Answer Key – Chapter 1

Exercise 1.1

    1. (i) Tens   (ii) 90
    2. (i) Hundreds   (ii) 300
    3. (i) Hundreds   (ii) 700
    1. (i) Ten thousands   (ii) 10,000
    2. (i) Ten thousands   (ii) 20,000
    3. (i) Millions   (ii) 6,000,000
    1. (i) Expanded form: 400 + 7   (ii) Word form: Four hundred seven
    2. (i) Expanded form: 2,000 + 50 + 6   (ii) Word form: Two thousand, fifty-six
    1. (i) Expanded form: 20,000 + 9,000 + 100 + 80 + 6
      (ii) Word form: Twenty-nine thousand, one hundred eighty-six
    2. (i) Expanded form: 400,000 + 60,000 + 4,000 + 400 + 40 + 8
      (ii) Word form: Four hundred sixty-four thousand, four hundred forty-eight
    1. (i) Expanded form: 2,000,000 + 600,000 + 4,000 + 300 + 20 + 5
      (ii) Word form: Two million, six hundred four thousand, three hundred twenty-five
    2. (i) Expanded form: 10,000,000 + 5,000,000 + 300,000 + 600 + 4
      (ii) Word form: Fifteen million, three hundred thousand, six hundred four
    1. (i) Standard form: 679   (ii) Word form: Six hundred seventy-nine
    2. (i) Standard form: 3,147   (ii) Word form: Three thousand, one hundred forty-seven
    1. (i) Standard form: 2,605   (ii) Word form: Two thousand, six hundred five
    2. (i) Standard form: 9,024   (ii) Word form: Nine thousand, twenty-four
    1. (i) Standard form:40,990   (ii) Word form: Forty thousand, nine hundred ninety
    2. (i) Standard form:10,053   (ii) Word form: Ten thousand, fifty-three
    1. (i) Standard form: 570   (ii) Expanded form: 500 + 70
    2. (i) Standard form: 803   (ii) Expanded form: 800 + 3
    1. (i) Standard form: 80,630   (ii) Expanded form: 80,000 + 600 + 30
    2. (i) Standard form: 75,025   (ii) Expanded form: 70,000 + 5,000 + 20 + 5
    1. (i) Standard form: 12,452,832
      (ii) Expanded form:10,000,000 + 2,000,000 + 400,000 + 50,000 + 2,000 + 800 + 30 + 2
    2. (i) Standard form: 32,684,256
      (ii) Expanded form: 30,000,000 + 2,000,000 + 600,000 + 80,000 + 4,000 + 200 + 50 + 6
    1. (i) Standard form: 125,000   (ii) Expanded form: 100,000 + 20,000 + 5,000
    2. (i) Standard form: 250,000   (ii) Expanded form: 200,000 + 50,000
    1. a number line starting at 5, 10, 15, and ending with 20. Four points plotted 7, 14, 15, 19.
    2. A number line starting at 5, 10, 15, and ending at 20. Four points plotted: 5, 8, 12, 17.
    1. 7 < 15
    2. 19 > 14
    3. 0 < 5
    4. 19 > 0
    1. (i) 6 is less than 9   (ii) 9 is greater than 6
    2. (i)11 is less than 18   (ii)18 is greater than 11
    3. (i) 5 is less than 11   (ii) 11 is greater than 5
    4. (i) 0 is less than 11   (ii) 11 is greater than 0
    1. 87, 96, 99, 103, 108
    2. 108, 139, 141, 159, 167
    1. 2,040; 2,067; 2,533; 2,638
    2. 78,812; 79,468; 79,487; 79,534
    1. (i) 259   (ii) 952
    2. (i) 1,789   (ii) 9,871
    3. (i) 3,458   (ii) 8,543
    1. (i) 520   (ii) 500   (iii) 1,000
    2. (i) 1,650   (ii) 1,600   (iii) 2,000
    3. (i) 53,560   (ii) 53,600   (iii) 54,000
    4. (i) 235,360   (ii) 235,400   (iii) 235,000
    1. (i) 880,000   (ii) 900,000   (iii) 1,000,000
    2. (i) 1,660,000   (ii)1,700,000   (iii) 2,000,000
    3. (i) 3,370,000   (ii) 3,400,000   (iii) 3,000,000
    4. (i) 4,570,000   (ii) 4,600,000   (iii) 5,000,000

