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4.6 Fractions and Percentages

GCSE Maths Foundation · Edexcel · Chapter 4: Fractions and percentages

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: converting between fractions, decimals and percentages, and comparing them. 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 percentage as a fraction in its simplest form and as a decimal
  • Write a fraction or a decimal as a percentage
  • Recall common fraction, decimal and percentage equivalents
  • Compare and order fractions, decimals and percentages in context

Key words

  • Percentage (%): A number out of 100. 35% means 35 out of 100.
  • Equivalent: Having the same value: 1/4, 0.25 and 25% are equivalent.
  • Convert: Change from one form to another without changing the value.
  • Proportion: A part compared with the whole, which can be written as a fraction, decimal or percentage.

Percentages to fractions and decimals

"Per cent" means "out of 100". Write the percentage over 100 and simplify to get a fraction. Divide by 100 to get a decimal.

Worked example: percentages

35% = 35/100 = 7/20 = 0.35
12.5% = 12.5/100 = 125/1000 = 1/8 = 0.125
150% = 150/100 = 3/2 = 1 1/2 = 1.5

Answer: 7/20 (0.35), 1/8 (0.125), 1 1/2 (1.5)

Fractions and decimals to percentages

To change a decimal to a percentage, multiply by 100. To change a fraction, either make an equivalent fraction out of 100, or change it to a decimal first.

Worked example: to percentages

3/5 = 60/100 = 60%
0.07 × 100 = 7%
7/8 = 7 ÷ 8 = 0.875 = 87.5%
1/3 = 0.333… = 33.3% (to 1 d.p.)

Answer: 60%, 7%, 87.5%, 33.3%

Equivalents to know

These come up all the time, so it is worth learning them by heart.

  • Decimal; 1/2 0.5; 1/4 0.25; 3/4 0.75; 1/5 0.2; 1/10 0.1; 1/8 0.125; 1/3 0.333…; 2/3 0.666…
  • Percentage; 1/2 50%; 1/4 25%; 3/4 75%; 1/5 20%; 1/10 10%; 1/8 12.5%; 1/3 33.3%; 2/3 66.7%

Worked example: using known facts

3/8 = 3 × 1/8 = 3 × 12.5% = 37.5%
0.6 = 3 × 0.2 = 3 × 20% = 60% (= 3/5)

Answer: 37.5% and 60%

Comparing fractions, decimals and percentages

To compare, change everything into the same form. Percentages are often easiest.

Worked example: which test went best?

Jas scored 18/25 in French, 70% in History and 0.74 of the marks in Art. Which was her best result?
French: 18/25 = 72/100 = 72%. History: 70%. Art: 0.74 = 74%.

Answer: Art (74%)

Key fact: A percentage can be more than 100%. 100% is the whole amount, so 150% is one and a half times as much.

Common mistakes

  • Writing 5% as 0.5 instead of 0.05.
  • Thinking 0.5% is the same as 1/2: 0.5% = 0.005 = 1/200.
  • Writing 3/5 as 35%: 3/5 = 60/100 = 60%.
  • Comparing a fraction and a percentage without converting them to the same form first.

Revision questions

Try these, then check your answers below each one.

Question 1. Write 3/4 as a percentage.

Answer: 75 %

Working: 3/4 = 75/100 = 75%.

Question 2. Write 35% as a fraction in its simplest form. (Type your answer like 2/5.)

Answer: 7/20

Working: 35/100 = 7/20.

Question 3. Write 0.08 as a percentage.

Answer: 8 %

Working: 0.08 × 100 = 8%.

Related lessons

Continue in the full course

This lesson is section 4.6 (EGCMF0406) 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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