Adding Fractions with Different Denominators
Question
Answer choices
- 1+1/6+6
- 1/3
- 12/36
- 2/3
- 1/4
B Correct answer: B) 1/3
Set up the problem carefully before computing. Common denominator is the product of the two denominators (or any common multiple). Add the converted numerators, then reduce.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
Find a common denominator: 6 × 6 = 36. Convert: 1/6 = 6/36, 1/6 = 6/36. Sum: 12/36. Simplify by dividing both by gcd 12 to get 1/3.
Why each wrong answer is wrong
- A) 1+1/6+6: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) 12/36: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 2/3: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) 1/4: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
When adding fractions with different denominators, never add numerators and denominators separately. Always convert to a common denominator first.
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