Top Tip: When multiplying, you can simplify before multiplying by cancelling common factors diagonally. This makes the maths easier!
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Last updated: February 2026 | UK national curriculum maths standards
Common Fractions Reference Chart
This reference chart shows the most commonly used fractions with their decimal and percentage equivalents. Useful for quick mental maths and checking your calculator results.
Fraction
Decimal
Percentage
Common Use
1/2
0.5
50%
Half price, half time
1/3
0.333...
33.33%
Splitting bills 3 ways
2/3
0.666...
66.67%
Two-thirds majority vote
1/4
0.25
25%
Quarter-hour, quarterly payment
3/4
0.75
75%
Three-quarters full
1/5
0.2
20%
VAT rate, one-fifth share
1/8
0.125
12.5%
Cooking measurements
1/10
0.1
10%
Tithe, tip calculation
3/8
0.375
37.5%
Imperial measurements
5/8
0.625
62.5%
Wrench sizes, bolts
7/8
0.875
87.5%
Nearly complete, close to full
1/16
0.0625
6.25%
Fine measurements, engineering
Fractions in UK Education: Key Stage Guide
Understanding fractions is a core part of the UK National Curriculum. Here is a breakdown of what students are expected to learn at each Key Stage:
Key Stage 1 (Ages 5-7, Years 1-2)
Children are introduced to basic fractions through practical activities. They learn to recognise 1/2, 1/4, 2/4 and 3/4 of shapes and quantities. At this stage, fractions are taught using physical objects like pizza slices, chocolate bars and building blocks.
Key Stage 2 (Ages 7-11, Years 3-6)
Students progress to comparing, ordering and adding fractions with the same denominator. By Year 5, they learn to add and subtract fractions with different denominators and multiply fractions by whole numbers. Year 6 covers dividing fractions and converting between fractions, decimals and percentages.
Key Stage 3 (Ages 11-14, Years 7-9)
Secondary school students work with algebraic fractions, complex calculations involving mixed numbers, and apply fractions to real-world problems including ratio, proportion and probability.
GCSE Mathematics (Ages 14-16)
GCSE maths requires confident manipulation of fractions in algebra, geometry and statistics. Students must be able to work with algebraic fractions, solve equations involving fractions, and apply fractional reasoning to problem-solving questions worth 3-5 marks.
Practical Uses of Fractions in Everyday UK Life
Cooking and baking ā UK recipes frequently use fractions: "add 3/4 cup of flour" or "cook for 1 1/2 hours." Converting between metric and imperial measurements often requires fraction knowledge.
DIY and home improvement ā Measuring timber, pipe fittings and hardware often involves fractions of an inch. A 3/8" drill bit or 5/16" bolt requires understanding fraction sizes.
Finance and budgeting ā Understanding that 1/3 of your income should go to housing (the 30% rule), or that you save 1/10 of each pay packet, makes fractions practically useful.
Time management ā We naturally use fractions for time: quarter past, half past, quarter to. A 45-minute meeting is 3/4 of an hour. Working out part-time hours often involves fractional calculations.
Shopping discounts ā "1/3 off" means multiply by 2/3. "Buy 2, get 1 free" is effectively 1/3 discount. Understanding these fractions helps you spot the best deals.
Step-by-Step Guide to Working with Fractions
Finding the Lowest Common Denominator
When adding or subtracting fractions with different denominators, you need to find the lowest common denominator. The lowest common denominator is the smallest number that both denominators divide into evenly. For example, when adding 2/3 and 1/4, the denominators are 3 and 4. The lowest common denominator is 12, because 12 is the smallest number divisible by both 3 and 4. You then convert each fraction: 2/3 becomes 8/12 (multiply top and bottom by 4) and 1/4 becomes 3/12 (multiply top and bottom by 3). Now you can add them: 8/12 plus 3/12 equals 11/12.
Converting Between Fractions, Decimals and Percentages
Converting between fractions, decimals and percentages is a fundamental mathematical skill tested in UK GCSE exams. To convert a fraction to a decimal, divide the numerator by the denominator. For instance, 3/8 equals 0.375 because 3 divided by 8 is 0.375. To convert a decimal to a percentage, multiply by 100, so 0.375 becomes 37.5 percent. To go from percentage back to a fraction, put the percentage over 100 and simplify: 37.5/100 simplifies to 3/8 by dividing both numerator and denominator by 12.5.
Working with Mixed Numbers in Real Situations
Mixed numbers appear frequently in everyday life. If a recipe calls for 2 and 3/4 cups of flour but you want to make 1 and 1/2 times the quantity, you need to multiply 2 3/4 by 1 1/2. First, convert both to improper fractions: 2 3/4 equals 11/4 and 1 1/2 equals 3/2. Then multiply: 11/4 times 3/2 equals 33/8. Convert back to a mixed number by dividing 33 by 8, which gives 4 remainder 1, so the answer is 4 and 1/8 cups of flour. This type of calculation is invaluable for UK home bakers adjusting recipes for different serving sizes.