Exercise 1.2

    1. (i) 80   (ii) 77
    2. (i) 140   (ii) 133
    1. (i) 930   (ii) 923
    2. (i) 650   (ii) 653
    1. (i) 420   (ii) 410
    2. (i) 1,520   (ii) 1,511
    1. (i) 670   (ii) 662
    2. (i) 1,830   (ii) 1,818
    1. (i) 1,400   (ii) 1,413
    2. (i) 600   (ii) 652
    1. (i) 7,400   (ii) 7,349
    2. (i) 5,700   (ii) 5,616
    1. (i) 4,500   (ii) 4,531
    2. (i) 3,800   (ii) 3,732
    1. (i) 30   (ii) 37
    2. (i) 10   (ii) 15
    1. (i) 130   (ii) 129
    2. (i) 270   (ii) 268
    1. (i) 610   (ii) 608
    2. (i) 490   (ii) 496
    1. (i) 1,060   (ii) 1,058
    2. (i) 2,040   (ii) 2,039
    1. (i) 400   (ii) 494
    2. (i) 600   (ii) 604
    1. (i) 700   (ii) 675
    2. (i) 2,200   (ii) 2,128
    1. (i) 700   (ii) 667
    2. (i) 2,300   (ii) 2,324
    1. (i) 4,800   (ii) 4,350
    2. (i) 3,600   (ii) 3,717
    1. (i) 38,000   (ii) 40,492
    2. (i) 56,000   (ii) 54,332
    1. (i) 80,000   (ii) 73,815
    2. (i) 129,000   (ii) 126,850
    1. (i) 8   (ii) Quotient: 15 Reminder: 3
    2. (i) 4   (ii) Quotient: 4 Reminder: 4
    1. (i) 3   (ii) Quotient: 3 Reminder: 5
    2. (i) 4   (ii) Quotient: 4 Reminder: 2
    1. (i) 65   (ii) Quotient: 46 Reminder: 10
    2. (i) 20   (ii) Quotient: 16 Reminder: 12
    1. (i) 128   (ii) Quotient: 142 Reminder: 6
    2. (i) 41   (ii) Quotient: 43 Reminder: 21
    1. (i) 15   (ii) Quotient: 14 Reminder: 148
    2. (i) 13   (ii) Quotient: 13 Reminder: 27
    1. [latex]6^4[/latex]
    2. [latex]12^2[/latex]
    1. [latex]3^6[/latex]
    2. [latex]9^4[/latex]
    1. Base: 2 Exponent: 9
    2. Base: 5 Exponent: 7
    1. Base: 1 Exponent: 20
    2. Base: 8 Exponent: 3
    1. 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000
    2. 3 × 3 × 3 × 3 × 3 = 243
    1. [latex]3^9 = 19,683[/latex]
    2. [latex]3^{11} = 177,147[/latex]
    1. 8
    2. 11
    1. 1
    2. 18
    1. 8
    2. 20
    1. $719
    2. $133
    1. $1,362
    2. $620
    1. 360 pens
    2. 12 pieces
    1. 45 weeks
    2. 352 chairs
  1. $53
  1. $2,130
  1. $450
  1. 42 weeks
  1. 762 students
  1. 125
  1. $163
    1. 24 boys
    2. 17 students

