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Ratio and scale

Ratio and scale for ESOL Computer Science: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • Computer Science
  • Spec P6 · P17
  • 7 min read
  • 7 revision boxes

Introduction

2 boxes
2 min read

What is ratio and scale?

Listen to this box

Transcript

A short spoken summary of ratio and scale and where it is used.

A spoken walk-through of ratio and scale before you read the notes.
The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
4 rows

The ratio and scale reference table

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing ratio and scale laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
49=7\sqrt{49} = 7
Row 2 column 4
Row 3 column 1
Row 3 column 2
49=7\sqrt{49} = 7
Row 3 column 4
Row 4 column 1
Row 4 column 2
49=7\sqrt{49} = 7
Row 4 column 4

Learning

3 boxes
4 steps

How to work with ratio and scale

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing ratio and scale laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for ratio and scale in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 49=7\sqrt{49} = 7.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Ratio and scale

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.

  • Rule 1

    How ratio and scale behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How ratio and scale behaves in the 2nd of the cases the specification names.
    ≈160\approx 160
4 steps

How to work with ratio and scale

The examiner marks the working, so a correct answer with no method still drops marks.
  1. Read the question and write down what is being asked for.
  2. Set out the working for ratio and scale in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: ×10\times 10 moves every digit one column left

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Examples

2 boxes
4 marks · worked

Worked example: ratio and scale

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing ratio and scale laid out step by step

The same idea drawn out, so the method is visible.
4 marks · worked

Practice question 7: ×10\times 10 moves every digit one column left

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

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Common questions

How many marks is ratio and scale usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the ESOL Computer Science paper?
Yes — it sits in the Waves and light strand.