A ratio compares two or more quantities. In engineering you'll use ratios every single day — gear ratios, fuel-to-air mixtures, concrete mixes, scale drawings and stress calculations all rely on this skill.
T Level Core 4.1Comparing quantitiesSimplifying & scalingSharing amountsEngineering context
Key IdeaA ratio shows HOW MUCH of each part compared to the others
The ratio 3:2 means "for every 3 of the first thing, there are 2 of the second". Here it's shown as a bar split into 5 equal parts — 3 navy, 2 red:
💡 The ratio 3:2 is read "3 to 2". Total parts = 3+2 = 5. The colon ( : ) separates each quantity in the ratio.
Ratios vs FractionsHow they're related
A ratio compares parts to parts. A fraction compares a part to the whole.
Ratio 3:2 → 5 total parts
Navy as fraction = 3/5 of total
Red as fraction = 2/5 of total
📌 In engineering, ratios appear as 3:2 or 3/2 (gear ratio) or 1:50 (scale). All the same idea — comparison of quantities!
What you need to master
① Simplify a ratio to its lowest terms
② Write equivalent ratios (scaling up/down)
③ Share an amount in a given ratio
④ Use scale ratios (maps, drawings)
⑤ Solve unequal sharing problems
✅ The method is always the same — find the value of 1 part first, then multiply!
✂️Simplifyinglowest terms
🔁Equivalentscaling up/down
➗Sharingdivide amounts
📐Scale & Mapsdrawings
⚖️Unequalfind the ratio
⚙️Engineeringreal uses
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Simplifying Ratios
Like simplifying fractions — divide all parts by their HCF until no whole number (other than 1) divides into every part.
MethodDivide ALL parts of the ratio by their HCF
Visual12:8 simplified to 3:2 — the proportion stays exactly the same
Step-by-StepHow to simplify any ratio
Find the HCF of all parts in the ratio
Divide every part by the HCF
Check: can any whole number still divide all parts? If no → done ✅
⚠️ You must divide ALL parts — not just two of them in a 3-part ratio!
✅ Three-part ratio 6:9:12 → HCF=3 → 2:3:4
Watch OutRatios with different units
Before simplifying, always convert to the same unit!
❌ Wrong: 30 cm : 2 m → "simplify 30:2 = 15:1"
✅ Correct: convert first → 30 cm : 200 cm → HCF=10 → 3:20
📌 Common unit pitfalls: cm/m, mm/cm, g/kg, ml/litres, minutes/hours
Equivalent ratios represent the same proportion — just scaled up or down. Like equivalent fractions, you multiply or divide all parts by the same number.
RuleMultiply OR divide ALL parts by the same number → equivalent ratio
Visual Proof2:3, 4:6 and 6:9 are all the same proportion — just scaled
🔑 All three bars split at exactly the same point (x=336). The navy and purple sections stay the same proportion — that's what "equivalent ratio" means!
Scaling UPMultiply all parts by the same number
2:5 × 3 → 6:15
1:4 × 7 → 7:28
3:2:1 × 4 → 12:8:4
✅ Used in engineering to convert a simplified ratio into actual measurements. E.g. gear ratio 2:3, scaled to 20 teeth → 30 teeth.
Missing valueFind the unknown in an equivalent ratio
If 3:5 = 12:? → what multiplied 3 to get 12? → ×4 → so ? = 5×4 = 20
3:5 = 12:? → factor = 12÷3 = 4 → ? = 5×4 = 20
4:7 = ?:35 → factor = 35÷7 = 5 → ? = 4×5 = 20
✅ Always find the scale factor first: new ÷ known = factor. Then multiply the other side.
🔁 Try it — Equivalent Ratio BuilderScale up or find missing value
:
Find missing value: A:B = Known:?
:
=
: ?
👆Scale up 2:3 × 5 · find missing: 4:7 = 20:? · try 3:8 = ?→12 on A side
➗
Sharing an Amount in a Given Ratio
Split a total quantity into parts according to a ratio. Always use the "find 1 part" method — it works every time.
Method① Add ratio parts → total parts ② Total ÷ parts = 1 part ③ Multiply each
Visual MethodShare £350 in the ratio 3:4 — three clear steps
Example 1 — Share 420 kg in ratio 5:2
Total parts: 5 + 2 = 7
1 part: 420 ÷ 7 = 60 kg
Part A: 5 × 60 = 300 kg
Part B: 2 × 60 = 120 kg
Check: 300 + 120 = 420 kg ✅
⚙️ Engineering — Concrete mix 1:2:3 using 360 kg total
Ratio: cement : sand : aggregate = 1:2:3
Total parts: 1+2+3 = 6
1 part: 360 ÷ 6 = 60 kg
Cement: 1 × 60 = 60 kg
Sand: 2 × 60 = 120 kg
Aggregate:3 × 60 = 180 kg ✅
Example 3 — Three-way share: 540 in ratio 2:3:4
Total parts: 2+3+4 = 9
1 part: 540 ÷ 9 = 60
Part A: 2×60 = 120
Part B: 3×60 = 180
Part C:4×60 = 240 ✅ Check: 120+180+240=540 ✅
➗ Try it — Share in a RatioUp to 3-part ratio
:
: (opt)
👆Try: £240 in 1:3 · 360 kg in 1:2:3 (concrete) · 4800N in 5:3 (cables) — leave Part C blank for 2-part ratios.
📐
Scale Ratios & Maps
Scale ratios compare a drawing (or model) size to the real size. Used on every engineering blueprint and technical drawing.
How Scale Ratios WorkScale 1:50 means "1 unit on drawing = 50 units in reality"
Drawing → RealMultiply by the scale factor
Real = Drawing × scale factor
Scale 1:50. Drawing shows 8 cm. Find real length.
