ using an area model, how should the numbers be decomposed based on place value?

    • A. $(40 + 8) \times (100 + 50 + 2)$
    • B. $(4 + 8) \times (1 + 5 + 2)$
    • C. $(40 \times 8) + (100 \times 50 \times 2)$
    • D. $(4 + 80) \times (100 + 5 + 20)$
  2. 2. When using an area model to multiply $36 \times 241$, what is the partial product of multiplying the tens place of $36$ by the hundreds place of $241$? ___

  3. 3. Using an area model for $32 \times 45$, what is the sum of all the partial products? ___

  4. 4. Which of the following is NOT a partial product when calculating $47 \times 162$ using an area model?

    • A. 2400
    • B. 700
    • C. 280
    • D. 14
  5. 5. To find the product of $145 \times 28$, the numbers are decomposed as $(100 + 40 + 5) \times (20 + 8)$. What is the partial product of $40 \times 8$? ___

  6. 6. To find the product of $6 \times 32$, you can decompose $32$ into $30 + 2$. Use partial products to find the final answer. The product is ___.

  7. 7. Which of the following are the partial products when you multiply $5 \times 43$?

    • A. $200$ and $15$
    • B. $20$ and $15$
    • C. $40$ and $3$
    • D. $200$ and $3$
  8. 8. The expression $7 \times 54$ can be written as $(7 \times 50) + (7 \times 4)$. What is the value of the partial product $7 \times 50$? ___

  9. 9. When you decompose factors to multiply, what are the results of the smaller multiplications called?

    • A. Partial products
    • B. Final sums
    • C. Decomposed factors
    • D. Quotients
  10. 10. Use partial products to calculate $32 \times 14$. The final product is ___.