Worksheet on simplifying ratios with various exercises including numerical and unit-based ratios, and real-world applications.

Let’s solve each problem step by step.

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1. Simplify these ratios:

We simplify by dividing both numbers by their greatest common factor (GCF).

a. 3:6 → GCF = 3 → 3÷3 : 6÷3 = 1:2
b. 2:10 → GCF = 2 → 2÷2 : 10÷2 = 1:5
c. 8:2 → GCF = 2 → 8÷2 : 2÷2 = 4:1
d. 15:3 → GCF = 3 → 15÷3 : 3÷3 = 5:1
e. 24:18 → GCF = 6 → 24÷6 : 18÷6 = 4:3
f. 9:12 → GCF = 3 → 9÷3 : 12÷3 = 3:4
g. 28:14 → GCF = 14 → 28÷14 : 14÷14 = 2:1
h. 9:21 → GCF = 3 → 9÷3 : 21÷3 = 3:7
i. 35:49 → GCF = 7 → 35÷7 : 49÷7 = 5:7
j. 120:140 → GCF = 20 → 120÷20 : 140÷20 = 6:7
k. 16:24 → GCF = 8 → 16÷8 : 24÷8 = 2:3
l. 60:32 → GCF = 4 → 60÷4 : 32÷4 = 15:8

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2. Simplify these three-part ratios:

Divide all parts by the GCF of all three numbers.

a. 4:8:2 → GCF = 2 → 4÷2 : 8÷2 : 2÷2 = 2:4:1
b. 25:15:10 → GCF = 5 → 25÷5 : 15÷5 : 10÷5 = 5:3:2
c. 24:30:18 → GCF = 6 → 24÷6 : 30÷6 : 18÷6 = 4:5:3
d. 8:12:20 → GCF = 4 → 8÷4 : 12÷4 : 20÷4 = 2:3:5
e. 45:30:75 → GCF = 15 → 45÷15 : 30÷15 : 75÷15 = 3:2:5
f. 120:80:72 → Let’s find GCF.
Factors of 120: 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Factors of 80: 1,2,4,5,8,10,16,20,40,80
Factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72
Common factors: 1,2,4,8 → GCF = 8
120÷8=15, 80÷8=10, 72÷8=9 → 15:10:9

Wait — let me double-check that last one. Is there a bigger common factor? 15,10,9 have no common factor except 1. So yes, 15:10:9 is correct.

But wait — maybe I made a mistake. Let me check again:

Original: 120:80:72

Divide by 4 first: 30:20:18
Then divide by 2: 15:10:9 → same result. Correct.

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3. Simplify ratios with units — convert to same unit first!

a. 2kg : 500g → Convert kg to g: 2kg = 2000g → 2000:500 → GCF=500 → 2000÷500 : 500÷500 = 4:1

b. 200cm : 3m → Convert m to cm: 3m = 300cm → 200:300 → GCF=100 → 2:3

c. £3.50 : 50p → Convert £ to p: £3.50 = 350p → 350:50 → GCF=50 → 7:1

d. 1 minute : 20 seconds → 1 min = 60 sec → 60:20 → GCF=20 → 3:1

e. 1.6kg : 600g → 1.6kg = 1600g → 1600:600 → GCF=200 → 1600÷200=8, 600÷200=3 → 8:3

f. 1m : 25mm → 1m = 1000mm → 1000:25 → GCF=25 → 1000÷25=40, 25÷25=1 → 40:1

g. 2 minutes : 1 hour → 1 hour = 60 min → 2:60 → GCF=2 → 1:30

h. £4.20 : 60p → £4.20 = 420p → 420:60 → GCF=60 → 420÷60=7, 60÷60=1 → 7:1

i. 4 weeks : 6 days → 4 weeks = 28 days → 28:6 → GCF=2 → 14:3

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4. Write in form 1:n → divide both sides by first number

a. 2:100 → divide by 2 → 1:50
b. 3:12 → divide by 3 → 1:4
c. 2:9 → divide by 2 → 1:4.5
d. 5:21 → divide by 5 → 1:4.2
e. 12:8 → divide by 12 → 1:(8/12) = 1:(2/3) → but better as decimal or fraction? Usually we write as simplified fraction or decimal. Since it says “form 1:n”, n can be fraction. But often they want decimal. Let’s do exact: 8÷12 = 2/3 → so 1 : 2/3 OR if decimal: 1 : 0.666... but probably keep as fraction. Wait — actually, sometimes they expect you to flip if needed? No — instruction is “write in form 1:n”, meaning first term becomes 1.

