Adding & Subtracting Fractions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
25 + 15 = 310.
Corrected: 25 + 15 = 35 because you add only the numerators and keep the denominator.
The corrected sentence is: "25 + 15 = 35 because you add only the numerators and keep the denominator.". The original sentence "25 + 15 = 310." contained an error that needed to be fixed.
2. Fix the sentence:
58 − 28 = 30.
Corrected: 58 − 28 = 38 because you subtract the numerators and keep the denominator.
The corrected sentence is: "58 − 28 = 38 because you subtract the numerators and keep the denominator.". The original sentence "58 − 28 = 30." contained an error that needed to be fixed.
3. Fix the sentence:
46 + 16 = 512.
Corrected: 46 + 16 = 56 because the denominator stays the same when adding like fractions.
The corrected sentence is: "46 + 16 = 56 because the denominator stays the same when adding like fractions.". The original sentence "46 + 16 = 512." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 37 + 27 = 57.
Add the numerators: 3 + 2 = 5. Keep the denominator 7. Answer: 57.
2. 69 − 49 = 29.
Subtract the numerators: 6 − 4 = 2. Keep the denominator 9. Answer: 29.
3. 14 + 24 = 34.
Add the numerators: 1 + 2 = 3. Keep the denominator 4. Answer: 34.
4. 710 − 310 = 410.
Subtract the numerators: 7 − 3 = 4. Keep the denominator 10. Answer: 410.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Why does the denominator stay the same when you add 25 + 15?
Sample answer: The denominator tells the size of each piece. Since both fractions are fifths, you are adding pieces of the same size, so the denominator remains 5.
When fractions have like denominators, only the numerators are added because the piece sizes are already the same.
2. Show how to solve 56 − 26 and explain each step.
Sample answer: Subtract the numerators: 5 − 2 = 3. Keep the denominator 6. The answer is 36, which simplifies to 12.
Subtracting fractions with like denominators: subtract numerators, keep denominator, simplify if possible.