Fractions with unlike denominators · Usually met around P5
Three fractions added and taken away
Use the L.C.M. of all three bottoms.
How to do it
Method
Use the L.C.M. of all three bottoms
12 + 13 − 14 = 612 + 412 − 312 = 712
Another way
Two at a time
12 + 13 = 56, 56 − 14 = 712
In full
To add and take away three fractions with different denominators, way 1: give all three a common denominator at once (the L.C.M. of the three bottoms) and work left to right: 12 + 13 − 14 = 612 + 412 − 312 = 712. Way 2: work left to right two at a time: 12 + 13 = 56, then 56 − 14 = 1012 − 312 = 712. Brackets come first; with a minus before a bracket, opening it flips the signs inside: a − (b − c) = a − b + c. Give the answer in its simplest form.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
15 + 12 + 19 = ?
Answer in simplest form
Show the answer and working
Answer: 7390
The L.C.M. of the three bottoms is 90; add the tops over 90 and simplify: 7390.
Example 2
23 − 19 − 25 = ?
Answer in simplest form
Show the answer and working
Answer: 745
Over a common denominator of 45, take away left to right: 745.
Example 3
Working out 14 + 15 − 16, which is the smallest common denominator?
- A. 120
- B. 15
- C. 6
- D. 60
Choose the right answer
Show the answer and working
Answer: D. 60
The L.C.M. of 4, 5 and 6 is 60.
Practise it in the game →Fractions with unlike denominators · Free to start, unlimited questions, no download