So for e. 12:8 → divide both by 12 → 1 : 8/12 = 1 : 2/3 → but maybe they want it as mixed number? Or perhaps reduce ratio first? Actually, 12:8 simplifies to 3:2, then 3:2 → 1 : 2/3. Same thing.

Alternatively, some might say 12:8 = 3:2, and to make first term 1, divide by 3 → 1 : 2/3. So answer is 1 : 2/3

But let’s see others:

f. 4:26 → divide by 4 → 1 : 26/4 = 1 : 13/2 = 1 : 6.5
g. 50:60 → divide by 50 → 1 : 60/50 = 1 : 6/5 = 1 : 1.2
h. 21:28 → divide by 21 → 1 : 28/21 = 1 : 4/3 ≈ 1 : 1.333...

i. 500g : 3kg → convert to same unit: 3kg = 3000g → 500:3000 → divide by 500 → 1:6
j. 5 hours : 1 day → 1 day = 24 hours → 5:24 → divide by 5 → 1 : 24/5 = 1 : 4.8
k. 64p : £1 → £1 = 100p → 64:100 → divide by 64 → 1 : 100/64 = 1 : 25/16 = 1 : 1.5625
l. 24km : 480m → convert to same unit: 24km = 24,000m → 24000:480 → divide by 24000 → 1 : 480/24000 = 1 : 1/50 = 1 : 0.02

Wait — that seems odd. Maybe better to simplify ratio first: 24000:480 → divide both by 480 → 50:1 → then to get 1:n, divide by 50 → 1 : 1/50 → which is 1:0.02. Yes.

But perhaps they expect us to write as 1 : 0.02 or 1 : 1/50. Either is fine, but since others are decimals, maybe use decimal.

Actually, let's recalculate l: 24km : 480m → 24,000m : 480m → divide both by 480 → 50:1 → so to write as 1:n, it’s 1 : 1/50 → which is 0.02. So 1:0.02

But maybe they want integer? No, the form is 1:n, n can be decimal.

Alternatively, perhaps I should have converted differently? No, this is correct.

Let me list them clearly:

a. 2:100 → 1:50
b. 3:12 → 1:4
c. 2:9 → 1:4.5
d. 5:21 → 1:4.2
e. 12:8 → simplify to 3:2 → then 1 : 2/3 → or 1:0.666... but let's write as fraction: 1 : \frac{2}{3} — but since others are decimal, perhaps 1:0.67? But better exact. Actually, in math problems like this, they often accept fractions. But looking at context, probably decimal is fine. However, for accuracy, I'll use fractions where needed.

To avoid confusion, let's do exact values:

e. 12:8 = 3:2 → 1 : 2/3
f. 4:26 = 2:13 → 1 : 13/2 = 1:6.5
g. 50:60 = 5:6 → 1 : 6/5 = 1:1.2
h. 21:28 = 3:4 → 1 : 4/3 ≈ 1:1.333...
i. 500g:3kg = 500:3000 = 1:6 → 1:6
j. 5h:24h → 5:24 → 1 : 24/5 = 1:4.8
k. 64p:100p = 64:100 = 16:25 → 1 : 25/16 = 1:1.5625
l. 24km:480m = 24000:480 = 50:1 → 1 : 1/50 = 1:0.02

I think for consistency, we can write decimals where possible, but for e, h, k, l, fractions might be better. But since the question doesn't specify, I'll use decimals rounded reasonably, but actually in math, exact is better.

Perhaps the expected way is to divide and leave as fraction or decimal. Let me check standard practice.

In many textbooks, for "1:n" form, they allow n to be fraction or decimal. For example, 2:9 becomes 1:4.5, which is acceptable.

So I'll go with:

a. 1:50
b. 1:4
c. 1:4.5
d. 1:4.2
e. 1:0.666... but better 1:\frac{2}{3} — but to match format, perhaps calculate decimal: 8÷12=0.666..., so 1:0.67? No, let's keep exact.

Actually, for e: 12:8, divide both by 12: 1 : 8/12 = 1 : 2/3. So I'll write 1 : \frac{2}{3} but since this is text, perhaps "1:2/3".

Similarly, f: 4:26 = 1 : 26/4 = 1 : 13/2 = 1:6.5
g: 50:60 = 1 : 60/50 = 1 : 6/5 = 1:1.2
h: 21:28 = 1 : 28/21 = 1 : 4/3 ≈ 1:1.333, but exactly 1:4/3
i: 1:6
j: 1:4.8
k: 1:1.5625 or 1:25/16
l: 1:0.02 or 1:1/50

This is messy. Perhaps the intention is to simplify the ratio first, then express as 1:n.

For example, e. 12:8 simplify to 3:2, then 3:2 = 1 : 2/3. Same thing.

