Edexcel GCSE Mathematics (1MA1) — Ratio, Proportion and Rates of Change
Simplify the ratio .
Step 1: Find the Highest Common Factor (HCF) of 30 and 18.
Step 2: Divide both parts by the HCF.
Step 3: Write the final equivalent ratio.
Simplify the ratio .
Step 1: Multiply by a power of 10 to remove decimals.
Step 2: Find the HCF of 16 and 24, then divide.
Step 3: Write the final equivalent ratio.
Students often reverse the order of the numbers (e.g., writing instead of ); this is a frequent 0-mark error, so always double-check the 'Part A to Part B' order requested in the question.
In Edexcel calculator papers, entering a two-part ratio as a fraction (e.g., ) on your scientific calculator will often output the simplified fraction (), which you can quickly write as — but remember this trick does NOT work for three-part ratios.
If you cannot spot the Highest Common Factor immediately, you will still earn process marks for dividing by any common factor, so just keep halving or dividing by obvious numbers until you reach the simplest form.
Always ensure units are consistent before simplifying a ratio; for example, you must convert and into and before you attempt to simplify.
Ratio
A way of comparing two or more quantities showing the relative sizes of each.
Ratio notation
The use of two or more numbers to represent a proportion.
Colon
The mathematical symbol (:) used to separate quantities in a ratio.
Parts of a whole
The concept that the individual numbers in a ratio add up to represent the total amount being shared.
Equivalent ratio
Ratios that represent the same relationship between quantities, found by multiplying or dividing all parts by the same non-zero number.
Simplest form
An equivalent ratio where the numbers are the smallest possible integers with no common factors other than 1.
Highest Common Factor (HCF)
The largest whole number that divides exactly into all parts of a ratio without leaving a remainder.
Integer ratio
A ratio where all parts are whole numbers, which is a strict requirement before a ratio can be considered fully simplified.
Put your knowledge into practice — try past paper questions for Mathematics
Ratio
A way of comparing two or more quantities showing the relative sizes of each.
Ratio notation
The use of two or more numbers to represent a proportion.
Colon
The mathematical symbol (:) used to separate quantities in a ratio.
Parts of a whole
The concept that the individual numbers in a ratio add up to represent the total amount being shared.
Equivalent ratio
Ratios that represent the same relationship between quantities, found by multiplying or dividing all parts by the same non-zero number.
Simplest form
An equivalent ratio where the numbers are the smallest possible integers with no common factors other than 1.
Highest Common Factor (HCF)
The largest whole number that divides exactly into all parts of a ratio without leaving a remainder.
Integer ratio
A ratio where all parts are whole numbers, which is a strict requirement before a ratio can be considered fully simplified.
