Fractions
Calculators, worked examples and guides — from simplifying basic fractions through to multiplying and dividing mixed numbers.
Fraction Calculator
Add, subtract, multiply and divide fractions with full working.
Simplify Fractions
Reduce any fraction to its lowest terms instantly.
Fraction to Decimal
Convert any fraction to a decimal with step-by-step working.
Mixed Number Calculator
Work with mixed numbers — add, subtract and convert.
Learning about Fractions
The key idea: a fraction is just a division. ¾ means 3 ÷ 4. The numerator (top) is divided by the denominator (bottom). Once students see fractions as numbers — not just shaded shapes — every operation becomes logical.
Adding fractions
"¼ + ⅓ = ?"
Step 1: Find common denominator → 12
Step 2: ¼ = 3/12, ⅓ = 4/12
Step 3: 3/12 + 4/12 = 7/12
Shortcut: Always find LCD first
Multiplying fractions
"⅔ × ¾ = ?"
Step 1: Multiply numerators: 2 × 3 = 6
Step 2: Multiply denominators: 3 × 4 = 12
Step 3: 6/12 = ½
Shortcut: Simplify before multiplying — cancel diagonally if possible
Dividing fractions
"⅔ ÷ ¼ = ?"
Step 1: Flip the second fraction: ¼ → 4/1
Step 2: Multiply: ⅔ × 4/1 = 8/3
Step 3: 8/3 = 2⅔
Shortcut: 'Keep, Change, Flip'
Fractions Formula Sheet & Rules
Need a printable revision sheet? Access rules for adding, subtracting, multiplying, dividing, simplifying, mixed numbers, and conversions with step-by-step worked examples and custom print export.
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Algebra
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Geometry
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Factors & Multiples
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Trigonometry
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Fraction Questions Answered
What is a fraction?
A fraction represents part of a whole. The numerator (top number) shows how many parts you have; the denominator (bottom number) shows how many equal parts the whole is divided into. So ¾ means 3 out of 4 equal parts.
How do I add fractions with different denominators?
Find the lowest common denominator, convert both fractions so they share it, then add the numerators. For example: ½ + ⅓ — the LCD is 6, so 3/6 + 2/6 = 5/6.
How do I divide fractions?
Flip the second fraction (find its reciprocal) then multiply. So ¾ ÷ ½ becomes ¾ × 2/1 = 6/4 = 1½.
What is an improper fraction?
An improper fraction has a numerator larger than its denominator, like 7/4. It represents a value greater than 1 and can be written as a mixed number: 1¾.
What is the difference between a fraction and a ratio?
A fraction shows one part relative to the whole (¾ means 3 of 4 equal parts). A ratio compares two or more quantities to each other — 3:1 means for every 3 of the first there is 1 of the second.