Fractions are parts of a whole. This guide explains the types of fractions and how to add, subtract, multiply, divide and simplify them, with worked examples you can check on the CalcSolver tools.
What is a fraction?
A fraction is a number that shows part of a whole, written as one number over another, such as 3/4. The top number is the numerator: it counts how many parts you have. The bottom number is the denominator: it shows how many equal parts the whole is divided into. In 3/4 you have 3 parts out of 4. Fractions are used in cooking, money, measurements and everyday maths.
Types of fractions
A proper fraction has a numerator smaller than the denominator, such as 3/4 or 2/5. An improper fraction has a numerator equal to or larger than the denominator, such as 7/4 or 5/5. A mixed number combines a whole number with a proper fraction, such as 1 3/4. To change 7/4 into a mixed number, divide 7 by 4: it goes once with 3 left over, so 7/4 = 1 3/4.
Adding and subtracting fractions
To add or subtract fractions, first make the denominators the same. Find the lowest common denominator, change each fraction to an equivalent fraction with that denominator, then add or subtract the numerators. For 3/8 + 5/12, the lowest common denominator is 24: 3/8 = 9/24 and 5/12 = 10/24, so the answer is 19/24.
Multiplying and dividing fractions
To multiply fractions, multiply the numerators together and the denominators together: 2/3 × 3/4 = 6/12 = 1/2. To divide fractions, flip the second fraction (take its reciprocal) and multiply: 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9. Always simplify the answer at the end.
Simplifying fractions
To simplify a fraction, divide the numerator and denominator by their greatest common factor. For 6/12 the greatest common factor is 6, so 6/12 = 1/2. Equivalent fractions have the same value: 1/2 = 2/4 = 3/6 = 4/8. A fraction is fully simplified when the numerator and denominator have no common factor except 1.
Fractions and decimals
To change a fraction to a decimal, divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. To change a decimal to a fraction, write it over a power of 10 and simplify: 0.75 = 75/100 = 3/4. To change a fraction to a percentage, multiply by 100: 3/4 = 75%.
Worked examples
Example 1: Work out 3/8 + 5/12
The lowest common denominator of 8 and 12 is 24. 3/8 = 9/24 and 5/12 = 10/24. Add the numerators: 9 + 10 = 19, so the answer is 19/24.
Example 2: Change 0.75 to a fraction
0.75 = 75/100. Divide the top and bottom by 25: 75 ÷ 25 = 3 and 100 ÷ 25 = 4, so 0.75 = 3/4.
Example 3: Work out 2/3 × 3/4
Multiply the numerators: 2 × 3 = 6. Multiply the denominators: 3 × 4 = 12. So 2/3 × 3/4 = 6/12 = 1/2.
Practice questions
- Work out 1/4 + 2/3.
- Work out 5/6 − 1/2.
- Work out 3/5 × 10/9.
- Work out 4/7 ÷ 2/3.
- Change 0.6 to a fraction in its simplest form.
Frequently Asked Questions
What is the difference between a proper and an improper fraction?
A proper fraction is less than 1, such as 3/4. An improper fraction is equal to or greater than 1, such as 7/4.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor. For example, 6/12 simplifies to 1/2 because both divide by 6.
How do I change a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
Try the tools: Fraction Calculator · Decimal to Fraction Calculator · Equivalent Fractions Calculator · Percentage Calculator