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Operations with Fractions (Edexcel IGCSE Maths)
Revision Note
Adding & Subtracting Fractions
Dealing with mixed numbers
- Always turn mixed numbers into top heavy fractions before adding or subtracting
Adding & subtracting
- Adding and subtracting are treated in exactly the same way:
- Find the lowest common denominator (the smallest whole number that each denominator divides)
- Write each fraction as an equivalent fraction over this denominator (by multiplying top-and-bottom by the same amount)
- Add (or subtract) the numerators and write this over a single lowest common denominator
- do not add the denominators
- Check for any cancellation (or if asked to turn top heavy fractions back into mixed numbers)
Worked example
(a) Find
Find the lowest common denominator of 3 and 5
15 is the smallest number that divides both 3 and 5
the lowest common denominator is 15
Write both fractions as equivalent fractions over 15 (by multiplying top and bottom by the same amount)
Add the numerators and write over a single denominator
There is no cancellation
(b) Find giving your answer as a mixed number
Change the mixed number into a top heavy fraction (by multiplying the denominator, 4, by the whole number, 3, then adding the numerator, 3)
To find first find the lowest common denominator of 4 and 8
8 is the smallest number that divides both 4 and 8
the lowest common denominator is 8
Write both fractions as equivalent fractions over 8 (by multiplying top and bottom by the same amount)
Subtract the numerators and write over a single denominator
Change into a mixed number (by dividing 25 by 8 to get 3 remainder 1)
There is no more cancellation
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Multiplying Fractions
Dealing with mixed numbers
- Always turn mixed numbers into top heavy fractions before multiplying
Multiplying fractions
- Cancel any numbers on the tops of the fractions with numbers on the bottoms of the fractions (either fraction)
- Multiply the tops
- Multiply the bottoms
- Cancel again if possible
- Turn top heavy fractions back into mixed numbers (if necessary / asked for)
Worked example
Find
The 15 and 25 can be cancelled before multiplying (to make the next step easier)
Multiply the numerators together and the denominators together
There is no further cancelling that can be done
Dividing Fractions
Dealing with mixed numbers
- Always turn mixed numbers into top heavy fractions before dividing
Dividing fractions
- Never try to divide fractions
- Instead “flip’n’times” (flip the second fraction and change ÷ into ×)
- So becomes
- Then multiply the fractions (multiply tops and multiply bottoms)
- Cancel the final answer (if possible)
Worked example
Divide by , giving your answer as a mixed number
Rewrite as an improper fraction
Turn the division into a multiplication, using the fact that dividing by a fraction is the same as multiplying by its reciprocal
Multiply the fractions
Simplify the fraction, by dividing the numerator and denominator by 4
Rewrite as a mixed number
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