IGCSE Maths / Fractions, decimals and rounding
Equivalent fractions and simplifying
Edexcel International GCSE Maths (4MA1), chapter 1: Fractions, decimals and rounding, specification point 1.2a. Free lesson.
Read the revision notes · IGCSE Maths past papers
Equivalent fractions have the same value, even when their numerators and denominators look different. You can make them by multiplying both parts by the same number, or simplify them by dividing both parts by a common factor.
How equivalent fractions keep the same value
The numerator is the top number and the denominator is the bottom number. Multiplying both by the same number is the same as multiplying the fraction by that number over itself, which equals 1. Dividing both by the same number also leaves the value unchanged. Use the same number on the top and bottom. Changing only one changes the fraction's value.
How to simplify in one step
To simplify, divide the numerator and denominator by a common factor. The highest common factor (HCF) is the biggest number that divides both exactly. Dividing by the HCF gets you to the lowest terms in one step.
How to make a required denominator
Work out what number changes the denominator into the one you need. Multiply the numerator by that same number, so the fraction's value stays the same.
Why you cannot cancel across a plus
Cancelling means dividing the whole numerator and the whole denominator by the same number. A number that is one part of a sum cannot be cancelled on its own. Cancelling works across multiplication, not across addition. For (6 + 3)/3, the whole numerator is 9, so 9/3 = 3. It is wrong to cancel the 3 in the sum and get 6 + 1 = 7.
What the size of a fraction tells you
A fraction's value depends on how the numerator compares with the denominator, not on how large the digits look. So fractions with larger numbers can still have the same value as fractions with smaller numbers. 50/100 = 1/2, even though 50 and 100 are larger than 1 and 2.
More lessons in Fractions, decimals and rounding
- Directed numbers
- Mixed numbers and improper fractions
- Adding and subtracting fractions
- A fraction of a quantity
- Multiplying and dividing fractions
- Ordering decimals
- Fractions, decimals and percentages
- Recurring decimals to fractions
- Mixed recurring decimals
- Rounding to decimal places and significant figures
- Estimating by rounding
- Finding upper and lower bounds
- Calculating with bounds