High School

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1. Write the number sentence and calculate the answers in Column A and Column B. Fill in <, =, or > in Column C.

| Column A | Column B | Column C |
|--------------|-------------|------------------------|
| a) 3x6 + 3x7 | 3(6 + 7) | 3x6 + 3x7 â–¡ 3(6 + 7) |
| b) 5x3x2 | 5(3 x 2) | 5x3x2 â–¡ 5(3 x 2) |
| c) 72 + 9 + 3| 72 + (9+3) | 72 ÷ 9 + 3 â–¡ 72 ÷ (9+3)|
| d) 2 + 7x5 | (2 + 7)x5 | 2 + 7x5 â–¡ (2 + 7)x5 |
| e) 32 - 8 + 4| (32 - 8) ÷ 4| 32 - 8 ÷ 4 â–¡ (32 - 8) ÷ 4|
| f) 5(10-1) | 5x10 + 5x1 | 5(10-1) â–¡ 5x10 + 5x1 |
| g) 9 + 6 - 5 + 9 | 9 + 9 + 6 - 5 | 9 + 6 - 5 + 9 â–¡ 9 + 9 + 6 - 5 |
| h) (7x5) + 5 | 7x(5 + 5) | (7x5) + 5 â–¡ 7x(5 ÷ 5) |

2. Does the second statement follow from the first statement in each of the following? Write 'yes' or 'no'.

a) If 77 - 62 = 15, then 15 + 62 = 77
b) If 39 + â–¡ = 100, then 100 + 39 = â–¡
c) If 39 + â–¡ = 100, then 100 - 39 = â–¡
d) If 49 x â–¡ = 490, then 490 ÷ 49 = â–¡
e) If â–¡ ÷ 40 = 30, then 40 x 30 = â–¡
f) If â–¡ ÷ 40 = 30, then 40 + 30 = â–¡

3. Find the missing value in each of the following number sentences:

a) â–¡ - 26 = 42
b) â–¡ x 9 = 99
c) â–¡ ÷ 50 = 9
d) 84 ÷ â–¡ = 21
e) 75 + â–¡ = 149
f) 8 x â–¡ = 320

Answer :

Let's solve each part of the question step-by-step:

  1. Column A and Column B Comparisons

    a) Expression:

    • [tex]3 \times 6 + 3 \times 7[/tex] in Column A = [tex]18 + 21 = 39[/tex]
    • [tex]3(6 + 7)[/tex] in Column B = [tex]3 \times 13 = 39[/tex]
    • Comparison: [tex]3 \times 6 + 3 \times 7 = 3(6 + 7)[/tex] so Column C is [tex]=[/tex].

    b) Expression:

    • [tex]5 \times 3 \times 2[/tex] in Column A = [tex]5 \times 6 = 30[/tex]
    • [tex]5(3 \times 2)[/tex] in Column B = [tex]5 \times 6 = 30[/tex]
    • Comparison: [tex]5 \times 3 \times 2 = 5(3 \times 2)[/tex] so Column C is [tex]=[/tex].

    c) Expression:

    • [tex]72 + 9 + 3[/tex] in Column A = [tex]84[/tex]
    • [tex]72 + (9 + 3)[/tex] in Column B = [tex]72 + 12 = 84[/tex]
    • Comparison: Both expressions equal [tex]84[/tex], hence Column C is [tex]=[/tex].

    d) Expression:

    • [tex]2 + 7 \times 5[/tex] in Column A = [tex]2 + 35 = 37[/tex]
    • [tex](2 + 7) \times 5[/tex] in Column B = [tex]9 \times 5 = 45[/tex]
    • Comparison: [tex]37 < 45[/tex], so Column C is [tex]<[/tex].

    e) Expression:

    • [tex]32 - 8 + 4[/tex] in Column A = [tex]24 + 4 = 28[/tex]
    • [tex](32 - 8) \div 4[/tex] in Column B = [tex]24 \div 4 = 6[/tex]
    • Comparison: [tex]28 > 6[/tex], so Column C is [tex]>[/tex].

    f) Expression:

    • [tex]5(10 - 1)[/tex] in Column A = [tex]5 \times 9 = 45[/tex]
    • [tex]5 \times 10 + 5 \times 1[/tex] in Column B = [tex]50 + 5 = 55[/tex]
    • Comparison: [tex]45 < 55[/tex], so Column C is [tex]<[/tex].

    g) Expression:

    • [tex]9 + 6 - 5 + 9[/tex] in Column A = [tex]19[/tex]
    • [tex]9 + 9 + 6 - 5[/tex] in Column B = [tex]19[/tex]
    • Comparison: Both expressions equal [tex]19[/tex], hence Column C is [tex]=[/tex].

    h) Expression:

    • [tex](7 \times 5) + 5[/tex] in Column A = [tex]35 + 5 = 40[/tex]
    • [tex]7 \times (5 + 5)[/tex] in Column B = [tex]7 \times 10 = 70[/tex]
    • Comparison: [tex]40 < 70[/tex], so Column C is [tex]<[/tex].

  2. Does the second statement follow from the first?

    a) If [tex]77 - 62 = 15[/tex], then [tex]15 + 62 = 77[/tex]: Yes

    b) If [tex]39 + x = 100[/tex], then [tex]100 + 39 = x[/tex]: No

    c) If [tex]39 + x = 100[/tex], then [tex]100 - 39 = x[/tex]: Yes

    d) If [tex]49 \times x = 490[/tex], then [tex]490 \div 49 = x[/tex]: Yes

    e) If [tex]x \div 40 = 30[/tex], then [tex]40 \times 30 = x[/tex]: Yes

    f) If [tex]x \div 40 = 30[/tex], then [tex]40 + 30 = x[/tex]: No

  3. Find the missing value in each number sentence:

    a) [tex]x - 26 = 42[/tex] implies [tex]x = 42 + 26 = 68[/tex]

    b) [tex]x \times 9 = 99[/tex] implies [tex]x = \frac{99}{9} = 11[/tex]

    c) [tex]x \div 50 = 9[/tex] implies [tex]x = 9 \times 50 = 450[/tex]

    d) [tex]84 \div x = 21[/tex] implies [tex]x = \frac{84}{21} = 4[/tex]

    e) [tex]75 + x = 149[/tex] implies [tex]x = 149 - 75 = 74[/tex]

    f) [tex]8 \times x = 320[/tex] implies [tex]x = \frac{320}{8} = 40[/tex]

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Rewritten by : Jeany

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