Fractions

A fraction shows a part of a whole or a part of a group. We write a fraction with two numbers separated by a line. The top number is called the numerator and the bottom number is the denominator. The denominator tells how many equal parts the whole is divided into. The numerator tells how many of those parts we have.

Fractions can describe parts of shapes, like a circle cut into equal pieces, or parts of a set, like 2 sweets out of 8. We use pictures and real objects to make fractions easy to understand. When all parts are equal, the fraction shows a fair share. If the fraction is 1/2, the whole is cut into two equal parts and we have one of them. If it is 3/4, the whole is cut into four equal parts and three are taken.

Using simple drawings and sharing activities helps students see what fractions mean. This first topic builds the language and ideas you will use in every other lesson about fractions.

The denominator tells us into how many equal pieces the whole is divided. The numerator tells how many pieces we have. For example, in 2/5 the whole is divided into 5 equal parts and we have 2 of them. It is important that parts are equal; otherwise the fraction does not correctly show equal shares.

We read 2/5 as "two fifths". If the numerator is smaller than the denominator, the fraction is less than one. If the numerator equals the denominator, the fraction equals one whole. If the numerator is larger, we have more than one whole and can write a mixed number (for example 5/3 = 1 2/3). For Class 4 we focus on proper fractions (numerator smaller than denominator) and simple examples of equal numerator and denominator.

Using counters and dividing them into bowls, or cutting fruit into equal slices, helps check that the denominator and numerator are used correctly. This topic strengthens reading fractions and checking equal parts in diagrams and sets.

We can draw fractions in many ways. Common models are circles, rectangles (strips), and sets of objects. To show a fraction correctly, first divide the shape into equal parts. For a circle, draw equal wedges; for a rectangle, draw equal strips; for a set, group objects so each group has the same number. Always check that parts look equal by measuring or folding paper.

Hands-on activities make these ideas clear. Fold a paper plate into halves, quarters and eighths; fold a paper strip repeatedly to get equal parts; or cut playdough into equal pieces. Use beads or counters to make sets and place a selected number in one group to show the numerator. Ask pupils to trace or colour the parts they take so they connect the picture to the fraction symbol. For example, to show 3/8 on a circle, draw eight equal wedges and shade three. To show 2/5 of a set of 15 marbles, group the marbles into 5 equal groups of 3 marbles each and count two groups.

Also demonstrate different shapes representing the same fraction: shade 1/2 of a circle and 1/2 of a rectangle to show that fraction value does not depend on shape. Encourage students to explain why parts must be equal and to redraw a shape if parts look unequal. Working with several models strengthens understanding and helps move from concrete objects to symbolic fractions. Regular practice with drawing, folding and grouping builds the habit of checking equal parts before writing the fraction.

If two fractions have the same denominator, the fraction with the larger numerator is the larger fraction. This is because both fractions use the same size parts; more parts mean a larger amount. For example, 3/8 is larger than 2/8 because three eighths are more pieces than two eighths.

Start by using pictures. Draw two identical rectangles and divide each into the same number of equal parts as the denominator. Shade the number of parts given by the numerators and compare the shaded areas. Also let students use counters placed on equal boxes: if each box is one part, count shaded boxes. Number lines give another view: mark fractions with equal denominators as equal steps between 0 and 1. The one with the larger numerator will lie further to the right and be greater.

Give varied practice so pupils see the rule in action repeatedly: compare 1/5, 2/5, 3/5 and so on; order fractions like 2/9, 4/9, 7/9; find which is greatest or smallest. Discuss special cases: if numerators are equal the fractions are equal; if numerator equals denominator both are 1 whole. Teach children to use simple statements: "Both are in fifths; five pieces make a whole, so three pieces are more than two."

Use benchmarks to support understanding. Compare fractions to 1/2 and to 1: for denominators that are even, show visually where half lies and decide whether a fraction is less than or greater than half. For example, 3/8 is less than 4/8 which equals 1/2. For classroom activities, give cards with fractions having the same denominator and ask pupils to arrange them in order, or race to draw the larger fraction on a strip. Such hands-on comparisons develop quick number sense and make the rule reliable for Class 4 students.

When denominators are different, comparing fractions needs care because parts are not the same size. A clear way for Class 4 is to use pictures or make equal parts so both fractions use the same size pieces. For example, to compare 1/2 and 1/4, draw two equal rectangles: divide one into 2 parts and the other into 4 parts. Shade one part in each. The shaded area of 1/2 covers more of the whole than 1/4, so 1/2 is larger.

