1 Review Exercises

    For Problems 1 and 2, write the numbers in (i) expanded form and (ii) word form.

  1. a. 7,502   b. 25,047   c. 620,025   d. 3,054,705
  2. a. 9,024   b. 38,024   c. 405,037   d. 2,601,071

    3. For Problems 3 and 4, write the the numbers in (i) standard form and (ii) expanded form.

  3. a. Five thousand, six hundred seven
    b. Thirty-seven thousand, forty
    c. Four hundred eight thousand, one hundred five
    d. One million, seventy thousand, fifty-five
  4. a. Nine thousand, nine hundred three
    b. Fifty-nine thousand, three hundred three
    c. Seven hundred thousand, eight hundred eighty-eight
    d. Seven million, seventy-six thousand, fifty-five

    5. For Problems 5 and 6, insert the proper sign of inequality (< or >) between each pair of numbers.

  5. a. 167 176   b. 2,067 2,097   c. 79,084 79,087   d. 162,555 162,507
  6. a. 159 139   b. 1,838 1,868   c. 52,109 51,889   d. 379,847 397,487

    7. For Problems 7 and 8, (i) estimate the answer by rounding each number to the nearest hundred, and (ii) calculate the exact answer.

  7. a. 3,495 + 276 + 85   b. 5,555 + 157 + 60   c. 7,836 – 655   d. 6,405 – 2,769
  8. a. 8,655 + 348 + 75   b. 3,450 + 645 + 50   c. 5,245 – 876   d. 2,056 – 444

    9. For Problems 9 and 10, perform the arithmetic operation.

  9. a. 465 × 23   b. 365 × 24   c. 315 ÷ 5   d. 2,532 ÷ 12
  10. a. 345 × 34   b. 237 × 25   c. 276 ÷ 6   d. 4,785 ÷ 15

    11. For Problems 11 and 12, find the LCM of the numbers.

  11. a. 12 and 20   b. 16 and 72   c. 16, 18, and 33
  12. a. 16 and 40   b. 36 and 54   c. 8, 24, and 32

    13. For Problems 13 and 14, find the GCF of the numbers.

  13. a. 8 and 12   b. 42 and 48   c. 24, 30, and 32
  14. a. 4 and 9   b. 40 and 72   c. 12, 16, and 60

    15. For Problems 15 to 28, perform the arithmetic operations.

  15. a. 6 + 8 – 6 × 2 ÷ 4   b. 15 – (7 – 5) ÷ 2
  16. a. 9 + 2 – 4 × 3 ÷ 2   b. 10 – (7 – 4) ÷ 3
  17. a. 12 – 2(9 – 6) + 10 ÷ 5 + 5   b. 9 – 8(7 – 5) ÷ (6 + 2)
  18. a. 8 – 4(6 – 4) + 16 ÷ 4 + 4   b. 10 – 4(9 – 7) ÷ (5 + 3)
  19. a. [latex] $\displaystyle{8(7 + 3) + 6^2 ÷ 4}$ [/latex]   b. [latex] $\displaystyle{8^2 ÷ 4 - 6(5 - 3)}$ [/latex]
  20. a. [latex] $\displaystyle{7(6 + 4) + 4^2 ÷ 2}$ [/latex]   b. [latex] $\displaystyle{9^2 ÷ 3(8 - 5) - 4(5 + 3)}$ [/latex]
  21. a. [latex] $\displaystyle{24 ÷ 2^2 × 3 + (5 - 2)^2}$ [/latex]   b. [latex] $\displaystyle{8(7 - 3)^2 ÷ 4 - 5}$ [/latex]
  22. a. [latex] $\displaystyle{64 ÷ (8 - 4)^2 + 5^2}$ [/latex]   b. [latex] $\displaystyle{9(8 - 5) ÷ 3 + (7 - 4)^2}$ [/latex]
  23. a. [latex] $\displaystyle{(16 + 4 × 2) ÷ (4^2 - 8)}$ [/latex]   b. [latex] $\displaystyle{6^2 - 2[(6 - 3)^2 + 4]}$ [/latex]
  24. a. [latex] $\displaystyle{(6 + 3 × 2) ÷ (2^2 - 1)}$ [/latex]   b. [latex] $\displaystyle{8^2 - 3[(7 - 3)^2 + 2]}$ [/latex]
  25. a. [latex] $\displaystyle{\sqrt{9} - (8 - 5) + 10 ÷ 5 + 7}$ [/latex]   b. [latex] $\displaystyle{15 - 15(8 - 6) ÷ \sqrt{36} + 15}$ [/latex]
  26. a. [latex] $\displaystyle{\sqrt{49} - 7(6 - 4) ÷ (5 - 3)}$ [/latex]   b. [latex] $\displaystyle{\sqrt{16} + (10 - 7) + 20 ÷ 4 - 3}$ [/latex]
  27. a. [latex] $\displaystyle{6^2 ÷ 9 + 6(5^2 - 2^2)}$ [/latex]   b. [latex] $\displaystyle{3[(7 - 4)^2 + 4] - (2 + 3)^2}$ [/latex]
  28. a. [latex] $\displaystyle{5(12^2 - 2^2) + 48 ÷ 4^2}$ [/latex]   b. [latex] $\displaystyle{(6 + 2)^2 - 4[(12 - 9)^2 + 3]}$ [/latex]
  29. After Martha gave 175 stamps to her brother, she had 698 stamps left. How many stamps did she have at the beginning?
  30. Amy spent $349 and had $167 left. How much did she have at the beginning?
  31. Each ticket for a concert costs $25. A total of $35,000 was collected from ticket sales for Saturday and Sunday. If 550 tickets were sold on Saturday, how many were sold on Sunday?
  32. A company manufactured printers for $40 a unit. Over two weeks, $46,000 was spent on manufacturing printers. If 500 printers were manufactured in the first week, how many printers were manufactured in the second week?
  33. At a concert, 245 tickets were sold for $125 each and 325 tickets were sold for $68 each. How much money was collected altogether?
  34. Susie held a bake sale. She sold 45 cookies for $2 each and 63 brownies for $3 each. How much money did she make altogether?
  35. Allan and Babar have a total of $2,550. Allan has $800 more than Babar. How much money does each of them have?
  36. Ayesha saved $5,500 more than Beth. If they saved $32,450 together, how much did each of them save?
  37. An elevator can carry a maximum of 540 kg. Two workers want to move 20 boxes of tiles, each weighing 24 kg. One of the workers weighs 72 kg and the other weighs 65 kg. What is the largest number of boxes that can be carried in the elevator if both workers are in it?
  38. A delivery truck can carry a maximum of 2,000 kg. Two workers want to move 100 planks of wood, each weighing 30 kg. One of the workers weighs 85 kg and the other weighs 77 kg. What is the largest number of planks that can be carried by the truck if both workers are in the truck?
  39. Three balls of yarn measuring 24 metres, 60 metres, and 36 metres are to be cut into pieces of equal lengths, without wastage. What is the maximum possible length of each piece?
  40. A store has 32 oranges, 48 bananas, and 72 apples. The owner decides to make fruit baskets each containing an equal number of fruits, without any left over. It was required that each basket have only one type of fruit in it. Find the maximum possible number of fruits in each basket.
  41. Amy, Bob, and Cathy go for a swim every 3rd, 7th, and 14th day, respectively. If they met each other on a particular day at the pool, how many days later would they meet again?
  42. Three gentlemen decided to go for a walk around a circular park. The first man takes 6 minutes, the second takes 10 minutes, and the third takes 8 minutes. If they start together, when will they meet again?
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