A fraction shows part of a whole.
The numerator (top) tells you how many parts you have.
The denominator (bottom) tells you how many equal parts the whole is split into.
The Golden Rules:
Simplifying fractions: Divide the top and bottom by their
Highest Common Factor (HCF). The fraction looks different but means exactly the same thing!
Equivalent fractions: Multiply or divide the top and bottom
by the same number. This is like multiplying by 1, so the value never changes.
Mixed numbers ↔ Improper fractions:
• Mixed → Improper: (whole × denominator) + numerator, keep the same denominator.
• Improper → Mixed: Divide top by bottom. The quotient is the whole number, the remainder is the new numerator.
Comparing fractions: Make the denominators the same (find a common multiple), then compare the numerators.
⭐ Key Vocabulary: numerator, denominator, equivalent, simplify, lowest terms, HCF (Highest Common Factor), improper fraction, mixed number, common denominator
📝 Worked Examples
Study all four types — they all appear in the practice!
Example 1: Simplifying a Fraction
Question: Simplify
1218
Find the 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.
Divide both top and bottom by 6: 12 ÷ 6 = 2, and 18 ÷ 6 = 3.
Answer:1218
=
23
(in its simplest form)
Example 2: Finding Equivalent Fractions
Question: Find a fraction equivalent to
34
with a denominator of 20.
What do you multiply 4 by to get 20? → 4 × 5 = 20.
Multiply the numerator by the same number: 3 × 5 = 15.
Answer:34
=
1520
Example 3: Mixed Number → Improper Fraction
Question: Convert 2¾ to an improper fraction.
Multiply the whole number by the denominator: 2 × 4 = 8.
Add the numerator: 8 + 3 = 11.
Keep the same denominator: 4.
Answer: 2¾ =
114
Example 4: Improper Fraction → Mixed Number
Question: Convert
175
to a mixed number.
Divide 17 by 5: 17 ÷ 5 = 3 remainder 2.
The whole number is 3, the remainder (2) becomes the new numerator, denominator stays 5.
Answer:175
= 3
25
🔧 The Fraction Simplifier
Type any fraction below and hit Simplify! to see it broken down step by step.
📊 Fraction Bar Visualizer
See how equivalent fractions look the same size even with different numbers!
Enter a fraction above and click Simplify to update the bars.
🧩 Drag 1: Simplify ⁴⁄₆
The HCF of 4 and 6 is 2. Divide both by 2. Drag the simplified fraction!
1
2
3
6
46=
💡 4 ÷ 2 = ? 6 ÷ 2 = ?
🧩 Drag 2: Simplify ¹⁰⁄₁₅
Find the HCF of 10 and 15, then divide both by it. Drag your answer!
2
3
5
10
1015=
💡 HCF of 10 and 15 = 5. 10 ÷ 5 = ? 15 ÷ 5 = ?
🧩 Drag 3: Equivalent Fractions
Make
14
equivalent with denominator 12. Drag the missing numbers!
3
4
8
12
14=
💡 4 × ? = 12 Then multiply the top by the same number.
🧩 Drag 4: Equivalent Fractions
Make
23
equivalent with denominator 15. Drag the missing numbers!
5
6
10
15
23=
💡 3 × ? = 15 Then multiply the top by the same number.
🧩 Drag 5: Mixed → Improper
Convert 1¾ to an improper fraction. Drag the correct numbers!
3
4
5
7
1¾ =
💡 (1 × 4) + 3 = ? Keep the denominator as 4.
🧩 Drag 6: Improper → Mixed Number
Convert
114
to a mixed number. Drag the correct numbers!
2
3
4
11
114=
💡 11 ÷ 4 = ? remainder ? The remainder becomes the new numerator.
📝 Practice Questions
Grab your pencil! Simplify all fraction answers fully.
Simplify 69
Simplify 812
Simplify 1520
Simplify 1421
Simplify 2436
Find an equivalent fraction: 13 = ?9
Find an equivalent fraction: 35 = ?20
Find an equivalent fraction: 27 = ?28
Convert to an improper fraction: 1½
Convert to an improper fraction: 2¼
Convert to an improper fraction: 3⅔
Convert to a mixed number: 94
Convert to a mixed number: 135
Convert to a mixed number: 226
Which is larger: 34 or 58? Show your working.
Which is larger: 23 or 35? Show your working.
Put in order (smallest first): 12, 38, 58
True or false: 45 = 1620
Simplify 3045
Write 74 as a mixed number, then convert it back to an improper fraction.
23 (÷3)
23 (÷4)
34 (÷5)
23 (÷7)
23 (÷12)
39
1220
828
32
94
113
214
235
346 = 323
34 = 68 > 58 — so ¾ is larger
23 = 1015 and 35 = 915 — so ⅔ is larger
38, 12, 58 (½ = 4/8)
True — 4×4=16 and 5×4=20 ✓
23 (÷15)
134 → back to 74
🔥 The Hard Challenge
Show all your working — these need careful thinking!
A pizza is cut into 12 equal slices. Sam eats 4 slices. Write the fraction eaten and simplify it fully.
Mia says that 34 and 916 are equivalent. Is she correct? Show your working.
Arrange these fractions in order from smallest to largest: 23, 34, 56, 712
A ribbon is 2436 metres long. Write this length in its simplest form.
Tom has completed 1520 of his homework. What fraction has he NOT completed yet? Give your answer in its simplest form.
A recipe uses 2¾ cups of flour. Write this as an improper fraction.
A running track is divided into sections. Jamie has run 176 laps. Write this as a mixed number.
Three friends each eat a different fraction of the same chocolate bar: Alex eats 13, Ben eats 39. Are they the same? Who ate more of the bar?
Which fraction is closest to 1: 78, 1112, or 910? Explain your reasoning.
A jug holds 315 litres. Write this as an improper fraction. Then simplify 4860 and explain what the two results have in common.