Key ideas
- A proper fraction has a smaller top than bottom, like 35. It is less than 1.
- An improper fraction (top-heavy) has a top that is the same as or bigger than the bottom, like 75. It is 1 or more.
- A mixed number is a whole number and a fraction, like 125. 125 = 75.
- One whole can be written as a fraction with the same top and bottom: 1 = 44 = 55 = 88.
- Adding to one: write 1 with the same bottom number, then add the tops. 1 + 35 = 55 + 35 = 85.
- Subtracting from one: write 1 with the same bottom number, then take away the tops. 1 − 38 = 88 − 38 = 58.
- The bottom number stays the same. Only the tops are added or taken away. Give answers as improper fractions.
Proper and improper fractions
Is 94 a proper or an improper fraction?(1 mark)
Compare the top and bottom.Top = 9, bottom = 49 > 4, so 94 is improper✓1
In plain EnglishThe top is bigger than the bottom, so it is top-heavy. It is more than one whole.
Mixed numbers
Write 234 as an improper fraction.(2 marks)
Change the wholes into quarters.2 = 84✓1
In plain EnglishEach whole one is 4 quarters, so 2 wholes are 2 × 4 = 8 quarters.
Add the fraction part.84 + 34 = 114✓2
In plain EnglishAdd the tops: 8 + 3 = 11. The bottom stays as 4.
Shortcut: whole number × bottom, then add the top. 2 × 4 + 3 = 11, so 2¾ = 11/4.
Write 135 as a mixed number.(2 marks)
How many whole ones?13 ÷ 5 = 2 remainder 3✓1
In plain EnglishEach whole one is 5 fifths. 13 fifths makes 2 wholes (10 fifths) with 3 fifths left over.
Write the mixed number.135 = 235✓2
In plain EnglishThe 2 whole ones, and the 3 fifths left over.
Adding to one
Calculate 1 + 35. Give your answer as an improper fraction.(2 marks)
Write 1 as fifths.1 = 55✓1
In plain EnglishThe fraction is in fifths, so write one whole as 5 fifths.
Add the tops.55 + 35 = 85✓2
In plain English5 fifths and 3 more fifths make 8 fifths. The bottom stays as 5.
Calculate 2 + 34. Give your answer as an improper fraction.(2 marks)
Write 2 as quarters.2 = 84✓1
In plain EnglishEach whole is 4 quarters, so 2 wholes are 8 quarters.
Add the tops.84 + 34 = 114✓2
In plain English8 quarters and 3 more quarters make 11 quarters.
Subtracting from one
Calculate 1 − 38.(2 marks)
Write 1 as eighths.1 = 88✓1
In plain EnglishThe fraction is in eighths, so write one whole as 8 eighths.
Take away the tops.88 − 38 = 58✓2
In plain EnglishStart with 8 eighths and take 3 away. 5 eighths are left.
Calculate 3 − 25. Give your answer as an improper fraction.(2 marks)
Write 3 as fifths.3 = 155✓1
In plain EnglishEach whole is 5 fifths, so 3 wholes are 3 × 5 = 15 fifths.
Take away the tops.155 − 25 = 135✓2
In plain English15 fifths take away 2 fifths leaves 13 fifths.
Problems in context
Amy has 1 bar of chocolate. She eats 26 of it. What fraction of the bar is left?(2 marks)
Start with one whole bar.1 = 66✓1
In plain EnglishThe bar is split into sixths, so the whole bar is 6 sixths.
Take away what she ate.66 − 26 = 46✓2
In plain English6 sixths take away 2 sixths leaves 4 sixths.
You may also see this written as 2/3, which is the same amount simplified.
0 of 0 complete
Your turn
Type fractions with a slash, like 8/5. Type mixed numbers with a space, like 2 3/4. Give answers as improper (top-heavy) fractions unless the question says otherwise. Stuck? Tap Need a hint?