Primary 4 Fractions
In Primary 4, learn to change between mixed numbers and improper fractions. You will also add and subtract fractions with up to two different denominators, each no greater than 12.
Keywords
- Numerator
- The top number: how many equal parts are counted.
- Denominator
- The bottom number: how many equal parts make one whole.
- Mixed number
- A whole number together with a proper fraction.
- Improper fraction
- A fraction whose numerator is equal to or greater than its denominator.
- Common denominator
- A shared denominator that gives both fractions parts of the same size.
Mixed numbers and improper fractions
A mixed number has a whole number and a fraction. An improper fraction has a numerator equal to or greater than its denominator. They can name the same amount.
Two ways to name the same amount
Each whole has 3 thirds. Two wholes and 1 third make 7 thirds.
See the full working
How are 2 and 1 third and 7 thirds alike?
- Each whole contains 3 thirds.
- Two wholes contain 6 thirds. Add 1 more third to make 7 thirds.
- Both names show the same amount: 2 and 1 third = 7 thirds.
Answer: 213 = 73.
Try together
Show 123 using thirds.
Reveal the answer
One whole is 3 thirds, so 123 = 53.
Change an improper fraction to a mixed number
Use long division: divide the numerator by the denominator. The quotient gives the wholes, and the remainder becomes the numerator of the fraction left over.
Change 73 to a mixed number
Show the first step.
See the full working
Change 73 to a mixed number using long division.
- Divide 7 by 3. Three fits into 7 two times, so the quotient is 2.
- Multiply 2 × 3 = 6 and subtract 7 − 6 = 1. The remainder is 1.
- The quotient is the whole number; put the remainder over the original denominator: 2 and 1 third.
Answer: 73 = 213.
Try together
Use division to change 114 to a mixed number.
Reveal the answer
11 ÷ 4 = 2 remainder 3, so 114 = 234.
Change a mixed number to an improper fraction
Multiply the whole number by the denominator, then add the numerator. Keep the same denominator because the size of each part has not changed.
Change 213 to an improper fraction
Show the first step.
See the full working
Change 213 to an improper fraction.
- Multiply the whole number by the denominator: 2 × 3 = 6 thirds.
- Add the numerator: 6 + 1 = 7 thirds.
- Write 7 over the unchanged denominator 3.
Answer: 213 = 73.
Try together
Change 325 to an improper fraction.
Reveal the answer
3 × 5 + 2 = 17, so 325 = 175.
Add and subtract fractions
When denominators differ, make the pieces the same size before adding or subtracting. These examples use two fractions with denominators no greater than 12.
Make the denominators match
Show the first step.
See the full working
Work out 12 + 13 and 56 − 14.
- For addition, use sixths: 1 half = 3 sixths and 1 third = 2 sixths.
- Add the numerators: 3 sixths + 2 sixths = 5 sixths.
- For subtraction, use twelfths: 5 sixths = 10 twelfths and 1 quarter = 3 twelfths. Subtract 10 − 3 = 7 twelfths.
Answer: 12 + 13 = 56; 56 − 14 = 712.
Try together
Work out 23 + 16 and 34 − 16.
Reveal the answer
23 + 16 = 46 + 16 = 56. 34 − 16 = 912 − 212 = 712.