Adding & Subtracting Fractions
How do I add or subtract two fractions?
- Addition and subtraction are treated in exactly the same way when dealing with fractions
- Find the lowest common denominator
- Write each fraction as an equivalent fraction over this denominator
- Add (or subtract) the numerators and write this over a single denominator
- do not add the denominators
- Simplify the fraction by cancelling common factors
What do I do if any of the fractions are mixed numbers?
- Convert any mixed numbers into improper fractions
- Then add or subtract the fractions as usual
- Remember to convert the answer back to a mixed number if required
Worked example
(a) Find .
Find the lowest common denominator of 3 and 5
15 is the smallest number that can be divided by both 3 and 5
15 is the smallest number that can be divided by both 3 and 5
The lowest common denominator is 15
Write both fractions as equivalent fractions with a common denominator of 15
Multiply the numerator and denominator of the first fraction by 5
Multiply the numerator and denominator of the second fraction by 3
Multiply the numerator and denominator of the first fraction by 5
Multiply the numerator and denominator of the second fraction by 3
Add the numerators and write over a single denominator
There are no common factors that will cancel
(b) Find giving your answer as a mixed number.
Change the mixed number into an improper fraction
Multiply the denominator by the whole part and add to the numerator
Write this value over the denominator
Find the lowest common denominator of 4 and 8
8 is the smallest number that by divided by both 4 and 8
8 is the smallest number that by divided by both 4 and 8
The lowest common denominator is 8
Write both fractions as equivalent fractions over 8
Multiply the numerator and denominator of the first fraction by 2
Multiply the numerator and denominator of the first fraction by 2
Subtract the numerators and write over a single denominator
Change into a mixed number
Divide 25 by 8 to get 3 remainder 1
Divide 25 by 8 to get 3 remainder 1