Primary 4 Maths Fractions – Jimmy Maths’ P4 Guide

Many students struggle in P4 Fractions due to a lack of understanding of the key concepts.

This revision guide is designed to provide a quick yet thorough review of key fraction concepts for Primary 4 students.

It covers essential topics such as identifying and representing fractions, working with number lines, simplifying and comparing fractions, and performing addition and subtraction. Practical applications like fractional measurements and finding a fraction of a set are also included to reinforce real-world understanding.

Below are the key concepts:

Content

Key Concept 1: Definition of a fraction
Key Concept 2: Fractions and number lines
Key Concept 3: Equivalent fractions
Key Concept 4: Expressing a fraction in its simplest form
Key Concept 5: Comparing and ordering of like and unlike fractions
Key Concept 6: Improper fractions and mixed number
Key Concept 7: Addition and subtraction of fractions
Key Concept 8: Fractional measurements
Key Concept 9: Fraction of a set
10 Tips and Common Errors

P4 Fractions Worksheet For Revision

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$secondary math revision notes$

Key Concept 1: Definition of a fraction

A fraction is a way of showing a part of a whole.

Imagine you have 1 whole pizza, and you cut it into 4 equal slices. Each slice is then 1/4 of a pizza.

$Definition of a fraction$

Example Question

Which of the following diagrams do not show a whole divided into equal parts?

$Definition of a fraction - Equal Parts$

Ans: (c) and (d)

Practice Question

Which of the following diagrams shows a whole divided into equal parts?

$Definition of a fraction - Equal Parts$

Ans: (c)

Key Concept 2: Fractions and number lines

The number of gaps between two consecutive numbers represents the denominator.

Study the number line below. What is the fraction indicated at X?

Fractions and number lines

There are 5 gaps. So 5 parts make a whole. We count 4 parts from 0 to X. So X represents 4/5.

Example Question

Study the number line below. What is the fraction indicated at X?

Fractions and number lines

Solution:

There are 9 gaps. So 9 parts make a whole. We count 5 parts to X. So X represents 5/9.

Key Concept 3: Equivalent fractions

Compare the shaded parts between the identical circles.

$Equivalent fractions$

See that the shaded parts for each circle are the same size. Hence we say that

1/2 = 2/4 = 3/6 = 4/8

Also 1/2 , 2/4 , 3/6 and 4/8 are equivalent fractions. Even though the numerators and denominators of the fractions are different, the fractions represent the same size.

Obtain equivalent fractions by cutting Into more parts

Recall: A whole can be cut or divided into equal parts in many ways, and the denominator of a fraction represents the total number of equal parts.

The diagram below shows 2/3 of a circle shaded.

$Equivalent fractions$

If each part is further cut into two, we have the following:

$Equivalent fractions$

Now, we have 4 shaded parts, and 6 parts make a whole. We say that 4/6 of the circle is shaded.

The above can be represented as

Note that the multiplication of 2 to the numerator and denominator means each part is cut into two.

If each part were cut into three instead, we would have the following:

$Equivalent fractions$

The above can be represented as

Obtain equivalent fractions by joining smaller parts

The diagram below shows a circle made up of 18 parts and 6 parts are shaded. So 6/18 of the circle is shaded.

$Equivalent fractions$

If we combine 2 parts together to make a larger part, we have the following:

$Equivalent fractions$

The above can be represented as

Note that the division of 2 for the numerator and denominator means two parts have been joined to form a larger part.

If three parts were joined instead, we would have the following:

$Equivalent fractions$

The above can be represented as

$Equivalent fractions$

Note that the division of 3 for the numerator and denominator means three parts have been joined to form a larger part.

In short, equivalent fractions can be obtained either by:

(i) cutting larger parts into smaller part: multiplying the numerator and denominator of the fraction by the same number, or

(ii) joining smaller parts into larger parts: dividing the numerator and denominator of the fraction by the same number.

Example Question 1

$Equivalent fractions$

What is the missing numerator in the box?

Solution:

Compare the denominators. See that 5 × 4 = 20.
So the numerator must be multiplied by 4 as well.

$Equivalent fractions$

The missing number in the box is 2 × 4 = 8 (Ans).

Example Question 2

Which of the following is an equivalent fraction of 6/8 ?

$Equivalent fractions question$

Solution:

$Equivalent fractions question$

Key Concept 4: Expressing a fraction in its simplest form

Recall that equivalent fractions can be obtained either by:

(i) cutting larger parts into smaller part, or

(ii) joining smaller parts into larger parts.

If we continue to join smaller parts to form a larger part until no more parts can be joined, we will obtain the simplest form of the fraction. For example,

$Expressing a fraction in its simplest form$

See that 1/3 is the simplest form.

The simplest form of a fraction need not have ‘1’ in the numerator. For example, the fraction 2/7 is the simplest form. It is not possible to combine two small parts into a larger part because one small part will be left over as shown below. Recall that a fraction must be made up of equal parts.

$Expressing a fraction in its simplest form$

Example Question

Express 9/12 as a fraction in its simplest form.

Solution:
The highest common factor of 9 and 12 is 3.

