High School

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Find the product using the expanded notation method for the following problems:

1. 315 x 7
2. 161 x 9
3. 96 x 9
4. 1534 x 8
5. 249 x 6
6. 3215 x 7
7. 776 x 5
8. 5593 x 4

Answer :

To find the product using the expanded notation method, we break down each number into its place value components and then multiply each component separately. Let's work through the problems step by step:

  1. 315 x 7

    • Break down 315:
      [tex]315 = 300 + 10 + 5[/tex]
    • Use expanded notation to multiply by 7:
      [tex]300 \times 7 = 2100[/tex]
      [tex]10 \times 7 = 70[/tex]
      [tex]5 \times 7 = 35[/tex]
    • Add the results:
      [tex]2100 + 70 + 35 = 2205[/tex]

  2. 161 x 9

    • Break down 161:
      [tex]161 = 100 + 60 + 1[/tex]
    • Use expanded notation to multiply by 9:
      [tex]100 \times 9 = 900[/tex]
      [tex]60 \times 9 = 540[/tex]
      [tex]1 \times 9 = 9[/tex]
    • Add the results:
      [tex]900 + 540 + 9 = 1449[/tex]

  3. 96 x 9

    • Break down 96:
      [tex]96 = 90 + 6[/tex]
    • Use expanded notation to multiply by 9:
      [tex]90 \times 9 = 810[/tex]
      [tex]6 \times 9 = 54[/tex]
    • Add the results:
      [tex]810 + 54 = 864[/tex]

  4. 1534 x 8

    • Break down 1534:
      [tex]1534 = 1000 + 500 + 30 + 4[/tex]
    • Use expanded notation to multiply by 8:
      [tex]1000 \times 8 = 8000[/tex]
      [tex]500 \times 8 = 4000[/tex]
      [tex]30 \times 8 = 240[/tex]
      [tex]4 \times 8 = 32[/tex]
    • Add the results:
      [tex]8000 + 4000 + 240 + 32 = 12272[/tex]

  5. 249 x 6

    • Break down 249:
      [tex]249 = 200 + 40 + 9[/tex]
    • Use expanded notation to multiply by 6:
      [tex]200 \times 6 = 1200[/tex]
      [tex]40 \times 6 = 240[/tex]
      [tex]9 \times 6 = 54[/tex]
    • Add the results:
      [tex]1200 + 240 + 54 = 1494[/tex]

  6. 3215 x 7

    • Break down 3215:
      [tex]3215 = 3000 + 200 + 10 + 5[/tex]
    • Use expanded notation to multiply by 7:
      [tex]3000 \times 7 = 21000[/tex]
      [tex]200 \times 7 = 1400[/tex]
      [tex]10 \times 7 = 70[/tex]
      [tex]5 \times 7 = 35[/tex]
    • Add the results:
      [tex]21000 + 1400 + 70 + 35 = 22505[/tex]

  7. 776 x 5

    • Break down 776:
      [tex]776 = 700 + 70 + 6[/tex]
    • Use expanded notation to multiply by 5:
      [tex]700 \times 5 = 3500[/tex]
      [tex]70 \times 5 = 350[/tex]
      [tex]6 \times 5 = 30[/tex]
    • Add the results:
      [tex]3500 + 350 + 30 = 3880[/tex]

  8. 5593 x 4

    • Break down 5593:
      [tex]5593 = 5000 + 500 + 90 + 3[/tex]
    • Use expanded notation to multiply by 4:
      [tex]5000 \times 4 = 20000[/tex]
      [tex]500 \times 4 = 2000[/tex]
      [tex]90 \times 4 = 360[/tex]
      [tex]3 \times 4 = 12[/tex]
    • Add the results:
      [tex]20000 + 2000 + 360 + 12 = 22372[/tex]

Using expanded notation helps break down the steps of multiplication, making it more manageable. This method emphasizes understanding how each digit contributes to the final product.

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