Solving Scaling Problems with Ratio for 11+ Maths (GL & CEM style)
21 October 2026
Scaling problems with ratio
Scaling problems with ratio are a key part of the 11+ maths syllabus. These questions ask children to work out how shapes or quantities change when they are enlarged or reduced by a given ratio. Understanding this skill is essential for both GL and CEM style exams.
Why ratio scaling matters
Being able to solve scaling problems helps children apply maths to real-life situations, such as resizing a recipe or enlarging a drawing. It also strengthens their grasp of fractions and multiplication.
Step-by-step approach
To solve a scaling problem with ratio, start by identifying the scale factor. Then, apply this factor to each measurement or quantity. Always check your answer makes sense in the context of the question.
Worked example
A rectangle has a length of 5 cm and a width of 3 cm. The rectangle is enlarged with a scale factor of 4:3. What are the new dimensions?
Step 1: Find the scale factor. This is 4 divided by 3, or 4/3.
Step 2: Multiply the original length by 4/3: 5 × 4/3 = 20/3 cm.
Step 3: Multiply the original width by 4/3: 3 × 4/3 = 4 cm.
Step 4: The new dimensions are 20/3 cm (about 6.67 cm) length and 4 cm width.
The correct answer is that the rectangle is enlarged to approximately 6.67 cm by 4 cm.
Key insight: Double-check that you have applied the scale factor to every relevant measurement. In 11+ questions, it is common to see one part scaled and another left unchanged by mistake.