I think for the purpose of this exercise, we can write the decimal equivalent where it terminates, otherwise fraction.

But to save time, I'll provide the answers as commonly expected:

a. 1:50
b. 1:4
c. 1:4.5
d. 1:4.2
e. 1:0.67 (but better 2/3) — let's use 1:\frac{2}{3} but since it's text, I'll write "1:2/3"
f. 1:6.5
g. 1:1.2
h. 1:1.333... or 1:4/3 — I'll use 1:4/3
i. 1:6
j. 1:4.8
k. 1:1.5625 or 1:25/16 — use 1:25/16
l. 1:0.02

This is not ideal. Perhaps I made a mistake in interpretation.

Another way: for "1:n", they might mean to make the first number 1 by dividing, and n can be any number.

So for e. 12:8, divide both by 12: 1 : 8/12 = 1 : 2/3. So answer is 1:2/3.

Similarly, for l. 24km:480m = 24000:480 = 50:1, so to make first 1, divide by 50: 1 : 1/50.

So I'll go with that.

But for the final answer, I'll list them as:

a. 1:50
b. 1:4
c. 1:4.5
d. 1:4.2
e. 1:2/3
f. 1:6.5
g. 1:1.2
h. 1:4/3
i. 1:6
j. 1:4.8
k. 1:25/16
l. 1:1/50

Or to make it cleaner, convert to decimals where possible:

e. 1:0.666... but usually written as fraction.

Perhaps the problem expects us to simplify the ratio first, then write as 1:n.

For example, e. 12:8 = 3:2, then 3:2 = 1 : 2/3. Same.

I think it's fine.

Let's move on and come back.

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5. Cake recipe: 200g butter and 4 eggs. How much butter per egg?

Butter per egg = total butter / number of eggs = 200g / 4 = 50g per egg

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6. Which paint is reddest?

Midnight purple: 3 tins red : 2 tins blue → ratio red:blue = 3:2
Aubergine purple: 8 tins red : 5 tins blue → ratio red:blue = 8:5

To compare which is redder, we need to see which has more red per tin of blue, or per total paint.

The hint says: write each ratio in the form 1:n — but 1:n for what? Probably for red:blue, make red=1.

So for Midnight: 3:2 → divide by 3 → 1 : 2/3 ≈ 1:0.666...
For Aubergine: 8:5 → divide by 8 → 1 : 5/8 = 1:0.625

Now, the smaller the n, the redder the paint, because less blue per red.

Here, 0.625 < 0.666..., so Aubergine has less blue per red, so it is redder.

We can also think in terms of red proportion.

Midnight: red/(red+blue) = 3/(3+2) = 3/5 = 0.6
Aubergine: 8/(8+5) = 8/13 ≈ 0.615

8/13 ≈ 0.615 > 0.6, so Aubergine has higher proportion of red, so redder.

Yes.

So Aubergine purple is redder.

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Now, let's compile all answers.

For section 4, to make it neat, I'll write the answers as:

a. 1:50
b. 1:4
c. 1:4.5
d. 1:4.2
e. 1:\frac{2}{3} or 1:0.666... but since it's homework, perhaps they expect decimal. Let's calculate numerically.

In many cases, they might expect:

e. 12:8 = 3:2, and 3:2 = 1.5:1, but the form is 1:n, so n=2/3.

I think it's best to provide the exact value.

For the final answer, I'll list them as requested.

Also, for 2f, I had 15:10:9, but let me confirm GCF of 120,80,72.

GCF of 120 and 80 is 40, GCF of 40 and 72 is 8, yes. 120÷8=15, 80÷8=10, 72÷8=9, and 15,10,9 have no common factor, so 15:10:9 is simplest.

Some might argue to divide by 2 first, but 15:10:9 is correct.

Now, for the final answer section, I need to box all answers.

Since there are many parts, I'll list them clearly.

Final Answer:

1. a. 1:2 b. 1:5 c. 4:1 d. 5:1 e. 4:3 f. 3:4 g. 2:1 h. 3:7 i. 5:7 j. 6:7 k. 2:3 l. 15:8

2. a. 2:4:1 b. 5:3:2 c. 4:5:3 d. 2:3:5 e. 3:2:5 f. 15:10:9

3. a. 4:1 b. 2:3 c. 7:1 d. 3:1 e. 8:3 f. 40:1 g. 1:30 h. 7:1 i. 14:3

4. a. 1:50 b. 1:4 c. 1:4.5 d. 1:4.2 e. 1:\frac{2}{3} f. 1:6.5 g. 1:1.2 h. 1:\frac{4}{3} i. 1:6 j. 1:4.8 k. 1:\frac{25}{16} l. 1:0.02

But for e,h,k,l, to make it consistent, perhaps write as decimals:

e. 1:0.666... but usually 1:0.67 is approximation, but better exact.

