Multiply Multi-Digit Numbers - 4th Grade Math

1. Use an area model split: If $23\times 15=(20+3)(10+5)$, what is the total?

   $345$. $200+100+30+15=345$ using area model sections.

2. What is the value of the product $4 \times 3{,}000$?

   $12{,}000$. Multiply $4 \times 3 = 12$, then add three zeros.

3. What is the value of the product $7 \times 5{,}000$?

   $35{,}000$. Multiply $7 \times 5 = 35$, then add three zeros.

4. Find and correct the error: A student wrote $18\times 30=5400$. What is the correct product?

   $540$. Student added extra zero; $18×30 = 540$.

5. What is $3{,}506\times 7$?

   $24{,}542$. Multiply each digit by $7$ and regroup as needed.

6. What is $27\times 34$?

   $918$. Split as $(20+7)(30+4) = 600+80+210+28$.

7. Identify the missing number: $3{,}214\times 6=(3{,}000\times 6)+(200\times 6)+(10\times 6)+(?\times 6)$.

   $4$. The ones place of $3{,}214$ is $4$.

8. Identify the missing number: $8 \times 4{,}000 = \square$.

   $32{,}000$. Multiply $8 \times 4 = 32$, then add three zeros.

9. What is $25\times 48$?

   $1{,}200$. Use partial products: $(25\times 40)+(25\times 8)$.

10. State the distributive property used to rewrite $a\times(b+c)$.

    $a\times(b+c)=a\times b+a\times c$. Multiply each term inside parentheses by the outside factor.

11. What is $36 \times 27$?

    $972$. $(30\times27) + (6\times27) = 810 + 162$.

12. What is $9{,}999\times 4$?

    $39{,}996$. Multiply each digit by $4$ and regroup as needed.

13. What is $4\times 8{,}019$?

    $32{,}076$. Break down by place value: $4×8000 + 4×10 + 4×9$.

14. Identify the missing product: $5\times(2{,}000+300+40+7)=10{,}000+1{,}500+200+?$.

    $35$. $5×7 = 35$ for the ones place.

15. State the equation for an area model with sides $(a+b)$ and $(c+d)$.

    $(a+b)(c+d)=ac+ad+bc+bd$. Each term in first parentheses multiplies each in second.

16. What is $7\times 3{,}462$?

    $24{,}234$. Multiply each place value: $7×3000 + 7×400 + 7×60 + 7×2$.

17. What property justifies rewriting $6 \times 3{,}000$ as $3{,}000 \times 6$?

    Commutative property of multiplication. Order doesn't matter when multiplying numbers.

18. What is $62\times 19$?

    $1{,}178$. Use $(60+2)(10+9) = 600+540+20+18$.

19. What is $3{,}090\times 9$?

    $27{,}810$. Multiply each digit by $9$ and regroup as needed.

20. What is $23 \times 14$ using partial products?

    $322$. $(20\times14) + (3\times14) = 280 + 42$.

21. What is $48\times 26$?

    $1{,}248$. Split as $(40+8)(20+6) = 800+240+160+48$.

22. What is $8\times 1{,}999$?

    $15{,}992$. Calculate $8×2000 - 8×1 = 16{,}000 - 8$.

23. What is $9\times 2{,}507$?

    $22{,}563$. Use place value: $9×2000 + 9×500 + 9×7 = 22{,}563$.

24. What is $59\times 32$?

    $1{,}888$. Use partial products: $(50\times 32)+(9\times 32)$.

25. What is the value of the product $8 \times 700$?

    $5{,}600$. Multiply $8 \times 7 = 56$, then add two zeros.

26. What is $4{,}213\times 3$?

    $12{,}639$. Multiply each digit by $3$ and regroup as needed.

27. Which partial products match $34\times 26$ using an area model split as $(30+4)(20+6)$?

    $30\times 20,\ 30\times 6,\ 4\times 20,\ 4\times 6$. Area model splits both factors into tens and ones.

28. What is $72 \times 34$?

    $2{,}448$. $(70\times34) + (2\times34) = 2380 + 68$.

29. Estimate using place value: $3{,}892\times 6\approx$ what (round $3{,}892$ to the nearest thousand)?

    $24{,}000$. Round $3{,}892$ to $4{,}000$, then $4{,}000\times 6$.

30. What is $2{,}048\times 6$?

    $12{,}288$. Multiply each digit by $6$ and regroup as needed.

31. What is $99\times 45$?

    $4{,}455$. Calculate $(100-1)×45 = 4{,}500 - 45$.

32. State the distributive property used to multiply: $a\times(b+c)$.

    $a\times b+a\times c$. Multiply $a$ by each term inside the parentheses.

33. What is $6\times 4{,}305$?

    $25{,}830$. Multiply by place value: $6×4000 + 6×300 + 6×5$.

34. Find the missing number: $5\times (800+40+6)=4{,}000+200+\square$.

    $30$. $5\times 6=30$, so the missing number is $30$.

35. Find the missing number: If $6\times 4{,}000=24{,}000$, then $6\times 400=?$.

    $2{,}400$. Divide by 10: $24{,}000÷10 = 2{,}400$.

36. What is $23\times 17$?

    $391$. Use area model: $(20+3)(10+7) = 200+140+30+21$.

37. Identify the correct regrouping: In $487\times 6$, what is $7\times 6$ and the carried value?

    $7\times 6=42$, carry $4$. Write $2$ in ones place and carry $4$ to tens place.

38. What is $6{,}125\times 8$?

    $49{,}000$. Multiply each digit by $8$ and regroup as needed.

39. What is $8{,}407\times 2$?

    $16{,}814$. Multiply each digit by $2$ and regroup as needed.

40. What is the value of the digit $6$ in $6{,}482$?

    $6{,}000$. The digit $6$ is in the thousands place.

41. What is the value of the product $9 \times 60$?

    $540$. Multiply $9 \times 6 = 54$, then add one zero.

42. What is $48 \times 15$?

    $720$. $(40\times15) + (8\times15) = 600 + 120$.

43. What is $7{,}030\times 5$?

    $35{,}150$. Multiply each digit by $5$ and regroup as needed.

44. What is $46\times 18$?

    $828$. Use partial products: $(40\times 18)+(6\times 18)$.

45. What is $73\times 16$?

    $1{,}168$. Use partial products: $(70\times 16)+(3\times 16)$.

46. Find the missing number: $70\times 8=560$, so $7\times 8=?$.

    $56$. Divide by 10: $560÷10 = 56$.

47. What equation matches a rectangular array with $6$ rows and $14$ columns?

    $6\times 14=84$. Total items equals rows times columns.

48. What is $34\times 27$?

    $918$. Use partial products: $(30\times 27)+(4\times 27)$.

49. What is $35\times 14$?

    $490$. Calculate $(30+5)(10+4) = 300+120+50+20$.

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