Exercise 1.3

    1. –5 < 0
    2. –2 < 6
    1. 8 > –3
    2. 1 > –2
    1. –6 > –8
    2. –5 < –2
    1. –8, –6, –5, 2, 5, 8
    2. –9, –8, –6, 3, 4, 7
    1. –8, –5, 3, 7, 9, 10
    2. –13, –8, –3, 2, 12, 15
    1. –20
    2. 6
    1. 12
    2. 14
    1. 7
    2. –3
    1. 30
    2. –24
    1. 8
    2. –9
    1. 2
    2. 17
    1. 70
    2. –72
    1. 265
    2. 30
  1.   –132
  1.   –111

Exercise 1.4

  1. 2, 3, 5, 7, 11, 13, 17 and 19
  1. 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27 and 28
    1. 13, 19 and 47
    2. 11, 29 and 43
    1. (i) Factors: 1, 3, 5 and 15    (ii) Prime factors: 3 and 5
    2. (i) Factors: 1, 2, 17 and 34    (ii) Prime factors: 2 and 17
    1. (i) Factors: 1, 2, 4, 8, 16, 32 and 64    (ii) Prime factors: 2
    2. (i) Factors: 1, 2, 3, 6, 9, 18, 27 and 54    (ii) Prime factors: 2 and 3
    1. (i) Factors: 1, 3, 7 and 21    (ii) Prime factors: 3 and 7
    2. (i) Factors: 1, 5, 25    (ii) Prime factors: 5
    1. (i) Factors: 1, 2, 3, 4, 6, 9, 12, 18 and 36    (ii) Prime factors: 2 and 3
    2. (i) Factors: 1, 5, 13 and 65    (ii) Prime factors: 5 and 13
    1. 6, 12, 18, 24, 30 and 36
    2. 8, 16, 24, 32, 40 and 48
    1. 9, 18, 27, 36, 45 and 54
    2. 10, 20, 30, 40, 50 and 60
    1. 30
    2. 90
    1. 72
    2. 315
    1. 64
    2. 120
    1. 24
    2. 180
    1. 150
    2. 108
    1. 84
    2. 54
    1. 72
    2. 90
    1. (i) Factors of 15: 1, 3, 5 and 15 Factors of 25: 1, 5 and 25
      (ii) Common factors: 1 and 5
      (iii) GCF: 5
    2. (i) Factors of 18: 1, 2, 3, 6, 9 and 18 Factors of 32: 1, 2, 4, 8, 16 and 32
      (ii) Common factors: 1 and 2
      (iii) GCF: 2
    1. (i) Factors of 18: 1, 2, 3, 6, 9 and 18 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48
      (ii) Common factors: 1, 2, 3 and 6
      (iii) GCF: 6
    2. (i) Factors of 32: 1, 2, 4, 8, 16 and 32 Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
      (ii) Common factors: 1, 2 and 4
      (iii) GFC: 4
    1. (i) Factors of 25: 1, 5 and 25 Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
      (ii) Common factors: 1 and 5
      (iii) GFC: 5
    2. (i) Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
      (ii) Common factors: 1, 2, 4, 5, 8, 10, 20 and 40
      (iii) GFC: 40
    1. (i) Factors of 8: 1, 2, 4 and 8 Factors of 12: 1, 2, 3, 4, 6 and 12 Factors of 15: 1, 3, 5 and 15
      (ii) Common factor: 1
      (iii) GFC: 1
    2. (i) Factors of 6: 1, 2, 3 and 6 Factors of 15: 1, 3, 5 and 15 Factors of 20: 1, 2, 4, 5, 10 and 20
      (ii) Common factor: 1
      (iii) GFC: 1
    1. (i) Factors of 12: 1, 2, 3, 4, 6 and 12 Factors of 18: 1, 2, 3, 6, 9 and 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
      (ii) Common factors: 1, 2, 3 and 6
      (iii) GFC: 6
    2. (i) Factors of 12: 1, 2, 3, 4, 6 and 12 Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30 Factors of 42: 1, 2, 3, 6, 7, 14, 21 and 42
      (ii) Common factors: 1, 2, 3 and 6
      (iii) GFC: 6
    1. (i) Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40 Factors of 50: 1, 2, 5, 10, 25 and 50 Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
      (ii) Common factors: 1, 2, 5 and 10
      (iii) GFC: 10
    2. (i) Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30 Factors of 75: 1, 3, 5, 15, 25 and 75 Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90
      (ii) Common factors: 1, 3, 5 and 15
      (iii) GFC: 15
  1. 32 cm
  1. Feb 28th
  1. 9 m
  1. 6 minutes

