Fraction definition
A fraction is a number that represents part of a whole or part of a set. It is usually written with one number above another, separated by a fraction bar. The top number is called the numerator, and the bottom number is called the denominator. For example, in the fraction 3 over 4, the numerator is 3 and the denominator is 4. This means 3 parts out of 4 equal parts.
The denominator tells you how many equal parts the whole has been split into. The numerator tells you how many of those parts are being considered. If a pizza is cut into 8 equal slices and you eat 3 slices, you have eaten 3 over 8 of the pizza. The equal parts are important. If the slices are not equal, the fraction does not describe the share accurately.
Fractions are used in many maths topics, including number, ratio, proportion, decimals, percentages, probability, algebra, geometry, measures and statistics. At GCSE level, students compare fractions, simplify fractions, convert between fractions and decimals, calculate with fractions and use fractions in worded problems. At A-Level, fractions still appear in algebraic manipulation, functions, calculus, statistics and mechanics.
Equivalent fractions have the same value even though they look different. For example, 1 over 2, 2 over 4 and 3 over 6 are equivalent because they all represent the same amount. You can create equivalent fractions by multiplying or dividing the numerator and denominator by the same number. This works because the value of the fraction has not changed, only the way it is written.
Simplifying a fraction means writing it in its lowest terms. For example, 12 over 18 can be simplified by dividing both numbers by 6 to get 2 over 3. Simplifying is useful because it makes the fraction easier to read and compare. A fraction is fully simplified when the numerator and denominator have no common factor other than 1.
Fractions can be proper, improper or mixed numbers. A proper fraction has a numerator smaller than the denominator, such as 3 over 5. An improper fraction has a numerator greater than or equal to the denominator, such as 7 over 4. A mixed number has a whole number and a fraction, such as 1 and 3 over 4. Students need to move between these forms when calculating and solving problems.
Fractions are strongly connected to decimals and percentages. The fraction 1 over 2 equals 0.5 and 50 percent. The fraction 1 over 4 equals 0.25 and 25 percent. These links help students choose the easiest form for a question. For example, a probability may be written as a fraction, while a discount may be easier to understand as a percentage.
Related ideas include numerator, denominator, equivalent fractions, simplifying, common denominators, mixed numbers, improper fractions, decimals, percentages, ratio and proportion. A clear definition of fraction helps students understand that a fraction is not just two numbers stacked together. It is a precise way of describing division, sharing and parts of a whole.