Foundations
Add and subtract fractions
ALEKS · foundation repairTEAS math
You can only add fractions that are cut into the same size pieces.
What this covers
ba+dc=bdad+bc- Find the least common denominator — the smallest number both denominators divide into.
- To find it, count up by the larger denominator until you reach a number the smaller denominator also divides into. For 6 and 4, that is 12.
- Multiplying the two denominators always gives a common denominator, but it can leave a larger fraction to reduce later.
- Rescale each fraction by multiplying its top and bottom by the same factor. Same factor on both keeps its value unchanged; that is the whole trick.
- Add or subtract the numerators only — the top numbers. The denominator, the bottom number, does not change.
- Reduce by the greatest common factor: list both numbers’ factors, choose the largest match, and divide the top and bottom by it.
- For example, 121/143 = 11/13 after dividing both by 11. A shared factor can be larger than 7.
- Why the bottoms never add: one half plus one half makes one whole, but adding tops and bottoms gives 2/4, which is only a half.
Worked example
Worked example
Add 5/6 + 3/4.
- 1210+129The LCD of 6 and 4 is 12, so scale by 2 and by 3.
- 1219Add the numerators and keep the denominator.
Another worked example
Add 5/9 + 7/9.
- 95+97=95+7=912Both fractions count ninths already. Add the counts of pieces and keep the piece size.
- 912=3⋅33⋅4=34Divide the top and bottom by their common factor 3.
A common mistake
A mistake Lemma catches
From 1210+129
1210+129=24191210+129=1219
“The denominators were added: 12 + 12 = 24. The denominator names the size of the pieces — twelfths — and twelfths added to twelfths are still twelfths. Add only the numerators: 10 + 9 = 19, so the sum is 19/12.”
Try one
Sample problem
Add and simplify.
65+61Practice fraction sums free
No account, no email. Every line you type is checked by the same computer algebra system as the worked example above.
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