$Expressing a fraction in its simplest form$

Key Concept 5: Comparing and ordering of like and unlike fractions

When fractions are like, they have the same denominators. For example, 2/5 and 4/5 are like fractions. We can compare like fractions easily. Since 4/5 is made up of 4 parts while 2/5 is made up of 2 parts, we say 4/5 is greater than 2/5.

When fractions are unlike, they have different denominators. For example, 2/5 and 3/7 are unlike fractions. When fractions are in different denominators, it can be difficult to tell which is greater. This is because the parts in both fractions are expressed in different sizes.

$Comparing and ordering of like and unlike fractions$

Using the fraction bars above, we can see that 3/7 is greater than 2/5. But we do not always have the diagram above to refer to. Furthermore, the diagram is limited to denominators up to 12. This means, the diagram will not be useful when we need to compare fractions with denominators larger than 12. For instance, 5/14 and 6/17.

To compare fractions expressed in different denominators, we can use one or a combination of the following methods:

(1) Comparing fractions with 1/2

(2) Expressing fractions in the same denominator

(3) Expressing fractions in the same numerator

Method 1: Comparing Fractions with 1/2

Fractions that are greater than 1/2 must be greater than fractions which are less than 1/2. We use 1/2 as a comparison point because it is convenient and easy to work with.

For example, when comparing 7/10 and 5/12:

See that the denominator of 7/10 is 10. So 1/2 = 5/10.

Comparing 7/10 and 5/10, we know 7/10 is greater than 1/2.

See that the denominator of 5/12 is 12. So 1/2 = 6/12.

Comparing 5/12 and 6/12, we know 5/12 is less than 1/2.

Ordering the fractions from smallest to greatest, we have:

5/12 , 1/2 , 7/10

So 7/10 is greater than 5/12.

Method 2: Expressing fractions in the same denominator

Recall that fractions with the same denominators are like fractions. When comparing fractions that are like, the greater the numerator, the greater the fraction. For instance, 4/5 is greater than 2/5 .

For example, when asked to compare 7/10 and 3/5, observe that the previous Method 1 of comparing to 1/2 would not be useful since both fractions are greater than 1/2 (half of 10 is 5; and half of 5 is 2.5).

However when we express 3/5 = 6/10, we see that 7/10 and 6/10 are like fractions, and 7 is greater than 6.

So we know 7/10 is greater than 3/5.

Further example:

Arrange the following fractions from the smallest to the largest.

2/5 , 1/3 , 4/7

Solution:

Apply Method 1 first and we can quickly see that 4/7 is greater than 1/2, while 2/5 and 1/3 are smaller than 1/2. This means we only need to compare 2/5 and 1/3 since 4/7 is the greatest fraction.

The lowest common multiple of 5 and 3 is 15. Changing the fractions into common denominators, we have:

$Comparing and ordering of like and unlike fractions$

So our answer is 1/3 , 2/5 , 4/7 .

Method 3: Expressing fractions in the same numerator

Using the fraction bar diagram, we see that as the denominator of a fraction increases, its unit size becomes smaller.

$Comparing and ordering of like and unlike fractions$

And so, when two fractions have the same numerator, the fraction with the smaller denominator is the fraction that is greater. For example, compare 2/5 , 2/4 and 2/5. See that all the fractions have the same numerator, but 2/3 is the greatest fraction since it has the largest unit size.

We use Method 3 when expressing the fractions into the same common denominator is difficult and tedious.

Let’s use the previous question as an example and apply Method 3.

Arrange the following fractions from the smallest to the largest.

2/5 , 1/3 , 4/7

Note that to express all the fractions into the same common denominator, we have to use 105 as the common denominator since the lowest common multiple of 3, 5 and 7 is 105. Three fractions must be changed.

However if we apply Method 3, then we have to only change 2/5 and 1/3 since the lowest common multiple of 1, 2 and 4 is 4, which is the numerator of 4/7.

Changing the fractions into common numerators, we have:

$Comparing and ordering of like and unlike fractions$

Arranging the fractions from the smallest to the greatest, we have: 1/3 ,2/5 , 4/7 .

*When we apply Method 3 in this case, numbers are easier to work with, as compared to applying Method 2 straight away on all the fractions:

$Comparing and ordering of like and unlike fractions$

Examples of Comparing and Ordering Fractions

1. Arrange the following fractions from the smallest to the greatest.

3/5 , 7/10 , 2/4

Key Concept 6: Improper fractions and mixed numbers

Recall:

A fraction is improper when the numerator is equal to or greater than the denominator.
A mixed number is a way to show a number that is made up of a whole number and a fraction.

Various representation differences between an improper fraction and its corresponding mixed number

$Improper fractions and mixed numbers$

Conversion between Improper Fractions and Mixed Numbers

$Improper fractions and mixed numbers$

Examples of Improper Fraction and Mixed Number

$Improper fractions and mixed numbers$

Key Concept 7: Addition and subtraction of fractions

Addition
When we add mixed numbers, we are adding wholes and parts — just like combining full pizzas and leftover slices! See the example below.