Key ideas
34
The numerator (top) tells you how many parts you have.
The denominator (bottom) tells you how many equal parts the whole is split into.
- Equivalent fractions are worth the same. Multiply or divide the top and bottom by the same number: 12 = 24 = 48.
- A fraction is in its simplest form when no number (except 1) divides into both the top and the bottom.
- An improper fraction is top-heavy, like 74. As a mixed number that's 134.
- To find a fraction of an amount: divide by the bottom, then multiply by the top.
Naming and shading
What fraction of this bar is shaded? What fraction is not shaded?(2 marks)
Count the equal parts.8 equal parts → denominator is 8
In plain EnglishFirst check the parts are all the same size. They are. There are 8 of them, so the bottom number is 8.
Count the shaded parts.Shaded = 38✓1
In plain English3 parts are shaded, so 3 goes on top: three eighths.
Find the part that isn't shaded.Not shaded = 58✓2
In plain English8 − 3 = 5 parts are not shaded. Check: 3 eighths and 5 eighths make 8 eighths, the whole bar.
⚠ Equal parts only. A fraction only works if every part is the same size.
Equivalent fractions from diagrams
These two bars are the same length. Use them to write two equivalent fractions.(2 marks)
Name the first bar.Top bar: 34
In plain English4 equal parts with 3 shaded: three quarters.
Name the second bar.Bottom bar: 68✓1
In plain English8 equal parts with 6 shaded: six eighths.
Compare the shading.34 = 68✓2
In plain EnglishThe shading reaches exactly the same point on both bars, so the same amount is shaded. The fractions are equivalent: they look different but they're worth the same.
Equivalence
(a) Find the missing number: 23 = ?15 (b) Write 1824 in its simplest form.(2 marks)
(a) What has the bottom been multiplied by?3 × 5 = 15
In plain EnglishTo get from 3 to 15 on the bottom, you multiply by 5.
Do the same to the top.23 = 2 × 53 × 5 = 1015✓1
In plain EnglishWhatever you do to the bottom, you must do to the top. 2 × 5 = 10.
(b) Find a number that divides into both.6 goes into 18 and 24
In plain EnglishLook for the biggest number that goes into both 18 and 24. That's 6. (You can use smaller steps, like ÷ 2 then ÷ 3, if that's easier.)
Divide the top and bottom.1824 = 18 ÷ 624 ÷ 6 = 34✓2
In plain English18 ÷ 6 = 3 and 24 ÷ 6 = 4. Nothing else divides into both 3 and 4, so it's in its simplest form.
⚠ Common mistake. Adding instead of multiplying. 2/3 is not equal to 14/15 just because you added 12 to the top and bottom.
Improper fractions and mixed numbers
(a) Write 175 as a mixed number. (b) Write 234 as an improper fraction.(4 marks)
(a) Divide the top by the bottom.17 ÷ 5 = 3 remainder 2✓1
In plain EnglishHow many whole 5s fit into 17? Three (that's 15), with 2 left over.
Write the mixed number.175 = 325✓2
In plain EnglishThe 3 is the whole number. The remainder 2 goes on top, and the bottom stays as 5 because the parts are still fifths.
(b) Change the wholes into quarters.2 × 4 = 8 quarters✓3
In plain EnglishEach whole one is 4 quarters, so 2 wholes are 2 × 4 = 8 quarters.
Add on the extra quarters.8 + 3 = 11 → 114✓4
In plain EnglishAdd the 3 quarters you already had: 8 + 3 = 11. The bottom stays as 4.
Ordering fractions
Put these fractions in order, smallest first: 34, 23, 56(2 marks)
Find a common denominator.4, 3 and 6 all go into 12
In plain EnglishYou can only compare fractions fairly when the parts are the same size. 12 is in the 4, 3 and 6 times tables, so change them all into twelfths.
Change each fraction.34 = 91223 = 81256 = 1012✓1
In plain English× 3, × 4 and × 2 on the top and bottom.
Order by the numerators.23, 34, 56✓2
In plain English8 twelfths is smallest, then 9, then 10. Write the answer using the original fractions.
Fractions and decimals
(a) Write 35 as a decimal. (b) Write 0.25 as a fraction in its simplest form.(4 marks)
(a) Make the denominator 10 or 100.35 = 610✓1
In plain EnglishDecimals are tenths and hundredths. Multiply the top and bottom by 2 to get tenths.
Write it as a decimal.= 0.6✓2
In plain EnglishSix tenths is 0.6.
(b) Read the decimal place value.0.25 = 25100✓3
In plain EnglishThe last digit is in the hundredths column, so 0.25 is 25 hundredths.
Simplify.25100 = 14✓4
In plain EnglishDivide the top and bottom by 25.
Worth learning: ½ = 0.5, ¼ = 0.25, ¾ = 0.75, ⅕ = 0.2, 1/10 = 0.1, 1/100 = 0.01
Fraction of an amount
There are 28 toucans in a flock. 34 of them are eating fruit. How many toucans are eating fruit?(2 marks)
Divide by the denominator.14 of 28 = 28 ÷ 4 = 7✓1
In plain EnglishThe bottom number is 4, so split the 28 toucans into 4 equal groups. Each group is 7. That's one quarter.
Multiply by the numerator.34 of 28 = 7 × 3 = 21✓2
In plain EnglishWe want 3 of those quarters, so 3 × 7 = 21 toucans. The bar model shows the same thing: 3 shaded boxes of 7.
Remember: divide by the bottom, times by the top.
0 of 0 complete
Your turn
Non-calculator. Type fractions with a slash, like 3/4, and mixed numbers with a space, like 2 1/2. Stuck? Tap Need a hint?