Common Fraction Mistakes and How to Avoid Them
One of the most common errors students and adults make with fractions is adding the numerators and denominators separately. For example, incorrectly calculating 1/3 plus 1/4 as 2/7 by adding the tops and bottoms. The correct answer is 7/12, obtained by finding a common denominator first. Another frequent mistake is forgetting to simplify the final answer. Always check whether both the numerator and denominator share a common factor. For instance, 6/8 should be simplified to 3/4 by dividing both numbers by their greatest common divisor of 2.
When multiplying fractions, a common error is to find a common denominator first, which is unnecessary for multiplication. Simply multiply straight across: numerator times numerator, denominator times denominator. Cross-cancellation before multiplying can make the calculation simpler and the result easier to simplify. For example, when multiplying 4/9 by 3/8, you can cancel the 4 with the 8 (giving 1 and 2) and the 3 with the 9 (giving 1 and 3), resulting in 1/6 without needing further simplification.
Division of fractions causes particular confusion. The key rule to remember is "keep, change, flip": keep the first fraction as it is, change the division sign to multiplication, and flip the second fraction. So 2/5 divided by 3/7 becomes 2/5 multiplied by 7/3, which equals 14/15. Understanding why this works mathematically, dividing by a fraction is the same as multiplying by its reciprocal, helps students remember the procedure rather than simply memorising a rule without understanding.
Fractions in UK Measurements: Imperial and Metric
The United Kingdom uses a mixture of imperial and metric measurements, and fractions are deeply embedded in the imperial system. Height is commonly expressed as feet and inches, with fractions of an inch used for precise measurements. A person might be 5 feet 7 and 1/2 inches tall. In construction and woodworking, timber dimensions in the UK are still frequently described using fractions of an inch, such as 3/4 inch plywood or 5/8 inch dowel rod, even though metric equivalents are increasingly used.
Understanding fractions also helps when converting between imperial and metric units. One inch equals exactly 25.4 millimetres, but in practice, tradespeople often work with approximate fractional equivalents. For instance, 1/4 inch is approximately 6 millimetres, 1/2 inch is approximately 13 millimetres, and 1 inch is approximately 25 millimetres. These fractional approximations are used daily by plumbers, electricians and carpenters throughout the United Kingdom.
Frequently Asked Questions
How do you simplify fractions?
To simplify a fraction, divide both the numerator (top) and denominator (bottom) by their greatest common divisor (GCD). For example, to simplify 12/18: the GCD of 12 and 18 is 6, so 12Ć·6=2 and 18Ć·6=3, giving the simplified fraction 2/3.
How do you add fractions with different denominators?
First, find the lowest common denominator (LCD). For example, to add 1/3 + 1/4: the LCD is 12. Convert: 1/3 = 4/12 and 1/4 = 3/12. Then add: 4/12 + 3/12 = 7/12.
What is a mixed number and how do you convert it?
A mixed number combines a whole number with a fraction, like 2 3/4. To convert to an improper fraction: multiply the whole number by the denominator, add the numerator, and keep the same denominator. So 2 3/4 = (2Ć4+3)/4 = 11/4.
How do you multiply and divide fractions?
To multiply fractions, multiply the numerators together and the denominators together: 2/3 Ć 3/4 = 6/12 = 1/2. To divide fractions, flip the second fraction (find its reciprocal) and multiply: 2/3 Ć· 3/4 = 2/3 Ć 4/3 = 8/9.
What are equivalent fractions and why do they matter?
Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, 3/6 and 50/100 are all equivalent fractions. You create equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. This concept is essential when comparing fractions, adding fractions with different denominators, and simplifying fractions to their lowest terms. In practical terms, understanding equivalence helps you realise that a 25 percent discount is the same as getting 1/4 off the price.
How are fractions used in probability?
Probability is expressed as a fraction between 0 and 1, where 0 means an event is impossible and 1 means it is certain. For example, the probability of rolling a 6 on a fair die is 1/6, and the probability of drawing a heart from a standard deck of cards is 13/52, which simplifies to 1/4. Understanding fractions is therefore essential for anyone studying probability and statistics, both in school and in real-world applications such as assessing risk, understanding betting odds, or interpreting medical test results.
There are many excellent free online resources available for practising fraction calculations, suitable for students, parents helping with homework, and adults who want to refresh their mathematical skills. The BBC Bitesize website offers comprehensive fraction tutorials aligned with the UK National Curriculum for Key Stage 1 through GCSE level. The Corbett Maths website provides practice questions, video tutorials and worksheets specifically designed for the UK GCSE maths specification. The NRICH project from the University of Cambridge offers challenging fraction problems that encourage mathematical thinking beyond routine calculation.
For younger children, websites like Top Marks and Primary Games offer interactive fraction games that make learning engaging and enjoyable. These resources use visual representations such as fraction walls, pie charts and bar models to help children develop a concrete understanding of fractions before moving to abstract numerical manipulation. Parents and teachers can use our fractions calculator alongside these resources to verify answers and demonstrate the step-by-step working that examiners expect to see in GCSE and A-level mathematics papers.
