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Solve the following arithmetic problems and estimate the answers by rounding.

Mathematics

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Here are the solutions to the problems:

Question 8:

a)

  1. Perform the subtraction.

    26−42=−1626 - 42 = -16

  2. Perform the addition.

    −16+19=3-16 + 19 = 3

    The answer is 3\boxed{3}.

    b)

  3. Perform the multiplication.

    34×12=40834 \times 12 = 408

  4. Perform the additions from left to right.

    408+3=411408 + 3 = 411 411+8=419411 + 8 = 419

    The answer is 419\boxed{419}.

    c)

  5. Perform the multiplication.

    70×40=280070 \times 40 = 2800

  6. Perform the division.

    2800÷8=3502800 \div 8 = 350

  7. Perform the subtraction.

    350−186=164350 - 186 = 164

    The answer is 164\boxed{164}.

    Question 9:
    Estimate the answer by rounding off each number to the nearest ten.

  8. Round 9476 to the nearest ten.

    The last digit is 6, so round up.

    9476≈94809476 \approx 9480

  9. Round 29 to the nearest ten.

    The last digit is 9, so round up.

    29≈3029 \approx 30

  10. Perform the division with the rounded numbers.

    9480÷30=3169480 \div 30 = 316

    The estimated answer is 316\boxed{316}.

    Question 10:
    Estimate the amount of water used in one day by rounding off the numbers to the nearest ten.

  11. Round the total litres of water (7643) to the nearest ten.

    The last digit is 3, so round down.

    7643≈76407643 \approx 7640

  12. Round the number of days (147) to the nearest ten.

    The last digit is 7, so round up.

    147≈150147 \approx 150

  13. Divide the estimated total water by the estimated number of days.

    7640150=76415\frac{7640}{150} = \frac{764}{15} 764÷15≈50.93764 \div 15 \approx 50.93

    Rounding to the nearest whole number for an estimate:

    50.93≈5150.93 \approx 51

    The estimated amount of water used in one day is 51 litres\boxed{51 \text{ litres}}.

    Question 1 (Fractions section):
    Find the least number of books that can be shared equally among 4 or 5 learners.
    This requires finding the Least Common Multiple (LCM) of 4 and 5.

  14. List multiples of 4.

    4,8,12,16,20,24,…4, 8, 12, 16, \textbf{20}, 24, \dots

  15. List multiples of 5.

    5,10,15,20,25,…5, 10, 15, \textbf{20}, 25, \dots

  16. The least common multiple is 20.

    The least number of books is 20\boxed{20}.

    Question 2:

    a)

    49+39\frac{4}{9} + \frac{3}{9}

  17. Add the numerators since the denominators are the same.

    4+39=79\frac{4+3}{9} = \frac{7}{9}

    The answer is 79\boxed{\frac{7}{9}}.

    b)

    25+310\frac{2}{5} + \frac{3}{10}

  18. Find a common denominator.

    The LCM of 5 and 10 is 10.

  19. Convert 25\frac{2}{5} to an equivalent fraction with a denominator of 10.

    25=2×25×2=410\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}

  20. Add the fractions.

    410+310=4+310=710\frac{4}{10} + \frac{3}{10} = \frac{4+3}{10} = \frac{7}{10}

    The answer is 710\boxed{\frac{7}{10}}.

    c)

    1516−78\frac{15}{16} - \frac{7}{8}

  21. Find a common denominator.

    The LCM of 16 and 8 is 16.

  22. Convert 78\frac{7}{8} to an equivalent fraction with a denominator of 16.

    78=7×28×2=1416\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}

  23. Subtract the fractions.

    1516−1416=15−1416=116\frac{15}{16} - \frac{14}{16} = \frac{15-14}{16} = \frac{1}{16}

    The answer is 116\boxed{\frac{1}{16}}.

    d)

    1114−37\frac{11}{14} - \frac{3}{7}

  24. Find a common denominator.

    The LCM of 14 and 7 is 14.

  25. Convert 37\frac{3}{7} to an equivalent fraction with a denominator of 14.

    37=3×27×2=614\frac{3}{7} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14}

  26. Subtract the fractions.

    1114−614=11−614=514\frac{11}{14} - \frac{6}{14} = \frac{11-6}{14} = \frac{5}{14}

    The answer is 514\boxed{\frac{5}{14}}.

    Question 3:
    A traffic camera takes a photo every 4 minutes. Another camera takes a photo every 6 minutes. After how long will the two cameras take a photo together?
    This requires finding the Least Common Multiple (LCM) of 4 and 6.

  27. List multiples of 4.

    4,8,12,16,20,…4, 8, \textbf{12}, 16, 20, \dots

  28. List multiples of 6.

    6,12,18,24,…6, \textbf{12}, 18, 24, \dots

  29. The least common multiple is 12.

    The two cameras will take a photo together after 12 minutes\boxed{12 \text{ minutes}}.

    Question 4:
    Khadija carried 78\frac{7}{8} litres of water to school. She took 12\frac{1}{2} litres of the water. How much water did she remain with?

  30. Set up the subtraction problem.

    78−12\frac{7}{8} - \frac{1}{2}

  31. Find a common denominator.

    The LCM of 8 and 2 is 8.

  32. Convert 12\frac{1}{2} to an equivalent fraction with a denominator of 8.

    12=1×42×4=48\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}

  33. Subtract the fractions.

    78−48=7−48=38\frac{7}{8} - \frac{4}{8} = \frac{7-4}{8} = \frac{3}{8}

    Khadija remained with 38 litres\boxed{\frac{3}{8} \text{ litres}} of water.

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