Three ways of saying “a bit of” something — converting, comparing and using them.
6 lessons · 35 questions (A–G) · 20 calculation + 15 word problems · no time pressure
Fractions, decimals and percentages are three ways of describing part of a whole, and each can be rewritten as the others — ½, 0.5 and 50% are the same value. Pupils most often slip on the conversions (lining up the decimal place, or turning a percentage into the wrong fraction) and on comparing values written in different forms.
At Improve Tuition, a qualified teacher shows how the three forms connect and a dependable way to convert between them, in small worked steps — with read-aloud, comfort spacing and a reading tint for pupils who take in maths more easily that way.
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Lesson 1
The big picture
Aim: See that a fraction, a decimal and a percentage can all describe the same amount, and know which move takes you between them.
A half can be written 1/2, 0.5 or 50% — the same amount in three different outfits. The skill is switching between them quickly.
Fraction → Decimaldivide top by bottom
Decimal → Percentage× 100
Percentage → Decimal÷ 100
Decimal → Fractionplace value, then reduce
Percentage → Fractionover 100, then reduce
Worked example
Show that 3/5, 0.6 and 60% are the same amount.
3/5 = 3 ÷ 5 = 0.6.
0.6 × 100 = 60%.
All three describe the same amount.
Watch out
“× 100” is not “add two zeros.” 0.6 × 100 = 60, not 0.600. Move the decimal point two places.
35.Which is bigger, 5/8 or 60%? Give the bigger value as a percentage.
Answer:
Show working
5/8 = 62.5%.
62.5% > 60%, so the bigger value is 62.5%.
5/8 = 0.625 is bigger than 60% = 0.60.
0 of 35 answered
Guide
What is the link between fractions, decimals and percentages?
A fraction, a decimal and a percentage can all describe the same part of a whole. Three quarters can be written as ¾, as 0.75, or as 75% — same value, three notations.
To convert: a fraction becomes a decimal by dividing the top by the bottom; a decimal becomes a percentage by multiplying by 100; and a percentage becomes a fraction by writing it over 100 and simplifying. To compare values in different forms, turn them all into the same form first.
Common mistakes. Misplacing the decimal point when multiplying or dividing by 100, forgetting to simplify a fraction, or comparing a fraction and a percentage without converting them first.
Common questionsHow do you turn a fraction into a percentage?
Divide the top number by the bottom to get a decimal, then multiply by 100. For example, 3 ÷ 4 = 0.75, and 0.75 × 100 = 75%.
How do you turn a percentage into a fraction?
Write the percentage over 100 and simplify. For example, 40% = 40/100 = 2/5.
How do you turn a decimal into a percentage?
Multiply by 100, which moves the decimal point two places to the right. So 0.6 becomes 60%.
How do you compare a fraction with a percentage?
Convert both to the same form, usually percentages, then compare. For example, 3/5 = 60%, which is more than 55%.
How do you find a percentage of an amount?
Turn the percentage into a decimal and multiply. For example, 20% of £30 is 0.2 × 30 = £6.
Stuck on this topic?
A teacher can find the exact gap
Practising fractions, decimals and percentages on your own is a strong start. If the same marks keep slipping, a qualified teacher can pinpoint the precise gap and fix it. Improve Tuition offers one-to-one maths tuition with our maths tutors in Batley and online — the first assessment is free.