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11.3 Ratios and Measures

GCSE Maths Foundation · Edexcel · Chapter 11: Ratio and Proportion

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: ratios with different units, ratios with decimals and fractions, the form 1 : n, and map scales. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Write a ratio of two measures by first changing them to the same units
  • Simplify ratios that contain decimals or fractions
  • Write a ratio in the form 1 : n or n : 1
  • Use a map scale written as a ratio to find real distances

Key words

  • Units: What a measure is counted in, such as cm, m, g, kg, minutes or hours.
  • Unit ratio: A ratio in which one part is 1, such as 1 : 2.5 or 4 : 1. The other part may be a decimal.
  • Scale: The ratio of a length on a map or model to the real length, such as 1 : 50 000.
  • Convert: Change a measure into different units, for example 2 m = 200 cm.

Ratios with different units

You can only compare like with like. Change both amounts into the same units (usually the smaller unit), drop the units, then simplify.

  • 1 cm = 10 mm; Mass 1 kg = 1000 g; Capacity 1 litre = 1000 ml; Time 1 hour = 60 minutes
  • 1 m = 100 cm; Mass 1 tonne = 1000 kg; Capacity 1 litre = 100 cl; Time 1 day = 24 hours
  • 1 km = 1000 m; Mass ; Capacity ; Time 1 minute = 60 seconds

Worked example: time

Write 45 minutes : 2 hours in its simplest form.
2 hours = 120 minutes, so the ratio is 45 : 120.
Divide both by 15: 3 : 8

Answer: 3 : 8

Worked example: mass

Write 750 g : 1.5 kg in its simplest form.
1.5 kg = 1500 g. 750 : 1500 = 1 : 2 (divide by 750)

Answer: 1 : 2

Decimals and fractions in ratios

Multiply every part by the same number to make whole numbers, then simplify as usual. With fractions, multiply by a common denominator.

Worked example: decimals

Simplify 2.5 : 4. Multiply both by 2: 5 : 8

Answer: 5 : 8

Worked example: fractions

Simplify 1/2 : 3/4. The common denominator is 4, so multiply both by 4.
1/2 × 4 = 2 and 3/4 × 4 = 3

Answer: 2 : 3

The form 1 : n and n : 1

To write a ratio as 1 : n, divide both parts by the first part. For n : 1, divide both by the second part. n can be a decimal. Unit ratios make comparisons easy.

Worked example: 1 : n

A school has 24 teachers and 420 students. Write teachers : students in the form 1 : n.
24 : 420. Divide both by 24: 420 ÷ 24 = 17.5

Answer: 1 : 17.5

Worked example: n : 1

Write 18 : 4 in the form n : 1. Divide both by 4: 18 ÷ 4 = 4.5

Answer: 4.5 : 1

Map scales

A map scale of 1 : 50 000 means 1 cm on the map is 50 000 cm in real life. Multiply to go from map to real. Divide to go from real to map. Then change the units.

Worked example: map to real

Ashby and Brook are 3 cm apart on a map with scale 1 : 50 000. How far apart are they in km?
3 × 50 000 = 150 000 cm. 150 000 ÷ 100 = 1500 m. 1500 ÷ 1000 = 1.5 km

Answer: 1.5 km

Worked example: real to map

A footpath is 4 km long. How long is it on the same map?
4 km = 400 000 cm. 400 000 ÷ 50 000 = 8 cm

Answer: 8 cm

Common mistakes

  • Simplifying before changing to the same units: 3 m : 50 cm is not 3 : 50.
  • Leaving units inside a ratio. A simplified ratio has no units.
  • For 1 : n, dividing only the second part. Both parts are divided by the first part.
  • With a map scale, forgetting that both numbers are in the same units (cm), so the answer must be converted to m or km.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 50 cm : 2 m in its simplest form. (Choose from: 25 : 1, 1 : 4, 50 : 2, 5 : 2.)

Answer: 1 : 4

Working: 2 m = 200 cm. 50 : 200 = 1 : 4.

Question 2. Write 45 minutes : 1 hour in its simplest form.

Answer: 3:4

Working: 45 : 60. Divide by 15: 3 : 4.

Question 3. Write 6 : 15 in the form 1 : n. What is n?

Answer: 2.5

Working: 15 ÷ 6 = 2.5, so 1 : 2.5.

Related lessons

Continue in the full course

This lesson is section 11.3 (EGCMF1103) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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