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Solve the following multiplication problems using the standard algorithm, showing all steps:

Mathematics

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Step-by-step solution

36 steps

here are the solutions to the multiplication problems.

  1. 584×46584 \times 46

  1. Multiply 584 by 6 (units digit).

    584×6=3504584 \times 6 = 3504

  2. Multiply 584 by 40 (tens digit).

    584×40=23360584 \times 40 = 23360

  3. Add the partial products.

    3504+23360=268643504 + 23360 = 26864 26864\boxed{\text{26864}}
    1. 671×38671 \times 38

  4. Multiply 671 by 8 (units digit).

    671×8=5368671 \times 8 = 5368

  5. Multiply 671 by 30 (tens digit).

    671×30=20130671 \times 30 = 20130

  6. Add the partial products.

    5368+20130=254985368 + 20130 = 25498 25498\boxed{\text{25498}}
    1. 807×54807 \times 54

  7. Multiply 807 by 4 (units digit).

    807×4=3228807 \times 4 = 3228

  8. Multiply 807 by 50 (tens digit).

    807×50=40350807 \times 50 = 40350

  9. Add the partial products.

    3228+40350=435783228 + 40350 = 43578 43578\boxed{\text{43578}}
    1. 943×27943 \times 27

  10. Multiply 943 by 7 (units digit).

    943×7=6601943 \times 7 = 6601

  11. Multiply 943 by 20 (tens digit).

    943×20=18860943 \times 20 = 18860

  12. Add the partial products.

    6601+18860=254616601 + 18860 = 25461 25461\boxed{\text{25461}}
    1. 648×19648 \times 19

  13. Multiply 648 by 9 (units digit).

    648×9=5832648 \times 9 = 5832

  14. Multiply 648 by 10 (tens digit).

    648×10=6480648 \times 10 = 6480

  15. Add the partial products.

    5832+6480=123125832 + 6480 = 12312 12312\boxed{\text{12312}}
    1. 428×49428 \times 49

  16. Multiply 428 by 9 (units digit).

    428×9=3852428 \times 9 = 3852

  17. Multiply 428 by 40 (tens digit).

    428×40=17120428 \times 40 = 17120

  18. Add the partial products.

    3852+17120=209723852 + 17120 = 20972 20972\boxed{\text{20972}}
    1. 687×64687 \times 64

  19. Multiply 687 by 4 (units digit).

    687×4=2748687 \times 4 = 2748

  20. Multiply 687 by 60 (tens digit).

    687×60=41220687 \times 60 = 41220

  21. Add the partial products.

    2748+41220=439682748 + 41220 = 43968 43968\boxed{\text{43968}}
    1. 489×56489 \times 56

  22. Multiply 489 by 6 (units digit).

    489×6=2934489 \times 6 = 2934

  23. Multiply 489 by 50 (tens digit).

    489×50=24450489 \times 50 = 24450

  24. Add the partial products.

    2934+24450=273842934 + 24450 = 27384 27384\boxed{\text{27384}}
    1. 715×83715 \times 83

  25. Multiply 715 by 3 (units digit).

    715×3=2145715 \times 3 = 2145

  26. Multiply 715 by 80 (tens digit).

    715×80=57200715 \times 80 = 57200

  27. Add the partial products.

    2145+57200=593452145 + 57200 = 59345 59345\boxed{\text{59345}}
    1. 973×66973 \times 66

  28. Multiply 973 by 6 (units digit).

    973×6=5838973 \times 6 = 5838

  29. Multiply 973 by 60 (tens digit).

    973×60=58380973 \times 60 = 58380

  30. Add the partial products.

    5838+58380=642185838 + 58380 = 64218 64218\boxed{\text{64218}}
    1. 389×85389 \times 85

  31. Multiply 389 by 5 (units digit).

    389×5=1945389 \times 5 = 1945

  32. Multiply 389 by 80 (tens digit).

    389×80=31120389 \times 80 = 31120

  33. Add the partial products.

    1945+31120=330651945 + 31120 = 33065 33065\boxed{\text{33065}}
    1. 583×97583 \times 97

  34. Multiply 583 by 7 (units digit).

    583×7=4081583 \times 7 = 4081

  35. Multiply 583 by 90 (tens digit).

    583×90=52470583 \times 90 = 52470

  36. Add the partial products.

    4081+52470=565514081 + 52470 = 56551 56551\boxed{\text{56551}}
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