From gear ratios to mixing concrete — fractions are everywhere in engineering. Work through each section, see the visuals, try the practice questions.
T Level Core 4.1Friendly ExplanationsVisual Diagrams15 Practice Questions
6Topics
20+Examples
15Questions
⚙️Engineering
📌 T Level Link: Fractions appear in Core Element 4.1 — you'll use them in gear ratios, tolerances, material mixing, scale drawings and more. Click any topic below to start!
🍕What is a Fraction?Start here →
✂️SimplifyingHCF method
🔄TypesMixed & improper
➕Add & SubtractLCM method
✖️Multiply & DivideKCF method
⚙️Engineering UsesReal context
🍕
What is a Fraction?
A fraction represents a PART of a whole — how many equal pieces you have out of the total pieces.
NumeratorDenominatorEqual partsNumber line
The BasicsParts of a fraction
Top = NUMERATOR → how many parts you HAVE
Bottom = DENOMINATOR → total equal parts
💡 The fraction line means ÷ so 3/4 = 3 ÷ 4 = 0.75
VisualClick the cells to shade them
Click any cell to fill or empty it — the fraction updates live:
3/4
= 0.75
4
Click cells to fill ▐ or empty □ them. Drag the slider to change how many parts.
Number LineDrag the marker — where does your fraction land?
Drag the red dot along the number line. Change the denominator to see different fractions snap into place:
4
⚠️ Memory trick:Denominator = Down below. Both start with D — you'll never mix them up again!
🎛️Try it — Build Your Own FractionDrag the sliders
3/8 = 0.375
✂️
Simplifying Fractions
Simplifying means writing a fraction in its lowest form by dividing top and bottom by the same number.
HCF MethodEquivalent FractionsLowest Terms
Key IdeaEquivalent fractions look different but are equal
👆 Click the boxes to shade them, or change the denominator — watch the simplified version update live.
MethodHCF Method — step by step
Find the HCF (Highest Common Factor) of top and bottom
Divide BOTH numerator AND denominator by the HCF
Check — can it simplify again? If no, you're done!
📌 HCF = biggest number that divides evenly into BOTH numbers. HCF of 12 and 18: factors of 12 → 1,2,3,4,6,12 factors of 18 → 1,2,3,6,9,18 → HCF = 6
Watch out!Common mistakes
❌ Only dividing one side: 12/20 → 3/20 ✗ — you MUST divide both top and bottom!
❌ Stopping too soon: 12/20 ÷ 2 = 6/10 — but 6/10 simplifies further to 3/5!
✅ Quick trick: if both are even, keep halving until one is odd!
🧮Try it — Fraction SimplifierEnter any fraction
✏️Worked Example — Simplify 18/24
Step 1: Factors of 18: 1, 2, 3, 6, 9, 18
Step 2: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
HCF = 6 (biggest number in both lists)
Divide: 18 ÷ 6 = 3 24 ÷ 6 = 4
Answer: 18/24 = 3/4 ✅
⚙️Engineering Example — Gear ratio 36/48
Context: Input gear = 36 teeth, output gear = 48 teeth. What is the simplified gear ratio?
HCF: HCF(36, 48) = 12
Simplify: 36 ÷ 12 = 3 48 ÷ 12 = 4
Answer: Gear ratio = 3/4 ✅ — for every 4 turns of input, output turns 3 times
🔄
Types of Fractions
There are 3 types. You need to recognise each one and convert between them confidently.
ProperImproperMixed NumbersConverting
Type 1Proper Fraction
Top is smaller than bottom. Value is less than 1.
e.g. 1/2 3/5 7/8 2/9
Type 2Improper Fraction
Top is bigger than bottom. Value is greater than 1.
e.g. 5/3 7/4 11/5 9/2
Type 3Mixed Number
A whole number plus a proper fraction. Always greater than 1.
Drag the sliders to pick any two fractions with the same denominator:
5
✅ Same denominator → add the tops, keep the bottom. Simplify if needed.
Case 2Different denominators — find LCM
Find the LCM of both denominators
Convert each fraction to have that denominator
Add or subtract the numerators
Simplify if you can
📌 LCM(3,4): multiples of 3 = 3,6,9,12… multiples of 4 = 4,8,12… → LCM = 12
🧮Try it — Add & Subtract CalculatorEnter two fractions
✏️Worked Example — 1/3 + 1/4 (step through it)
Start:1/3 + 1/4 — different denominators, so find LCM first.
LCM(3,4):Multiples of 3: 3, 6, 9, 12… Multiples of 4: 4, 8, 12… → LCM = 12
Convert 1/3:Multiply top and bottom by 4 → 4/12
Convert 1/4:Multiply top and bottom by 3 → 3/12
Add:4/12 + 3/12 = 7/12 ✅
Step 1 of 5
✏️Worked Example — 5/6 − 2/9 (step through it)
Start:5/6 − 2/9 — different denominators, find LCM.
LCM(6,9):6, 12, 18… 9, 18… → LCM = 18
Convert 5/6:×3 top and bottom → 15/18
Convert 2/9:×2 top and bottom → 4/18
Subtract:15/18 − 4/18 = 11/18 ✅
Step 1 of 5
✖️
Multiplying & Dividing Fractions
Good news — multiplying is easier than adding! No common denominator needed at all.
Top × TopBottom × BottomKCFReciprocal
MultiplyStraight across!
Formula
a
b
← numerator
← denominator
×
c
d
=
(a×c)
(b×d)
← tops multiplied
← bottoms multiplied
Multiply the numerators (top × top)
Multiply the denominators (bottom × bottom)
Simplify the result
Pick any two fractions and watch the multiplication happen:
First
×
Second
=
Answer
815
DivideKeep · Change · Flip (KCF)
Dividing by a fraction = multiplying by its reciprocal (flipped fraction).
Keep the first fraction as is
Change ÷ to ×
Flip the second fraction upside down
Multiply and simplify
Formula
a
b
← numerator
← denominator
÷
c
d
=
a
b
KEEP as-is
×
CHANGE ÷→×
d
c
FLIP ↕ swap
⚠️ Only flip the SECOND fraction — d/c not a/b!
✏️ Try it — KCF Step by Step
Enter any two fractions — then step through Keep · Change · Flip
First fraction
÷
Second fraction
Press Next Step to begin →
Step 0 of 4
🧠 Why does KCF work? "How many halves fit into ¾?" — answer is 1½. Multiplying by the reciprocal gives the same result because dividing by a fraction and multiplying by its flip are mathematically identical operations.
🧮Try it — Multiply & Divide CalculatorEnter two fractions
⚙️
Fractions in Engineering
Where you'll actually use these skills — in your T Level exam and on the job.
Gear RatiosTolerancesMixingScale DrawingsCNC
⚙️ Gear Ratios
A gearbox has 24 teeth on the drive gear and 36 on the output. The ratio is 24/36 — simplify using HCF(24,36)=12 → ratio is 2/3. For every 3 turns of the drive gear, the output turns 2 times.
An alloy contains copper, zinc and tin in ratio 5:3:2. What fraction is zinc? If the batch is 4.8 kg, how much zinc is needed?
[4]
Total parts = 5+3+2 = 10 Fraction of zinc = 3/10 Zinc = 3/10 × 4.8 = 1.44 kg
Q12
A gear has 48 teeth meshing with a gear of 32 teeth. Simplify the gear ratio. If the smaller gear makes 15 revolutions, how many does the larger gear make?
[4]
Ratio 32/48 → HCF=16 → 2/3 Revs of larger = 15 × 2/3 = 10 revolutions
Q13
A component is 37½ mm long. How many fit in a 450 mm rail with no gaps?