Since the problem likely expects simplified forms, and for 1:n, n can be fraction, I'll keep as is.

For practical purposes, in the answer, I'll write:

4. a. 1:50 b. 1:4 c. 1:4.5 d. 1:4.2 e. 1:2/3 f. 1:6.5 g. 1:1.2 h. 1:4/3 i. 1:6 j. 1:4.8 k. 1:25/16 l. 1:1/50

But 1/50 is 0.02, so 1:0.02 is fine.

To avoid fractions, for e, 12:8 = 3:2, and 3:2 = 1.5:1, but the form is 1:n, so n=2/3.

I think it's acceptable.

5. 50g

6. Aubergine purple

Now for the boxed answer, since it's multiple parts, I'll list them.

Perhaps the user expects the answers in order.

Let me write the final answer as:

Final Answer:

1. a. 1:2 b. 1:5 c. 4:1 d. 5:1 e. 4:3 f. 3:4 g. 2:1 h. 3:7 i. 5:7 j. 6:7 k. 2:3 l. 15:8

2. a. 2:4:1 b. 5:3:2 c. 4:5:3 d. 2:3:5 e. 3:2:5 f. 15:10:9

3. a. 4:1 b. 2:3 c. 7:1 d. 3:1 e. 8:3 f. 40:1 g. 1:30 h. 7:1 i. 14:3

4. a. 1:50 b. 1:4 c. 1:4.5 d. 1:4.2 e. 1:\frac{2}{3} f. 1:6.5 g. 1:1.2 h. 1:\frac{4}{3} i. 1:6 j. 1:4.8 k. 1:\frac{25}{16} l. 1:0.02

5. 50g

6. Aubergine purple

For 4e, h, k, l, to make it uniform, perhaps calculate the decimal:

e. 2/3 ≈ 0.6667, so 1:0.6667 — but usually left as fraction.

I recall that in some curricula, they might expect to simplify the ratio first, then express as 1:n with n as decimal.

For example, e. 12:8 = 3:2, then 3:2 = 1 : 2/3, and 2/3 is approximately 0.67, but for accuracy, fraction is better.

Perhaps for this level, they want the division done.

Another thought: for "1:n", they might mean to make the first number 1, and n is the second number divided by the first, so for e. 8/12 = 2/3, so 1:2/3.

I think it's fine.

For the sake of completing, I'll use the following for 4:

a. 1:50
b. 1:4
c. 1:4.5
d. 1:4.2
e. 1:0.67 (rounded) — but let's not round; use exact.

Upon second thought, in the context, for c. 2:9 = 1:4.5, which is exact, similarly d. 5:21 = 1:4.2, exact.

For e. 12:8 = 1:0.666... which is repeating, so better as fraction.

But to match the format, perhaps the expected answer for e is 1:2/3, etc.

I think for the final answer, I'll write it as is.

So here is the complete final answer.

Note: For 4l, 1:0.02 is correct, as 480/24000 = 0.02.

Yes.

So:

Final Answer:

1. a. 1:2 b. 1:5 c. 4:1 d. 5:1 e. 4:3 f. 3:4 g. 2:1 h. 3:7 i. 5:7 j. 6:7 k. 2:3 l. 15:8

2. a. 2:4:1 b. 5:3:2 c. 4:5:3 d. 2:3:5 e. 3:2:5 f. 15:10:9

3. a. 4:1 b. 2:3 c. 7:1 d. 3:1 e. 8:3 f. 40:1 g. 1:30 h. 7:1 i. 14:3

4. a. 1:50 b. 1:4 c. 1:4.5 d. 1:4.2 e. 1:\frac{2}{3} f. 1:6.5 g. 1:1.2 h. 1:\frac{4}{3} i. 1:6 j. 1:4.8 k. 1:\frac{25}{16} l. 1:0.02

5. 50g

6. Aubergine purple

To make 4 look better, perhaps write the fractions as decimals where possible, but for e, h, k, l, it's fine.

For k. 64p:£1 = 64:100 = 16:25, so 1:25/16 = 1:1.5625, which is exact decimal.

Similarly, l. 1:0.02 is exact.

For e. 1:2/3 = 1:0.666... not terminating, so fraction is better.

But in the answer, I'll keep it as is.

Perhaps the problem has a typo or something, but I think it's correct.

So I'll go with that.

For the boxed answer, since it's long, I'll present it clearly.

In the response, I can write:

After careful calculation, the answers are:

[then list]

But for the Final Answer section, I need to put it there.

So: