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:
59 + 39 = 818.
Corrected: 59 + 39 = 89 because you add the numerators and the denominator stays 9.
The original wrote 818 by adding the denominators together. With like fractions, the denominator stays the same -- just add numerators: 5 + 3 = 8, so the correct answer is 89.
2. Fix the sentence:
67 − 37 = 30.
Corrected: 67 − 37 = 37 because you subtract only the numerators and keep the denominator 7.
The original got 30 by subtracting the denominators (7 − 7). Only the numerators should be subtracted: 6 − 3 = 3, and the denominator stays 7, so the answer is 37.
3. Fix the sentence:
210 + 610 = 820.
Corrected: 210 + 610 = 810 because like fractions share the same denominator, so it does not change.
The original incorrectly added the denominators (10 + 10 = 20). Because both fractions are tenths, you keep 10 as the denominator and add numerators: 2 + 6 = 8, so it should be 810.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 15 + 35 = 45.
Both fractions have fifths as the denominator, so add the numerators: 1 + 3 = 4, giving 45.
2. 1012 − 712 = 312.
Keep the denominator 12 and subtract the numerators: 10 − 7 = 3, so the answer is 312.
3. 311 + 511 = 811.
Since both fractions already share the denominator 11, just add the tops: 3 + 5 = 8, making 811.
4. 89 − 69 = 29.
The denominator stays 9 because these are like fractions, and 8 − 6 = 2, so the difference is 29.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. What is 610 + 410? Can the answer be written as a whole number?
Sample answer: 610 + 410 = 1010, which equals 1 whole. Whenever the numerator and denominator are the same, the fraction equals 1.
Add the numerators: 6 + 4 = 10, giving 1010. Since the numerator and denominator are both 10, the fraction equals exactly 1 whole.
2. A pizza is cut into 8 equal slices. You eat 38 and your friend eats 28. How much is left?
Sample answer: First add the eaten slices: 38 + 28 = 58. Then subtract from the whole: 88 − 58 = 38. There are 38 of the pizza left.
First find how much was eaten: 38 + 28 = 58. The whole pizza is 88, so subtract: 88 − 58 = 38 of the pizza remains.