Year 7 Mathematics | Victorian Curriculum 2.0
Ratios
Topic 03 | Number & Algebra | Answer key

Year 7 core - answers

Fluency

Simplify and find missing parts

    1. 2:32 : 3
    2. 5:25 : 2
    3. 2:3:52 : 3 : 5
    4. 1:41 : 4. Method: convert both to grams, 250:1000250 : 1000; divide by 250250.
    5. 3:83 : 8. Method: 45:12045 : 120; divide by 1515.
    6. 2020
    7. 1212
    8. 1212. Method: 2×6=122 \times 6 = 12, since 3×6=183 \times 6 = 18.
Fluency

Dividing a quantity in a ratio

    1. $15 : $25
    2. $16 : $56
    3. 8, 16, 248,\ 16,\ 24 sweets. Method: 1+2+3=61 + 2 + 3 = 6 parts; each part =8= 8.
    4. 140140 g. Method: flour is 55 parts, so 11 part =70= 70 g; sugar =2×70= 2 \times 70.
    5. 4040 and 5050. Method: 4+5=94 + 5 = 9 parts; each part =90÷9=10= 90 \div 9 = 10.
    6. 1818 boys, 1212 girls. Method: 3+2=53 + 2 = 5 parts; each =6= 6.

Explain and spot the mistake - answers

Reasoning

Explain and spot the mistake

    1. A ratio of 4:64 : 6 compares one group to the other, not to the whole. To find “what fraction of the total is boys” you need boys over total: 44+6=410=40%\dfrac{4}{4 + 6} = \dfrac{4}{10} = 40\%. Ben wrote 46≈66.67%\dfrac{4}{6} \approx 66.67\%, which is the ratio of boys to girls, not boys to total.
    2. In a 1:41 : 4 ratio the parts are 11 concentrate plus 44 water, giving 55 parts total. So concentrate is 15=20%\dfrac{1}{5} = 20\% of the drink, not 14=25%\dfrac{1}{4} = 25\%. Jen forgot to add the parts to find the total.
    3. Dividing both 66 and 99 by 33 gives 2:32 : 3, so the parts scale down by the same factor. For 2:52 : 5 the same multiplier would need to take 2→62 \to 6 and 5→95 \to 9, but 2×3=62 \times 3 = 6 while 5×3=15≠95 \times 3 = 15 \neq 9. The proportion doesn’t match, so 6:9≠2:56 : 9 \neq 2 : 5.
    4. 24:36=2:324 : 36 = 2 : 3. In plain words: for every 22 turns of the first gear, the second gear makes 33 turns (or equivalently, the first gear turns 1.51.5 times faster than the second).

Real-world problems - answers

Problem solving

Real-world problems

    1. Flour 750750 g, sugar 450450 g, eggs 1010. Method: scale factor =30÷12=2.5= 30 \div 12 = 2.5.
    2. 22 km. Method: 8×25 000=200 0008 \times 25\,000 = 200\,000 cm =2= 2 km.
    3. Anna $90, Ben $60. Method: ratio 180:120=3:2180 : 120 = 3 : 2; 55 parts = $150; each part = $30.
    4. Length 1515 m, width 99 m. Method: 5+3=85 + 3 = 8 parts; total length-plus-width (half of perimeter) =24= 24 m, so 11 part =3= 3 m.
    5. 120, 160, 200120,\ 160,\ 200. Method: 3+4+5=123 + 4 + 5 = 12 parts; each part =480÷12=40= 480 \div 12 = 40.
    6. 1.51.5 L red. Method: 7+3=107 + 3 = 10 parts; each part =0.5= 0.5 L; red =3= 3 parts.
Year 7 Mathematics study companion | Answer key