Ratio Notation

What is a Ratio?

Every time you mix squash with water, you are using a mathematical concept without even realising it.
A ratio is a way of comparing two or more quantities showing the relative sizes of each.
We write this using ratio notation, which separates the numbers with a colon (e.g., $1:4$ ).
The order of the numbers must strictly match the order of the items in the question; "4 parts flour to 1 part sugar" is always written as $4:1$ .

Parts of a Whole

Numbers in a ratio tell you the proportion of the whole amount.
To understand parts of a whole, you must add all the numbers in the ratio together to find the total number of parts.
For example, in the ratio $3:7$ , there are $3 + 7 = 10$ parts in total.
The first quantity represents $\frac{3}{10}$ of the whole, and the second represents $\frac{7}{10}$ .

Simplifying Ratios

You wouldn't say "I have 50 pence for every 100 pence you have" — you'd simply say "I have 1 for every 2."
This is an equivalent ratio, which is a ratio that represents the exact same proportion but is scaled up or down.
A ratio is in its simplest form when all numbers are the smallest possible integers with no common factors other than 1.
To reduce a ratio to its simplest form, you must divide all parts by the Highest Common Factor (HCF).

Dealing with Units and Decimals

Before simplifying, all quantities must be in the exact same units (e.g., convert $50\text{p}$ and $\pounds 2$ to $50:200$ ).
Once the units are identical, they are removed because ratios themselves do not have units.
A simplest form ratio must be an integer ratio, meaning it contains no decimals or fractions.
If a ratio contains decimals, multiply all parts by a power of 10 to create whole numbers before you start simplifying.

Worked Example: Basic Simplification

Simplify the ratio $30:18$ .

Step 1: Find the Highest Common Factor (HCF) of 30 and 18.

Factors of 30: $1, 2, 3, 5, 6, 10, 15, 30$
Factors of 18: $1, 2, 3, 6, 9, 18$
The HCF is $6$ .

Step 2: Divide both parts by the HCF.

$30 \div 6 = 5$
$18 \div 6 = 3$

Step 3: Write the final equivalent ratio.

$5:3$

Worked Example: Decimals in Ratios

Simplify the ratio $1.6:2.4$ .

Step 1: Multiply by a power of 10 to remove decimals.

$1.6 \times 10 = 16$
$2.4 \times 10 = 24$
The ratio is now $16:24$ .

Step 2: Find the HCF of 16 and 24, then divide.

The HCF of 16 and 24 is $8$ .
$16 \div 8 = 2$
$24 \div 8 = 3$

Step 3: Write the final equivalent ratio.

$2:3$

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Exam Tips

Common Mistake
Students often reverse the order of the numbers (e.g., writing $3:5$ instead of $5:3$ ); this is a frequent 0-mark error, so always double-check the 'Part A to Part B' order requested in the question.
2
In Edexcel calculator papers, entering a two-part ratio as a fraction (e.g., $30/18$ ) on your scientific calculator will often output the simplified fraction ( $5/3$ ), which you can quickly write as $5:3$ — but remember this trick does NOT work for three-part ratios.
3
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.
4
Always ensure units are consistent before simplifying a ratio; for example, you must convert $50\text{p}$ and $\pounds 2$ into $50\text{p}$ and $200\text{p}$ before you attempt to simplify.

Key Terms(8)

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.

Previous Subtopic: Fractional QuantitiesFractional Quantities Next Subtopic: Ratio ProblemsRatio Problems

Back to Ratio Notation

Put your knowledge into practice — try past paper questions for Mathematics

Key Terms(8)

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.

Ratio Notation

What is a Ratio?

Every time you mix squash with water, you are using a mathematical concept without even realising it.
A ratio is a way of comparing two or more quantities showing the relative sizes of each.
We write this using ratio notation, which separates the numbers with a colon (e.g., $1:4$ ).
The order of the numbers must strictly match the order of the items in the question; "4 parts flour to 1 part sugar" is always written as $4:1$ .

Parts of a Whole

Numbers in a ratio tell you the proportion of the whole amount.
To understand parts of a whole, you must add all the numbers in the ratio together to find the total number of parts.
For example, in the ratio $3:7$ , there are $3 + 7 = 10$ parts in total.
The first quantity represents $\frac{3}{10}$ of the whole, and the second represents $\frac{7}{10}$ .

Simplifying Ratios

You wouldn't say "I have 50 pence for every 100 pence you have" — you'd simply say "I have 1 for every 2."
This is an equivalent ratio, which is a ratio that represents the exact same proportion but is scaled up or down.
A ratio is in its simplest form when all numbers are the smallest possible integers with no common factors other than 1.
To reduce a ratio to its simplest form, you must divide all parts by the Highest Common Factor (HCF).

Dealing with Units and Decimals

Before simplifying, all quantities must be in the exact same units (e.g., convert $50\text{p}$ and $\pounds 2$ to $50:200$ ).
Once the units are identical, they are removed because ratios themselves do not have units.
A simplest form ratio must be an integer ratio, meaning it contains no decimals or fractions.
If a ratio contains decimals, multiply all parts by a power of 10 to create whole numbers before you start simplifying.

Worked Example: Basic Simplification

Simplify the ratio $30:18$ .

Step 1: Find the Highest Common Factor (HCF) of 30 and 18.

Factors of 30: $1, 2, 3, 5, 6, 10, 15, 30$
Factors of 18: $1, 2, 3, 6, 9, 18$
The HCF is $6$ .

Step 2: Divide both parts by the HCF.

$30 \div 6 = 5$
$18 \div 6 = 3$

Step 3: Write the final equivalent ratio.

$5:3$

Worked Example: Decimals in Ratios

Simplify the ratio $1.6:2.4$ .

Step 1: Multiply by a power of 10 to remove decimals.

$1.6 \times 10 = 16$
$2.4 \times 10 = 24$
The ratio is now $16:24$ .

Step 2: Find the HCF of 16 and 24, then divide.

The HCF of 16 and 24 is $8$ .
$16 \div 8 = 2$
$24 \div 8 = 3$

Step 3: Write the final equivalent ratio.

$2:3$

Sign up to continue reading

Get full access to revision notes, key terms, and exam tips for every subtopic.

Exam Tips

Common Mistake
Students often reverse the order of the numbers (e.g., writing $3:5$ instead of $5:3$ ); this is a frequent 0-mark error, so always double-check the 'Part A to Part B' order requested in the question.
2
In Edexcel calculator papers, entering a two-part ratio as a fraction (e.g., $30/18$ ) on your scientific calculator will often output the simplified fraction ( $5/3$ ), which you can quickly write as $5:3$ — but remember this trick does NOT work for three-part ratios.
3
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.
4
Always ensure units are consistent before simplifying a ratio; for example, you must convert $50\text{p}$ and $\pounds 2$ into $50\text{p}$ and $200\text{p}$ before you attempt to simplify.

Key Terms(8)

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.

Previous Subtopic: Fractional QuantitiesFractional Quantities Next Subtopic: Ratio ProblemsRatio Problems

Back to Ratio Notation

Put your knowledge into practice — try past paper questions for Mathematics

Key Terms(8)

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.