GradeGen.AI

Understanding Ratios as Fractions

If you mix a squash drink, you might use one part syrup to four parts water. This is a ratio, which compares one part of a mixture directly to another part.
In contrast, a fraction of the whole compares one specific part to the entire mixture combined.
While ratios show a part-to-part proportion, they do not show the total amount on their own.

The Denominator Rule

To turn a ratio into a fraction, you need to find the sum of parts (often called the total parts).
This total value becomes the denominator (ratio context) for your fraction.
If a quantity is shared in the ratio $a:b$ , the total number of parts is $a+b$ .
The first part represents the following fraction of the whole:

\frac{b}{a+b}

For Higher tier papers, you might encounter a three-part ratio like $a:b:c$ . The exact same logic applies, making the fraction for the first part $\frac{a}{a+b+c}$ .

Visualising the Concept

Drawing a bar model can help you visualise this relationship.
For a ratio of $2:3$ , you would draw a bar with $5$ equal boxes.
This clearly shows that the whole is split into fifths, meaning the parts represent $\frac{2}{5}$ and of the whole.

Worked Example 1: Finding the Fractions

A box contains green and yellow counters in the ratio $4:5$ . What fraction of the counters are green and what fraction are yellow?

Step 1: Calculate the sum of parts.

Total parts = $4 + 5 = 9$

Step 2: Form the fraction for the green counters.

Green fraction = $\frac{\text{green parts}}{\text{total parts}}$ = $\frac{4}{9}$

Step 3: Form the fraction for the yellow counters.

Yellow fraction = $\frac{\text{yellow parts}}{\text{total parts}}$ = $\frac{5}{9}$

Worked Example 2: Simplifying Fractions

A prize fund is shared between Leo and Maya in the ratio $6:14$ . What fraction of the total prize fund does Leo receive?

Step 1: Calculate the sum of parts.

Total parts = $6 + 14 = 20$

Step 2: Create the initial fraction for Leo.

Leo's fraction = $\frac{6}{20}$

Step 3: Simplify the fraction.

Divide the numerator and denominator by their Highest Common Factor ( $2$ ).
Leo's simplified fraction = $\frac{3}{10}$

Dealing with Different Units

Sometimes OCR questions mix units, such as pence and pounds or millimetres and centimetres.
You must convert both sides of the ratio to a common unit before adding them together to find the denominator.

Worked Example 3: Unit Consistency

Express the ratio $80\text{p}$ to £ $3$ as a fraction of the total for the first part.

Step 1: Convert to a consistent unit.

Convert £ $3$ into pence: £ $3 = 300\text{p}$

Step 2: Write the ratio and simplify it.

Ratio = $80 : 300$
Divide both sides by $20$ to simplify to $4 : 15$ .

Step 3: Find the total parts and create the fraction.

Total parts = $4 + 15 = 19$
First part fraction = $\frac{4}{19}$

Reversing the Process

Exams may also require you to work backwards from a fraction to a ratio.
If $\frac{2}{9}$ of a class are left-handed, the remaining parts must be right-handed.
The ratio of left-handed to right-handed students is found by subtracting the numerator from the denominator: $2 : (9-2)$ , which simplifies to .

Students often fall into the 'denominator trap' by using one of the ratio numbers as the denominator (e.g., turning a $3:5$ ratio into $\frac{3}{5}$ instead of $\frac{3}{8}$ ). Always add the parts together first!

In OCR exams, simply showing the sum of the ratio parts (e.g., writing $4 + 7 = 11$ ) often secures the first method mark (M1), even if your final fraction is incorrect.

If an exam question uses the command word 'Interpret', you must clearly demonstrate your understanding of how the individual ratio parts add up to create the total whole.

Always check the units before creating your fraction; if a ratio compares millimetres to centimetres, convert them to a common unit before summing the parts.

A mathematical format for comparing one part of a whole directly to another part.

A numerical representation where the numerator is the specific part of interest and the denominator is the sum of all parts in the ratio.

The total value obtained by adding all the numbers in a ratio together, representing the entire quantity.

Another term for the sum of parts, representing the whole amount that a ratio is dividing.

The total number of equal shares or parts that make up the whole, placed at the bottom of the fraction.