Real: 8 × 50 = 400 cm = 4 m ✅
Real → DrawingDivide by the scale factor
Drawing = Real ÷ scale factor
Scale 1:25. Real length = 3.5 m. Find drawing length.
Convert: 3.5 m = 350 cm
Drawing: 350 ÷ 25 = 14 cm ✅
📐 Try it — Scale ConverterDrawing ↔ Real
Enter ONE of these — the other is calculated:
↔
👆Scale 1:50: drawing 8 cm → real? · Scale 1:25: real 350 cm → drawing? · Scale 1:200: drawing 4.5 cm → real in metres?
📌 Common engineering scales: 1:1 (full size), 1:2 (half size), 1:5, 1:10, 1:20, 1:50, 1:100. Blueprints always state the scale in the title block.
⚖️
Unequal Sharing Problems
Harder ratio questions where you're given one share and need to find the total, the other shares, or the original ratio.
Type AGiven one person's share — find the rest
Tom and Sam share money in ratio 3:5. Tom gets £120. Find Sam's share and the total.
Tom has 3 parts = £120 → 1 part = £120 ÷ 3 = £40
Sam has 5 parts → 5 × £40 = £200
Total = 8 parts → 8 × £40 = £320
✅ Always find 1 part first, then multiply for each person.
Type BGiven the difference — find total and shares
Two forces are in ratio 2:7. The difference between them is 150N. Find each force.
Difference = 7−2 = 5 parts = 150N
1 part = 150 ÷ 5 = 30N
Small force = 2×30 = 60N
Large force = 7×30 = 210N
✅ Difference in parts = difference in value → find 1 part.
⚙️ Engineering — Gear teeth in ratio 3:8, smaller gear has 18 teeth. Find larger.
Ratio: 3:8, small gear = 3 parts = 18 teeth
1 part: 18 ÷ 3 = 6 teeth
Large gear: 8 × 6 = 48 teeth ✅
⚙️ Two cables carry loads in ratio 5:3. Together they support 4800N. Find each load.
Total parts: 5+3 = 8
1 part: 4800 ÷ 8 = 600N
Cable A: 5 × 600 = 3000N
Cable B:3 × 600 = 1800N ✅ Check: 3000+1800=4800 ✅
⚖️ Try it — Unequal SharingGiven one share or the difference
⚠️ Most common mistake: Students add the ratio numbers instead of using "1 part" method. In ratio 3:5, the bigger share is NOT simply the bigger number — it depends on the total value!
⚙️
Applications
Where this topic is used in engineering, manufacturing, maintenance and daily life.
Total parts = 3+4+7 = 14 1 part = 560÷14 = 40 kg A=3×40=120kg B=4×40=160kg C=7×40=280kg Answer: 120 kg : 160 kg : 280 kg ✅
Q8
A blueprint uses scale 1:25. A wall measures 7 cm on the drawing. What is the real length in metres?
[3]
Real = 7 × 25 = 175 cm = 1.75 m ✅
Q9
Ali and Ben share prize money in the ratio 5:3. Ali receives £650. How much does Ben receive? What is the total prize?
[3]
5 parts = £650 → 1 part = £130 Ben = 3×130 = £390 Total = 8×130 = £1040 ✅
Q10
Two forces are in ratio 3:7. They differ by 200N. Find both forces.
[4]
Difference in parts = 7−3 = 4 parts = 200N 1 part = 50N Small force = 3×50 = 150N Large force = 7×50 = 350N ✅
🔴 Tier 3 — T Level Challenge
Q11
A two-stroke engine requires fuel and oil in the ratio 40:1. A mechanic has 4.1 litres of mixed fuel. How many millilitres of oil does the mix contain?
[4]
Total parts = 40+1 = 41 1 part = 4100 ml ÷ 41 = 100 ml Oil = 1 × 100 = 100 ml ✅
Q12
A drive gear has 36 teeth and meshes with a gear of 54 teeth. Express the gear ratio in simplest form. If the drive gear rotates at 600 rpm, find the speed of the driven gear.
[4]
Gear ratio = 36:54 → HCF=18 → 2:3 Speed ratio is inverse of tooth ratio: 3:2 Driven gear speed = 600 × (36÷54) = 600 × 2/3 = 400 rpm ✅
Q13
A concrete mix uses cement : sand : gravel in ratio 1:3:5. How much sand is needed to mix with 4.5 kg of cement?
[3]
Cement = 1 part = 4.5 kg → 1 part = 4.5 kg Sand = 3 parts = 3 × 4.5 = 13.5 kg ✅
Q14
A scale drawing of a factory floor uses scale 1:200. On the drawing, a machine occupies a rectangle of 4.5 cm × 2.8 cm. Find the actual floor area of the machine in m².
[5]
Real length = 4.5 × 200 = 900 cm = 9 m Real width = 2.8 × 200 = 560 cm = 5.6 m Real area = 9 × 5.6 = 50.4 m² ✅
Q15
Three engineers share a project bonus in ratio 2:3:5. The engineer with the largest share receives £3,500 more than the one with the smallest share. Calculate the total bonus and each person's share.
[5]
Largest share = 5 parts, smallest = 2 parts Difference = 3 parts = £3,500 1 part = £3500 ÷ 3 = £1166.67 ≈ use exact: let 1 part = x 3x = 3500 → x = £1166.67
Total parts = 2+3+5 = 10 Total = 10x = 10 × 1166.67 = £11,666.67 Shares: A=2x=£2333.33 B=3x=£3500 C=5x=£5833.33 ✅