Number
Fractions: Equivalent, Adding/Subtracting, and Multiplying
3rd Class · 4th Class · 5th Class · 6th Class
- ✓By the end of this lesson students will be able to understand and identify equivalent fractions.
- ✓By the end of this lesson students will be able to add and subtract fractions with the same denominator (like fractions).
- ✓By the end of this lesson students will be able to add and subtract fractions with different denominators (unlike fractions).
- ✓By the end of this lesson students will be able to multiply a fraction by a whole number.
Key concepts
A fraction represents a part of a whole. It is written with two numbers separated by a line. The top number is called the 'numerator' and the bottom number is called the 'denominator'. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we are considering.
Equivalent fractions are fractions that look different but represent the same value or the same amount of a whole. You can find an equivalent fraction by multiplying or dividing both the numerator and the denominator by the same non-zero number. For example, 1/2 is equivalent to 2/4 because if you multiply the numerator (1) and the denominator (2) by 2, you get 2/4.
Like fractions are fractions that have the same denominator. For example, 1/5, 2/5, and 4/5 are all like fractions.
Unlike fractions are fractions that have different denominators. For example, 1/2, 1/3, and 1/4 are all unlike fractions.
When adding or subtracting unlike fractions, we need to change them into equivalent fractions that have the same denominator. This shared denominator is called a 'common denominator'. Often, we use the 'Lowest Common Multiple' (LCM) of the original denominators as our common denominator.
Key facts to remember
- 1A fraction represents a part of a whole, with a numerator (top) and a denominator (bottom).
- 2The denominator tells you how many equal parts the whole is divided into.
- 3Equivalent fractions have the same value, even if they look different (e.g., 1/2 = 2/4).
- 4To find equivalent fractions, multiply or divide both the numerator and denominator by the same non-zero number.
- 5To add or subtract fractions with the same denominator (like fractions), add or subtract the numerators and keep the denominator the same.
- 6To add or subtract fractions with different denominators (unlike fractions), you must first find a common denominator (often the LCM) and convert them to equivalent fractions.
- 7To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same.
- 8Always simplify your final fraction answer to its simplest form if possible.
Worked examples
Example 1
a) Write two equivalent fractions for 3/4. b) Simplify the fraction 10/15 to its simplest form.
Answer
a) 6/8 and 9/12 (other answers are possible). b) 2/3
There are many equivalent fractions for any given fraction. Simplifying a fraction means writing it in its simplest form, where the numerator and denominator have no common factors other than 1.
Example 2
Calculate: a) 2/7 + 3/7 b) 1/3 + 1/2
Answer
a) 5/7 b) 5/6
Remember to always look for the simplest form for your final answer, though 5/7 and 5/6 are already in simplest form.
Example 3
Calculate: a) 5/8 - 1/8 b) 3/4 - 1/2
Answer
a) 1/2 b) 1/4
Subtracting fractions follows the same common denominator rule as adding fractions.
Example 4
Calculate 2/5 × 3.
Answer
6/5 or 1 and 1/5
In Primary school, answers can often be left as improper fractions unless specifically asked for a mixed number.
Common mistakes
- ✗Adding or subtracting the denominators when adding or subtracting fractions.
- ✗Not finding a common denominator before adding or subtracting unlike fractions.
- ✗Multiplying both the numerator and the denominator by the whole number when multiplying a fraction by a whole number.
- ✗Forgetting to simplify fractions to their simplest form at the end of a calculation.
- ✗Confusing the numerator and the denominator.
Exam tips
- ★Always show all your working steps clearly, especially when finding common denominators or simplifying.
- ★Draw diagrams (like circles or rectangles divided into parts) to help you visualise fractions and equivalent fractions.
- ★Check your answer to see if it makes sense. For example, if you add two fractions that are each less than 1, your answer should also be less than 2.
- ★Practice finding the Lowest Common Multiple (LCM) quickly, as it's key for adding and subtracting unlike fractions.
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