Exercise 1.5

    1. 21
    2. 16
    1. 16
    2. 32
    1. 16
    2. 20
    1. 256
    2. 72
    1. 35
    2. 9
    1. 70
    2. 25
    1. 15
    2. 5
    1. 12
    2. 42
    1. 4
    2. 8
    1. 5
    2. 12
    1. 2
    2. 7
    1. 9
    2. 125
    1. 108
    2. 10
    1. 32
    2. 28
  1. 126
  1. 36
  1. 407
  1. 10
  1. 4
  1. 14
  1. 148
  1. 3
  1. 11

Review Exercises 1

    1. (i) 7,000 + 500 + 2   (ii) Seven thousand, five hundred two
    2. (i) 20,000 + 5,000 + 40 + 7   (ii) Twenty-five thousand, forty-seven
    3. (i) 600,000 + 20,000 + 20 + 5   (ii) Six hundred twenty thousand, twenty-five
    4. (i) 3,000,000 + 50,000 + 4,000 + 700 + 5   (ii) Three million, fifty-four thousand, seven hundred five
    1. (i) 5,607   (ii) 5,000 + 600 + 7
    2. (i) 37,040   (ii) 30,000 + 7,000 + 40
    3. (i) 408,105   (ii) 400,000 + 8,000 + 100 + 5
    4. (i) 1,070,055   (ii) 1,000,000 + 70,000 + 50 + 5
    1. 167 < 176
    2. 2,067 < 2,097
    3. 79,084 < 79,087
    4. 162,555 > 162,507
    1. (i) 3,900   (ii) 3,856
    2. (i) 5,900   (ii) 5,772
    3. (i) 7,100   (ii) 7,181
    4. (i) 3,600   (ii) 3,636
    1. 10,695
    2. 8,760
    3. 63
    4. 211
    1. 3.98
    2. 50
    1. 96.57
    2. 24
    1. –19
    2. 27
    1. 7,180.08
    2. 1,817.28
    1.  164,593.54
    2.  –17,668.97
    1. 0
    2. –7
    1. 60
    2. 144
    3. 1,584
    1. 4
    2. 6
    3. 2
    1. 11
    2. 14
    1. 13
    2. 7
    1. 89
    2. 4
    1. 27
    2. 27
    1. 3
    2. 10
    1. 9
    2. 25
    1. 130
    2. 14
  1. 873 stamps
  1. 850 tickets
  1. $52,725
  1. Babar: $875, Allan: $1,675
  1. 16 boxes
  1. 12 metres
  1. 42 days

Self-Test Exercises 1

    1. (i) 6900 (ii) 6,864
    2. (i) 520,000 (ii) 445,900
    3. (i) 67 (ii) 60
    1. 34
    2. 3
    3. 3
    1. 56
    2. 36
    3. 2
    1. 7
    2. 168
    3. 40
    1. 2
    2. 20
    3. 9
  1. Hari: $1,275   Bob: $6,375
  2. 25,995 kg
  3. $940
  4. 320
  5. 1,008 sec or 16 min 48 sec
  6. 6 metres

Unless otherwise indicated, this chapter is an adaptation of the eTextbook Foundations of Mathematics (3rd ed.) by Thambyrajah Kugathasan, published by Vretta-Lyryx Inc., with permission. Adaptations include supplementing existing material and reordering chapters.

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