Equivalent Ratio Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step.

We are given a ratio (like “8 kg in 2 bags”) and asked to find:
1. The rate — which is how much per one unit (e.g., kg per bag).
2. The equivalent ratio in simplest form — divide both numbers by their greatest common factor.

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Problem 1: 8 kg in 2 bags (8 : 2)
- Rate = 8 ÷ 2 = 4 kg/bag
- Simplify 8:2 → divide both by 2 → 4:1

✔ Check: 4 kg per bag × 2 bags = 8 kg ✔️
✔ Ratio 4:1 means for every 4 kg, there’s 1 bag ✔️

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Problem 2: 12 rooms in 3 floors (12 : 3)
- Rate = 12 ÷ 3 = 4 rooms/floor
- Simplify 12:3 → divide both by 3 → 4:1

✔ Check: 4 rooms per floor × 3 floors = 12 rooms ✔️
✔ Ratio 4:1 means for every 4 rooms, there’s 1 floor ✔️

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Problem 3: 20 mangoes in 5 cartons (20 : 5)
- Rate = 20 ÷ 5 = 4 mangoes/carton
- Simplify 20:5 → divide both by 5 → 4:1

✔ Check: 4 mangoes per carton × 5 cartons = 20 mangoes ✔️
✔ Ratio 4:1 means for every 4 mangoes, there’s 1 carton ✔️

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Problem 4: 55 people in 11 groups (55 : 11)
- Rate = 55 ÷ 11 = 5 people/group
- Simplify 55:11 → divide both by 11 → 5:1

✔ Check: 5 people per group × 11 groups = 55 people ✔️
✔ Ratio 5:1 means for every 5 people, there’s 1 group ✔️

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Problem 5: 24 animals in 4 cages (24 : 4)
- Rate = 24 ÷ 4 = 6 animals/cage
- Simplify 24:4 → divide both by 4 → 6:1

✔ Check: 6 animals per cage × 4 cages = 24 animals ✔️
✔ Ratio 6:1 means for every 6 animals, there’s 1 cage ✔️

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Problem 6: 32 boys in 8 groups (32 : 8)
- Rate = 32 ÷ 8 = 4 boys/group
- Simplify 32:8 → divide both by 8 → 4:1

✔ Check: 4 boys per group × 8 groups = 32 boys ✔️
✔ Ratio 4:1 means for every 4 boys, there’s 1 group ✔️

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Problem 7: 8 legs in 4 animals (12 : 4) ← Wait! This says “8 legs” but writes “(12:4)” — that must be a typo.

Looking at the text: “8 legs in 4 animals (12 : 4)” — this doesn’t match. If it’s 8 legs in 4 animals, then the ratio should be 8:4, not 12:4.

But since the problem explicitly writes (12 : 4), we’ll go with that — maybe it’s meant to be 12 legs? Let’s assume it’s correct as written: 12 legs in 4 animals.

- Rate = 12 ÷ 4 = 3 legs/animal
- Simplify 12:4 → divide both by 4 → 3:1

✔ Check: 3 legs per animal × 4 animals = 12 legs ✔️
✔ Ratio 3:1 means for every 3 legs, there’s 1 animal ✔️

*(Note: Real animals have 4 legs, so this might be a trick or error — but mathematically, we follow what’s written.)*

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Problem 8: 55 candles in 5 packets (55 : 5)
- Rate = 55 ÷ 5 = 11 candles/packet
- Simplify 55:5 → divide both by 5 → 11:1

✔ Check: 11 candles per packet × 5 packets = 55 candles ✔️
✔ Ratio 11:1 means for every 11 candles, there’s 1 packet ✔️

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Problem 9: 16 people in 2 cars (16 : 2)
- Rate = 16 ÷ 2 = 8 people/car
- Simplify 16:2 → divide both by 2 → 8:1

✔ Check: 8 people per car × 2 cars = 16 people ✔️
✔ Ratio 8:1 means for every 8 people, there’s 1 car ✔️

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Final Answer:
1) Rate = 4 kg/bag, Equivalent Ratio = 4:1
2) Rate = 4 rooms/floor, Equivalent Ratio = 4:1
3) Rate = 4 mangoes/carton, Equivalent Ratio = 4:1
4) Rate = 5 people/group, Equivalent Ratio = 5:1
5) Rate = 6 animals/cage, Equivalent Ratio = 6:1
6) Rate = 4 boys/group, Equivalent Ratio = 4:1
7) Rate = 3 legs/animal, Equivalent Ratio = 3:1
8) Rate = 11 candles/packet, Equivalent Ratio = 11:1
9) Rate = 8 people/car, Equivalent Ratio = 8:1