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Vermenigvuldig die getalle deur die tweede getal (vermenigvuldigtal) tot die naaste 100 af te rond. a. 6 572 x 209 = b. 7 436 x 689 = c. 9 365 x 545 = d. 8 274 x 374 =

Mathematics

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4. Vermenigvuldig die getalle deur die tweede getal (vermenigvuldigtal) tot die naaste 100 af te rond.
(Multiply the numbers by rounding the second number (multiplicand) to the nearest 100.)

  • a. 6 572×2096\,572 \times 209
  1. Round 209 to the nearest 100.

    $$
    209 \approx 200
    $$
    
  2. Multiply 6 5726\,572 by the rounded number.

    $$
    6\,572 \times 200 = 1\,314\,400
    $$
    The estimated product is $\boxed{\text{1 314 400}}$.
    
    • b. 7 436×6897\,436 \times 689
  3. Round 689 to the nearest 100.

    $$
    689 \approx 700
    $$
    
  4. Multiply 7 4367\,436 by the rounded number.

    $$
    7\,436 \times 700 = 5\,205\,200
    $$
    The estimated product is $\boxed{\text{5 205 200}}$.
    
    • c. 5 853×8225\,853 \times 822
  5. Round 822 to the nearest 100.

    $$
    822 \approx 800
    $$
    
  6. Multiply 5 8535\,853 by the rounded number.

    $$
    5\,853 \times 800 = 4\,682\,400
    $$
    The estimated product is $\boxed{\text{4 682 400}}$.
    
    • d. 4 634×2464\,634 \times 246
  7. Round 246 to the nearest 100.

    $$
    246 \approx 200
    $$
    
  8. Multiply 4 6344\,634 by the rounded number.

    $$
    4\,634 \times 200 = 926\,800
    $$
    The estimated product is $\boxed{\text{926 800}}$.
    
    • e. 9 365×5459\,365 \times 545
  9. Round 545 to the nearest 100.

    $$
    545 \approx 500
    $$
    
  10. Multiply 9 3659\,365 by the rounded number.

    $$
    9\,365 \times 500 = 4\,682\,500
    $$
    The estimated product is $\boxed{\text{4 682 500}}$.
    
    • f. 8 274×3748\,274 \times 374
  11. Round 374 to the nearest 100.

    $$
    374 \approx 400
    $$
    
  12. Multiply 8 2748\,274 by the rounded number.

    $$
    8\,274 \times 400 = 3\,309\,600
    $$
    The estimated product is $\boxed{\text{3 309 600}}$.
    

    5. Vermenigvuldig die getalle deur die eerste getal (vermenigvuldiger) en die tweede getal (vermenigvuldigtal) tot die naaste 100 af te rond.
    (Multiply the numbers by rounding the first number (multiplier) and the second number (multiplicand) to the nearest 100.)

    • a. 7 697×8637\,697 \times 863
  13. Round 7 6977\,697 to the nearest 100.

    $$
    7\,697 \approx 7\,700
    $$
    
  14. Round 863 to the nearest 100.

    $$
    863 \approx 900
    $$
    
  15. Multiply the rounded numbers.

    $$
    7\,700 \times 900 = 6\,930\,000
    $$
    The estimated product is $\boxed{\text{6 930 000}}$.
    
    • b. 6 427×4786\,427 \times 478
  16. Round 6 4276\,427 to the nearest 100.

    $$
    6\,427 \approx 6\,400
    $$
    
  17. Round 478 to the nearest 100.

    $$
    478 \approx 500
    $$
    
  18. Multiply the rounded numbers.

    $$
    6\,400 \times 500 = 3\,200\,000
    $$
    The estimated product is $\boxed{\text{3 200 000}}$.
    

    6. Gaan terug na vrae 2 - 5. Kontroleer om te sien hoe naby jou antwoorde was deur die getalle met 'n sakrekenaar te vermenigvuldig.
    (Go back to questions 2 - 5. Check how close your answers were by multiplying the numbers with a calculator.)
    This step requires you to use a calculator to find the exact products for questions 2, 3, 4, and 5, and then compare them to your estimated answers. This helps you understand the accuracy of your rounding.

    7. Skat wat die antwoorde sal wees. Bereken en kontroleer jou berekeninge teenoor jou skatting.
    (Estimate what the answers will be. Calculate and check your calculations against your estimation.)

    • a. 35 421+42 36535\,421 + 42\,365
  19. Estimate by rounding to the nearest 1 000.

    $$
    35\,421 \approx 35\,000
    $$
    $$
    42\,365 \approx 42\,000
    $$
    Estimated sum: $35\,000 + 42\,000 = 77\,000$.
    
  20. Calculate the exact sum.

    $$
    35\,421 + 42\,365 = 77\,786
    $$
    The estimated sum is $\boxed{\text{77 000}}$ and the exact sum is $\boxed{\text{77 786}}$.
    
    • b. 4 235×764\,235 \times 76
  21. Estimate by rounding 4 2354\,235 to the nearest 100 and 76 to the nearest 100.

    $$
    4\,235 \approx 4\,200
    $$
    $$
    76 \approx 100
    $$
    Estimated product: $4\,200 \times 100 = 420\,000$.
    
  22. Calculate the exact product.

    $$
    4\,235 \times 76 = 321\,860
    $$
    The estimated product is $\boxed{\text{420 000}}$ and the exact product is $\boxed{\text{321 860}}$.
    

    Probleemoplossing: Verjaarsdag geld
    (Word Problem: Birthday money)
    My ma verkoop verjaarsdag geskenkpakkies. In elke geskenkpakkie is sjokolade ter waarde van R25, lekkers ter waarde van R22 en toffies ter waarde van R18. Die boks vir die lekkers kos R5. My ma voeg nog R20 by vir die maak daarvan en vir haar aflewering koste. Sy het laas jaar R2 320 se geskenkpakkies verkoop. Wat was die totale bedrag geld wat my ma gekry het?

    (My mom sells birthday gift packages. Each gift package contains chocolate worth R25, sweets worth R22, and toffees worth R18. The box for the sweets costs R5. My mom adds another R20 for making it and for her delivery costs. Last year she sold R2 320 worth of gift packages. What was the total amount of money my mom received?)

    Assumption: The phrase "R2 320 se geskenkpakkies verkoop" means she sold 2 320 packages, and the question asks for the total revenue from these sales, given the price breakdown per package.

  23. Calculate the total price of one gift package.

    Price per package=Chocolate+Sweets+Toffees+Box+Making/Delivery\text{Price per package} = \text{Chocolate} + \text{Sweets} + \text{Toffees} + \text{Box} + \text{Making/Delivery} Price per package=R25+R22+R18+R5+R20=R90\text{Price per package} = \text{R}25 + \text{R}22 + \text{R}18 + \text{R}5 + \text{R}20 = \text{R}90
  24. Calculate the total amount of money received for 2 320 packages.

    Total money received=Number of packages×Price per package\text{Total money received} = \text{Number of packages} \times \text{Price per package} Total money received=2 320×R90=R208 800\text{Total money received} = 2\,320 \times \text{R}90 = \text{R}208\,800

    The total amount of money your mom received was R208 800\boxed{\text{R208 800}}.

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