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Introduction to fractions
A fraction shows a part of a whole that has been divided into equal parts. When you cut a pizza into four equal slices and take one slice, you have one out of four parts. We write this as 1/4. The line between the numbers tells us that we are talking about parts of one thing. Fractions are useful when we cannot use whole numbers to show size or amount. Children see fractions in daily life: pieces of fruit, slices of cake, parts of a metre or groups of objects shared among friends.
We learn fractions best with pictures and objects. Draw a circle, split it into equal parts and colour some parts. Count how many parts are coloured and write that number on top. Count how many equal parts make the whole and write that number below. This gives a clear idea of what a fraction means. Practice with different shapes and different numbers of parts helps build a strong sense of fractions before moving to rules and symbols.
Understanding numerator and denominator
A fraction has two numbers separated by a line. The top number is called the numerator and the bottom number is the denominator. The denominator tells us how many equal parts make one whole. For example, if a chocolate is cut into 8 equal pieces, the denominator is 8 because the whole chocolate becomes 8 equal parts. The numerator tells how many of those equal parts we are counting or using. If you eat 3 pieces out of those 8, the numerator is 3 and the fraction is 3/8.
It is important that the parts are equal in size. If parts are not equal, the fraction does not correctly show a part of the whole. You can practise by drawing shapes and dividing them carefully into equal parts. Always ask two questions: how many equal parts make the whole? (that is the denominator) and how many parts are shaded or taken? (that is the numerator). When the numerator is 0, the fraction is 0 because none of the parts are taken. If numerator equals denominator, the fraction equals 1, because all parts together make one whole. Using simple objects like apples, pencils or strips of paper helps children see these roles clearly.
Also teach words: 'numerator' is sometimes called the 'part' number and 'denominator' the 'whole division' number. Practice naming them from pictures and writing small sentences such as 'In 4/5, denominator 5 means 5 equal parts; numerator 4 means 4 of them are taken.' This habit helps pupils describe fractions in words as well as in symbols.
Types of fractions
Fractions are grouped by the size of numerator compared to denominator. A proper fraction has a numerator smaller than its denominator (for example 3/4). This means the fraction is less than one whole. An improper fraction has a numerator equal to or larger than the denominator (for example 5/4 or 4/4). An improper fraction can be more than or equal to one whole. A mixed number has a whole number and a proper fraction together, such as 1 1/4, and it represents one whole plus a part.
We can change an improper fraction into a mixed number by dividing the numerator by the denominator. The quotient is the whole number and the remainder becomes the new numerator. Practise this with small numbers so the idea becomes clear. Use drawings: show 5/3 as one whole (3/3) plus 2/3, so it becomes 1 2/3. Knowing these forms helps when adding, subtracting or understanding measurements in later classes.
Fractions that mean the same
Equivalent fractions are different written forms that represent the same part of a whole. For example, 1/2 and 2/4 look different but they show the same amount. To make an equivalent fraction, multiply or divide both numerator and denominator by the same whole number (not zero). This does not change the value, only the way it is written. Teaching equivalent fractions helps children see that one part can be split further yet still be the same total amount when combined.
Use many visual activities: colour a half of a sheet, then fold the half into two equal parts and show those two parts as quarters; this makes 1/2 = 2/4 clear. Try making groups with strips of paper: cut a strip into 3 parts and another into 6 parts; show that 1 of 3 parts equals 2 of 6 parts. Emphasise multiplication by small numbers like 2, 3 and 4 so pupils can make equivalents quickly. Also introduce the cross-check: two fractions a/b and c/d are equivalent if a×d = b×c. For Class 5, practise with many pairs so children recognise patterns and can convert to common denominators when needed.
Activities like matching cards, colouring equivalent regions, and writing equivalent lists (1/3 = 2/6 = 3/9) build confidence. Always connect visual work with the rule to strengthen both understanding and skill.
