Fractions

A fraction shows a part of a whole. When we divide something equal into parts, each part is a fraction. For example, if a chocolate bar is cut into 4 equal pieces, one piece is called one quarter or 1/4. A fraction has two numbers separated by a line. The top number is the numerator and tells how many parts we have. The bottom number is the denominator and tells how many equal parts the whole is divided into. Fractions are used for sharing food, measuring lengths, and describing shapes. We can show fractions by shading parts of a shape, by splitting an object like an apple into pieces, or by using counters for parts of a set. It is important that the parts are equal — unequal parts do not give correct fractions. Children learn the language of fractions, such as half, third, quarter and whole. They also learn that a whole is 1, and fractions like 2/4 can be two of the four parts. Hands-on activities with paper folding, cutting, and colouring help make fractions clear and fun.

Unit fractions are fractions with numerator 1, such as 1/2, 1/3, 1/4. They tell us one equal part of a whole. Naming unit fractions helps build the idea of other fractions. The denominator gives the name: 1/2 is one half, 1/3 is one third, 1/4 is one quarter. When we write fractions, we must write the small line between the top and bottom numbers or use a slash like 1/2. We can show many unit fractions using folding paper: fold a sheet into two equal parts to show 1/2, into three equal parts to show 1/3. Using rulers, measure a 12 cm strip and mark equal parts to show 1/6 or 1/12. Unit fractions help when we add or compare fractions: for instance, two 1/4 pieces make 2/4. Children practise saying the name and matching shapes to the written fraction. Using everyday language — half, third, quarter — and matching these to pictures makes learning easier. Teachers can use story contexts: share one cake among two friends (each gets 1/2) or share sweets among three children (each gets 1/3).

The numerator and denominator are the two parts of a written fraction and both have clear jobs. The denominator is the bottom number and it tells how many equal parts make up the whole. For example, in 3/5 the denominator is 5, so the whole is split into five equal pieces. The numerator is the top number and it shows how many of those equal pieces we are counting. In 3/5 the numerator is 3, so three of the five equal parts are taken. When children see a picture, they should count the total parts first (the denominator) and then count the shaded parts (the numerator). If the numerator equals the denominator, such as 4/4, the fraction means one whole — all parts are taken. If the numerator is 0, as in 0/3, it means none of the parts are taken. If the numerator is smaller than the denominator, the fraction is less than one. Learning these meanings helps when comparing fractions, because with the same denominator the larger numerator makes a larger fraction. Teachers can use hands-on materials: draw shapes divided into parts, place stickers for the numerator, and label both numbers. Practice saying 'three fifths' for 3/5 or 'one quarter' for 1/4 encourages correct vocabulary and understanding.

Equivalent fractions are different fractions that mean the same amount. For class 3, we learn simple examples like 1/2 = 2/4 and 1/2 = 4/8 by drawing pictures. To find equivalents, split each part of a fraction into equal smaller parts. For example, take a half (1/2). If we cut each half into two equal pieces, each of the new pieces is 1/4. Two of these 1/4 pieces together make the same as 1/2, so 1/2 = 2/4. Using paper folding or colouring bars helps see equivalence clearly. Children also make fraction strips of the same length and mark halves, quarters and eighths to compare. Number sentences can show this relation, such as 1/2 = 2/4 = 4/8. We do not yet teach multiplication or division rules to make equivalents formally; instead, we use visual splitting and counting to show equality. Practise helps children recognise when two fractions are equal in size though they look different on paper.

When fractions have the same denominator, each part is the same size and so comparison becomes simple. The denominator tells us the size of each part, and because that size is equal for both fractions, we only need to look at the numerators. The fraction with the larger numerator has more of those equal parts and is therefore larger. For example, compare 3/8 and 5/8: both are eighths but 5/8 has five such parts while 3/8 has three, so 5/8 is greater. Use visual aids: draw two bars divided into the same number of parts and shade the required number in each; lining them up helps children see which shaded area is larger. Also teach use of the symbols <, > and = for comparison and read them aloud as 'less than', 'greater than' and 'equal to'. For ordering several fractions with the same denominator, arrange them by their numerators from smallest to largest. Real-life examples help: if one glass is 2/6 full and another is 4/6 full, the second glass has more liquid. Practice with counters, stickers and number lines where equal parts are marked will make comparing concrete and easy for learners.

Addition of fractions with the same denominator is simply joining the number of equal parts taken. Since the size of each part (given by the denominator) is the same, we add the numerators to find the total number of those parts. For example, if we add 1/6 and 2/6, we colour one sixth and two sixths; together they become three sixths, so 1/6 + 2/6 = 3/6. Teach children to write the number sentence as (1 + 2)/6 = 3/6 and then read it as 'three sixths'. Use fraction strips or shapes so pupils can lay pieces side by side and count how many parts are shaded in total. Sometimes the sum equals a whole: 3/4 + 1/4 = 4/4 = 1 whole. Show this with a circle or rectangle: shade three quarters and then one more quarter to fill the whole. Remind students that addition works only when parts are the same size—do not add 1/2 and 1/4 directly without changing to like parts. Encourage checking by counting shaded parts and relating the total to the whole. Use simple word problems like 'A shop sold 2/8 of its apples in the morning and 3/8 in the afternoon; how many eighths were sold altogether?'

Subtracting fractions with the same denominator means we remove a certain number of equal parts from another number of equal parts. Because the parts are of equal size, we subtract the numerators while keeping the denominator the same. For example, to do 5/7 − 2/7, picture seven equal parts and imagine five are shaded; now remove two shaded parts and three remain, so 5/7 − 2/7 = 3/7. Teachers should use drawing and physical objects like counters to show the action of taking away. Start with a shaded diagram and cross out the parts to be removed; then count the shaded parts left. If all parts are removed, the result is 0 (for example 3/3 − 3/3 = 0). Make pupils practise story problems: 'There were 6/8 of a ribbon left. If 2/8 is used, how much remains?' Show that 6/8 − 2/8 = 4/8. Emphasise that subtraction only works directly when the denominators are the same. Encourage checking by adding the subtracted part to the remainder to see if the original amount returns. Use clear language like 'take away' and 'left' and have pupils write the subtraction sentence as (a − c)/b.

Word problems help pupils use fractions in everyday situations and practise the steps of reading, drawing, calculating and writing answers. For class 3 we use problems with like denominators or simple unit fractions. Start by reading the problem slowly and deciding what is the whole and what parts are taken or shared. Draw a picture: a circle, bar or groups of objects split into equal parts and shade or mark the parts named. From the drawing, write the fraction for each quantity and then add or subtract numerators if needed. For example: 'Rani ate 1/4 of a cake and her brother ate 2/4. How much was eaten together?' Draw a cake in four parts, shade one and two parts, count shaded parts = 3, so 3/4 eaten. Use set models too: if Sam has 6 sweets and gives 1/3 to a friend, divide 6 into 3 equal groups and count one group to see how many sweets were given. Teach pupils to answer in a full sentence, such as 'Three quarters of the cake were eaten.' Also check answers by reversing steps or using simple addition. Practise with real objects like ribbon, fruit or paper strips makes these problems easy and meaningful.