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:
38 + 48 = 716.
Corrected: 38 + 48 = 78 because the denominator stays 8 when adding like fractions.
The corrected sentence is: "38 + 48 = 78 because the denominator stays 8 when adding like fractions.". The original sentence "38 + 48 = 716." contained an error that needed to be fixed.
2. Fix the sentence:
912 − 512 = 40.
Corrected: 912 − 512 = 412 because you subtract the numerators and keep the denominator 12.
The corrected sentence is: "912 − 512 = 412 because you subtract the numerators and keep the denominator 12.". The original sentence "912 − 512 = 40." contained an error that needed to be fixed.
3. Fix the sentence:
23 + 13 = 36.
Corrected: 23 + 13 = 33, which equals 1 whole.
The corrected sentence is: "23 + 13 = 33, which equals 1 whole.". The original sentence "23 + 13 = 36." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 512 + 312 = 812.
Add the numerators: 5 + 3 = 8. Keep the denominator 12. Answer: 812.
2. 810 − 510 = 310.
Subtract the numerators: 8 − 5 = 3. Keep the denominator 10. Answer: 310.
3. 16 + 46 = 56.
Add the numerators: 1 + 4 = 5. Keep the denominator 6. Answer: 56.
4. 78 − 38 = 48.
Subtract the numerators: 7 − 3 = 4. Keep the denominator 8. Answer: 48 (= 12).
Part C: Short Answer
Answer each question in one or two complete sentences.
1. If you add 45 + 15, what do you get and can you simplify it?
Sample answer: 45 + 15 = 55, which equals 1 whole. Since the numerator equals the denominator, the fraction simplifies to 1.
When the numerator and denominator are equal, the fraction equals 1 whole.
2. Explain why 69 − 29 = 49 and not 40.
Sample answer: You only subtract the numerators: 6 − 2 = 4. The denominator 9 stays the same because the size of each piece does not change.
The denominator represents piece size, which never changes when adding or subtracting fractions with like denominators.