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Fill in the blanks and find the products using properties of multiplication.

Mathematics

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Step-by-step solution

22 steps

5:

1. Fill in the blanks.

a) 134×245=245×134134 \times \boxed{245} = 245 \times 134

b) 8×2513×125=(8×125)×2513=1000×2513=25130008 \times 2513 \times 125 = (8 \times 125) \times 2513 = 1000 \times 2513 = 2513000 (This is an example, already filled)

c) 519×3105=3105×519519 \times \boxed{3105} = 3105 \times 519

d) 8175×6213=8175×62138175 \times \boxed{6213} = \boxed{8175} \times 6213

e) 1×8367=8367\boxed{1} \times 8367 = 8367

f) 0×93653=0\boxed{0} \times 93653 = 0

g) 27×(121+23)=(27×121)+(27×23)27 \times (121 + 23) = (27 \times \boxed{121}) + (27 \times \boxed{23})

h) 119×(100+17)=(119×100)+(119×17)119 \times (100 + 17) = (\boxed{119} \times 100) + (119 \times \boxed{17})

2. Write the product without actually multiplying.

a) 6323×10=632306323 \times 10 = \boxed{63230}

b) 2799×10=279902799 \times 10 = \boxed{27990}

c) 4215×100=4215004215 \times 100 = \boxed{421500}

d) 3612×100=3612003612 \times 100 = \boxed{361200}

e) 2530×1000=25300002530 \times 1000 = \boxed{2530000}

f) 4795×1000=47950004795 \times 1000 = \boxed{4795000}

3. Find the products.

a) 3058×403058 \times 40

  1. Multiply 3058 by 4.

    3058×4=122323058 \times 4 = 12232
  2. Add the zero from 40.

    12232×10=12232012232 \times 10 = 122320

    The product is 122320\boxed{122320}.

    b) 1978×3001978 \times 300

  3. Multiply 1978 by 3.

    1978×3=59341978 \times 3 = 5934
  4. Add the two zeros from 300.

    5934×100=5934005934 \times 100 = 593400

    The product is 593400\boxed{593400}.

    c) 7200×5007200 \times 500

  5. Multiply 72 by 5.

    72×5=36072 \times 5 = 360
  6. Add the four zeros (two from 7200 and two from 500).

    360×10000=3600000360 \times 10000 = 3600000

    The product is 3600000\boxed{3600000}.

    d) 800×6000800 \times 6000

  7. Multiply 8 by 6.

    8×6=488 \times 6 = 48
  8. Add the five zeros (two from 800 and three from 6000).

    48×100000=480000048 \times 100000 = 4800000

    The product is 4800000\boxed{4800000}.

    4. Find the products using suitable arrangements.

    a) 2×1768×502 \times 1768 \times 50

  9. Group 2 and 50.

    (2×50)×1768(2 \times 50) \times 1768
  10. Multiply the grouped numbers, then by 1768.

    100×1768=176800100 \times 1768 = 176800

    The product is 176800\boxed{176800}.

    b) 4×927×254 \times 927 \times 25

  11. Group 4 and 25.

    (4×25)×927(4 \times 25) \times 927
  12. Multiply the grouped numbers, then by 927.

    100×927=92700100 \times 927 = 92700

    The product is 92700\boxed{92700}.

    c) 8×291×1258 \times 291 \times 125

  13. Group 8 and 125.

    (8×125)×291(8 \times 125) \times 291
  14. Multiply the grouped numbers, then by 291.

    1000×291=2910001000 \times 291 = 291000

    The product is 291000\boxed{291000}.

    d) 625×16×57625 \times 16 \times 57

  15. Group 625 and 16.

    (625×16)×57(625 \times 16) \times 57
  16. Multiply 625×16625 \times 16.

    625×16=10000625 \times 16 = 10000
  17. Multiply the result by 57.

    10000×57=57000010000 \times 57 = 570000

    The product is 570000\boxed{570000}.

    e) 25×80×1725 \times 80 \times 17

  18. Group 25 and 80.

    (25×80)×17(25 \times 80) \times 17
  19. Multiply 25×8025 \times 80.

    25×80=200025 \times 80 = 2000
  20. Multiply the result by 17.

    2000×17=340002000 \times 17 = 34000

    The product is 34000\boxed{34000}.

    f) 125×40×8125 \times 40 \times 8

  21. Group 125 and 8.

    (125×8)×40(125 \times 8) \times 40
  22. Multiply the grouped numbers, then by 40.

    1000×40=400001000 \times 40 = 40000

    The product is 40000\boxed{40000}.

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