Another simple rule is for unit fractions (fractions with numerator 1): the smaller the denominator, the larger the fraction, because dividing the whole into fewer pieces gives bigger pieces. Thus 1/3 > 1/5. For fractions with different numerators, convert one or both to an equivalent fraction with a common denominator using small multipliers that students can manage, such as doubling or tripling. For example, to compare 3/8 and 1/4, convert 1/4 to 2/8 and then compare 3/8 and 2/8 visually or by counting parts.

Number lines help greatly: draw a single number line from 0 to 1 and mark both fractions; the one placed further to the right is larger. Teach pupils to try pictures first and then simple conversions to common parts for more practice. Emphasise checking with drawings so learners build confidence before learning formal methods later.

Equivalent fractions are different fractions that name the same part of a whole. For young learners, the easiest way to see this is with pictures. Take a rectangle and shade half of it; then redraw the same rectangle divided into four equal parts and shade two parts. The shaded area looks the same even though the fractions are 1/2 and 2/4. This shows they are equivalent.

To make equivalent fractions use multiplication or division of numerator and denominator by the same number. For example, multiply both top and bottom by 2: 1/3 becomes 2/6. Or divide both by a common factor to simplify: 4/8 divided by 4 gives 1/2. Teach pupils to look for small multipliers such as 2 or 3 so they can easily find equivalents. Making a table of a few equivalents for common fractions like 1/2, 1/3 and 1/4 helps memorise patterns: 1/2 = 2/4 = 3/6, 1/3 = 2/6 = 3/9, and so on.

Use hands-on activities: cut different shapes (circles, strips) into different numbers of equal parts and shade to show the same area. Encourage converting fractions to simplest form to check equivalence. Also connect equivalent fractions to adding and comparing fractions: to add 1/4 and 1/4 you get 2/4, which is equivalent to 1/2. Repeated practice with drawing, matching cards and small calculations will make the idea strong and clear for Class 4 students.

When two fractions have the same denominator, adding or subtracting is straightforward because the parts are the same size. You add (or subtract) only the numerators and keep the denominator unchanged. For example, 1/6 + 2/6 = (1 + 2)/6 = 3/6. This rule follows from counting parts: if each part is one sixth, one sixth plus two sixths equals three sixths.

Begin with concrete models. Use counters or shaded strips and combine the shaded pieces to show addition, or remove shaded pieces to show subtraction. Draw a rectangle divided into 8 equal parts, shade 3 parts for one fraction and 2 parts for another, then count shaded parts to get 5/8. After performing the operation, check whether the result can be simplified, for example 3/6 simplifies to 1/2. For subtraction, choose examples where the first numerator is larger than or equal to the second to avoid borrowing at this stage. If a question requires borrowing, use pictures to break a whole into equal parts and exchange one whole for the required number of parts so pupils can visualise the process.

Teach children to write the steps: (a/b) + (c/b) = (a+c)/b and (a/b) − (c/b) = (a−c)/b, and to always check with a drawing. Word problems such as sharing sweets, joining pieces of ribbon, or removing slices from a cake make the skill useful and interesting. Plenty of practice with different denominators kept the same helps students gain speed and accuracy.

Fractions often describe parts of a set: a number of items from a total number. For example, if 3 out of 12 students wear glasses, we write 3/12 of the class wears glasses. Begin by counting objects and then write the fraction selected over the total. Use counters, beads or pictures to represent items and group them to find the fraction easily.

Teach problem solving with steps: read the question, decide whether it asks for part of a shape or a part of a set, make a drawing or use objects, and then write the fraction. For sharing problems, connect fractions to division: if 8 apples are shared equally among 4 children, each child gets 8 ÷ 4 = 2 apples, so each child gets 1/4 of the apples because 2 out of 8 equals 2/8 = 1/4. Show how to simplify fractions in answers. Include problems about remaining parts: if 3/4 of a cake is eaten, how much remains? Use subtraction of fractions from 1: 1 − 3/4 = 1/4.

Use real-life contexts: sweets shared among friends, part of a school bag filled, or colours in a box of crayons. Encourage children to check answers by recounting or redrawing the grouping. Word problems with small numbers build confidence and help pupils apply fraction ideas beyond drawings into useful everyday tasks.