How to tell which fraction is larger
Comparing fractions means deciding which is greater, equal, or smaller. Begin with pictures: show two bars of the same length divided into different numbers of equal parts so students see sizes directly. If fractions have the same denominator (like 3/8 and 1/8), comparing is easy: the fraction with the larger numerator is larger because the parts are the same size. If fractions have the same numerator (like 3/4 and 3/8), the one with the smaller denominator is larger because the whole is split into fewer, bigger parts.
For different numerators and denominators, use equivalent fractions with a common denominator so both can be compared part by part. To find a common denominator, use small multiples of the denominators until a match appears. Another fast method is cross-multiplication: to see if a/b > c/d, compute a×d and c×b; whichever product is larger tells which fraction is larger. Always pair these rules with drawings so children understand why they work, not just that they work.
Practice with examples and real-life choices: which slice of pizza is bigger? Which recipe portion is larger? Encourage students to justify answers with a sentence, for example: '3/5 is larger than 2/5 because 3 parts of the same size are more than 2 parts.' This helps them explain and not just compute.
Working with same and different denominators
Fractions are easier to compare or combine when they have the same denominator. Fractions with the same denominator are called like fractions. For like fractions, you can compare or add them by looking at the numerators: more shaded parts means a larger fraction. For example, 4/7 is bigger than 2/7 because both are parts of sevenths and 4 parts are more than 2 parts.
Fractions with different denominators are called unlike fractions. To work with unlike fractions, change them into like fractions by making their denominators the same. Find a common denominator, usually the lowest common denominator (LCD), by looking for the smallest number that both denominators divide into. For Class 5, practice with small denominators such as 2, 3, 4 and 5. Once you have the LCD, convert each fraction to an equivalent fraction with that denominator by multiplying numerator and denominator by the same number.
Use drawing to show why this works: redraw both fractions using bars split into the LCD number of parts so they match visually. For example, to compare 1/2 and 1/3, change to sixths: 1/2 = 3/6 and 1/3 = 2/6; now it is clear that 3/6 > 2/6. Practise converting and then comparing or adding because this skill is needed for later operations with fractions.
Making fractions simplest
A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. Writing fractions in simplest form makes them easier to compare and use later. For example, 4/6 can be written more simply as 2/3 because both 4 and 6 are divisible by 2. Teach pupils to look for common small factors first, such as 2, 3 and 5, because many numbers used in Class 5 are small.
To simplify a fraction, find a common factor of numerator and denominator and divide both by it. Repeat this process until there is no common factor left. Another method is to use the greatest common divisor (GCD); divide numerator and denominator by the GCD to get the simplest form in one step. Encourage pupils to use times tables and factor lists to spot common factors quickly.
Use visual checks: if a picture of 8 shaded parts out of 12 can be regrouped into 4 shaded parts out of 6 or 2 out of 3, then 8/12 = 2/3. Practice many examples and ask students to say why the result is simpler, for instance: 'We reduced 6/9 to 2/3 because both numbers are divisible by 3; 2/3 has no common factor greater than 1.' This explanation habit builds number sense and prepares pupils for addition and subtraction of fractions in later classes.
Placing fractions on a number line
A number line helps us see the size of fractions and where they lie between whole numbers. To place a fraction like 3/4, draw a line and mark 0 and 1. Divide the segment between 0 and 1 into 4 equal parts because the denominator is 4. Then count three parts from 0 and mark that point; that is 3/4. To place fractions greater than 1, extend the line beyond 1 and keep dividing each unit into the same number of parts.
Use number lines to compare fractions quickly: the point that lies further to the right is larger. Number lines also help show mixed numbers as points beyond 1, for example 5/4 appears one quarter beyond 1. Encourage students to label the divisions and practise with several denominators to gain confidence. Always draw clearly and count divisions aloud when learning.
Fractions appear in many real-life situations. Recipes tell us to use parts of a cup, a quarter hour is 15 minutes, and measuring lengths may need halves or quarters of a metre. Use class activities: measure cloth in halves and quarters, time short activities and write the fractions of an hour, or share objects among students and mark the results on a number line. Linking number-line skills to everyday contexts helps children understand why fractions matter and how to use them practically.