Year 7 Mathematics | Victorian Curriculum 2.0
Integers
Topic 01 | Number & Algebra | Answer key

This answer key follows the three sections of the practice: Year 7 core, Extension, and Challenge. Each answer gives the final result and a short method hint where the work is more than one step.

Year 7 core - answers

Fluency

Ordering and absolute value

    1. −10, −7, −2, 0, 3, 5-10,\ -7,\ -2,\ 0,\ 3,\ 5
    2. −9-9 (further left on the number line)
    3. 1313
    4. 55
    5. True
Fluency

Adding and subtracting

    1. −2-2 (start at −6-6, jump 44 right)
    2. −13-13 (same signs, add the sizes)
    3. −3-3 (different signs: 15−12=315 - 12 = 3, keep the sign of the larger size)
    4. 77
    5. −12-12
    6. 33 (minus a minus: −7+10-7 + 10)
    7. 1515 (minus a minus: 4+114 + 11)
    8. 00
    9. −7-7
    10. −4-4. Method: −2+(−6)=−8-2 + (-6) = -8; then −8−(−4)=−8+4=−4-8 - (-4) = -8 + 4 = -4.
Reasoning

Fill in the missing number

    1. 55. Method: □=−2−(−7)=5\square = -2 - (-7) = 5.
    2. −5-5. Method: □=−1−4=−5\square = -1 - 4 = -5.
    3. 77. Method: −5−□=−12-5 - \square = -12 gives □=−5−(−12)=7\square = -5 - (-12) = 7.
    4. 55. Method: □=8+(−3)=5\square = 8 + (-3) = 5.
Problem solving

Real-world problems

    1. 10 ∘10\,^\circC. Method: −8+6×3=−8+18-8 + 6 \times 3 = -8 + 18.
    2. −133-133 m (or 133133 m below sea level). Method: −120+35−48-120 + 35 - 48.
    3. $37. Method: −45+120−38-45 + 120 - 38.
    4. Floor 11. Method: −3+7−5+2-3 + 7 - 5 + 2.
    5. 10 ∘10\,^\circC rise. Method: 4−(−6)=4+64 - (-6) = 4 + 6.
    6. −15-15 m. Method: −24+9=−15-24 + 9 = -15.

Extension - answers

Fluency

Multiplying and dividing

    1. −42-42
    2. 4040 (negative times negative is positive)
    3. −36-36
    4. 7272 (two negatives cancel, then multiply)
    5. −8-8 (three negatives: odd)
    6. 2525 (two negatives: even)
    7. −4-4
    8. 44
    9. −9-9
    10. 44
Reasoning

Sign reasoning and missing values

    1. Negative. Reason: there are three negative factors, and three is an odd number, so the product must be negative.
    2. −7-7. Method: □=42÷(−6)=−7\square = 42 \div (-6) = -7.
    3. −6-6. Method: □=−48÷8=−6\square = -48 \div 8 = -6.
    4. 33. Method: (−4)×5=−20(-4) \times 5 = -20; the third number satisfies −20×□=−60-20 \times \square = -60, so □=3\square = 3.

Challenge - answers

Reasoning

Harder reasoning

    1. −7-7. Method: (−3)3=−27(-3)^3 = -27; (−2)2=4(-2)^2 = 4, so 5×4=205 \times 4 = 20; then −27+20=−7-27 + 20 = -7.
    2. >>. Reason: (−5)2=25(-5)^2 = 25 and −52=−25-5^2 = -25. Since 25>−2525 > -25, the left side is greater.
    3. Jamie is not correct. The correct answer is −9-9. The notation −32-3^2 means −(3×3)=−9-(3 \times 3) = -9 (the power applies only to the 33, with the minus sign in front). Jamie has read it as (−3)2=9(-3)^2 = 9, but without brackets the squaring does not include the negative sign.
    4. n=−2n = -2. Method: let the number be nn. Then (2n−7)×(−3)=33(2n - 7) \times (-3) = 33, so 2n−7=−112n - 7 = -11; 2n=−42n = -4; n=−2n = -2. Check: 2(−2)=−42(-2) = -4; minus 77 gives −11-11; times −3-3 gives 3333.
Year 7 Mathematics study companion | Answer key