Multiply Multi-Digit Whole Numbers - 5th Grade Math

1. When multiplying $63 \times 24$, why is a $0$ placeholder used in the second partial product?

   Because the second partial product is in the tens place ($\times 20$). The 2 in 24 represents 20, not 2.

2. Which estimate is closest to $298\times 51$: $15000$, $30000$, or $60000$?

   $15000$. Round to $300 \times 50 = 15000$ for estimation.

3. What is the product $408\times 23$ using the standard algorithm?

   $9384$. $408 \times 3 = 1224$, $408 \times 20 = 8160$, sum is $9384$.

4. What is the product $1\,024\times 6$ using the standard algorithm?

   $6144$. $1024 \times 6 = 6000 + 120 + 24 = 6144$.

5. What is the product $999\times 7$ using the standard algorithm?

   $6993$. $9 \times 7 = 63$, carry $6$; repeat for each digit.

6. What is the product $208\times 4$ using the standard algorithm?

   $832$. $208 \times 4 = 800 + 0 + 32 = 832$.

7. Find the product $325\times 12$ using the standard algorithm.

   $3900$. $325 \times 2 = 650$, $325 \times 10 = 3250$, sum is $3900$.

8. What is the value of the carry in $79\times 8$ after computing $9\times 8=72$?

   $7$. Write $2$, carry $7$ tens from $72$.

9. What is the product $123 \times 45$ using the standard algorithm?

   $5535$. Add partial products: $123×5=615$ and $123×40=4920$.

10. What is the product $507\times 6$ using the standard algorithm?

    $3042$. $507 \times 6 = 3000 + 0 + 42 = 3042$.

11. What is the product $208 \times 34$ using the standard algorithm?

    $7072$. Add partial products: $208×4=832$ and $208×30=6240$.

12. What is the first step in the standard algorithm for $34\times 27$?

    Multiply $7$ by each digit of $34$ from right to left. Start with the ones digit of the bottom number.

13. What is the product $305 \times 4$ using the standard algorithm?

    $1220$. Multiply each digit by 4: $5×4=20$, $0×4=0$, $3×4=12$.

14. What is the product $48 \times 7$ using the standard algorithm?

    $336$. Multiply each digit of 48 by 7, carrying as needed.

15. What is the product $46 \times 30$ using the standard algorithm?

    $1380$. $46×3=138$, then multiply by 10 for the tens place.

16. In $326 \times 47$, what place value does the first partial product (from $7$) represent?

    Ones place value (it is $326 \times 7$). The 7 is in the ones place of 47.

17. What is the product $236\times 40$ using the standard algorithm?

    $9440$. Multiply by $40$ means multiply by $4$ and add a zero.

18. Identify the missing digit: $68\times 5=3\square 0$.

    $4$. $68 \times 5 = 340$, so the missing digit is $4$.

19. What is the product $47\times 32$ using the standard algorithm?

    $1504$. $47 \times 2 = 94$, $47 \times 30 = 1410$, sum is $1504$.

20. What zero is placed in the second row when multiplying $47\times 32$ using the standard algorithm?

    A $0$ is placed in the ones place of the second partial product. When multiplying by tens, shift one place left.

21. What is the product $46\times 3$ using the standard algorithm?

    $138$. $46 \times 3 = (40 \times 3) + (6 \times 3) = 120 + 18$.

22. What is the product $63\times 24$ using the standard algorithm?

    $1512$. $63 \times 4 = 252$, $63 \times 20 = 1260$, sum is $1512$.

23. What is the product $64 \times 9$ using the standard algorithm?

    $576$. $4×9=36$, $6×9=54$, carry 5 to get 576.

24. In $326 \times 47$, what place value does the second partial product (from $4$) represent?

    Tens place value (it is $326 \times 40$). The 4 is in the tens place of 47.

25. What is the product $79 \times 12$ using the standard algorithm?

    $948$. Add partial products: $79×2=158$ and $79×10=790$.

26. What is the product $237 \times 8$ using the standard algorithm?

    $1896$. Multiply each digit by 8, carrying when products exceed 9.

27. Find and correct the error: In $25 \times 34$, a student shifts the $3$ partial product by $2$ places.

    Shift by $1$ place because $3$ is in the tens place ($30$). 3 in 34 is tens, so shift once, not twice.

28. What is the product $407 \times 26$ using the standard algorithm?

    $10582$. Add partial products: $407×6=2442$ and $407×20=8140$.

29. What is the first step in the standard algorithm to multiply $347 \times 6$?

    Multiply $6$ by the ones digit: $6 \times 7$. Start with the rightmost digit of the first number.

30. What is the product $412 \times 5$ using the standard algorithm?

    $2060$. $2×5=10$, $1×5=5$, $4×5=20$, giving 2060.

31. What is the product $508 \times 60$ using the standard algorithm?

    $30480$. $508×6=3048$, then multiply by 10 for the tens place.

32. What does the carried digit represent in $58\times 6$ when $8\times 6=48$?

    It represents $4$ tens to add to the next product. The carried digit shows tens from the ones multiplication.

33. What is the product $312 \times 28$ using the standard algorithm?

    $8736$. Add partial products: $312×8=2496$ and $312×20=6240$.

34. What does the carried digit represent in $58 \times 6$ when $6 \times 8 = 48$?

    It represents $4$ tens to add in the next place value. The 4 from 48 carries to the tens column.

35. What is the product $705\times 14$ using the standard algorithm?

    $9870$. $705 \times 4 = 2820$, $705 \times 10 = 7050$, sum is $9870$.

36. In the standard algorithm for $63\times 24$, what place value does the second partial product represent?

    It represents multiplying by $2$ tens (the $20$). The $2$ in $24$ is in the tens place, so multiply by $20$.

37. What is the product $125\times 8$ using the standard algorithm?

    $1000$. $125 \times 8 = 1000$ (or $8 \times 125 = 8 \times \frac{1000}{8}$).

38. What is the product $312\times 15$ using the standard algorithm?

    $4680$. $312 \times 5 = 1560$, $312 \times 10 = 3120$, sum is $4680$.

39. What is the product $906 \times 3$ using the standard algorithm?

    $2718$. Multiply each digit by 3: $6×3=18$, $0×3=0$, $9×3=27$.

40. What is the product $23 \times 45$ using the standard algorithm?

    $1035$. Add partial products: $23×5=115$ and $23×40=920$.

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