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:
14 + 24 = 38.
Corrected: 14 + 24 = 34 because you add only the numerators and the denominator stays 4.
The original wrote 38 by accidentally adding the denominators (4 + 4). When fractions share a denominator, you only add the numerators: 1 + 2 = 3, so the correct answer is 34.
2. Fix the sentence:
710 − 410 = 30.
Corrected: 710 − 410 = 310 because you subtract the numerators and keep the denominator 10.
The original gave 30 by mistakenly subtracting the denominators (10 − 10). You should only subtract the numerators: 7 − 4 = 3, keeping the denominator 10, so the answer is 310.
3. Fix the sentence:
39 + 59 = 818.
Corrected: 39 + 59 = 89 because both fractions share the denominator 9, so it does not change.
The original doubled the denominator (9 + 9 = 18) instead of keeping it. Since both fractions are ninths, you add only the numerators: 3 + 5 = 8, giving 89.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 26 + 36 = 56.
Since both fractions have the same denominator (6), you add only the numerators: 2 + 3 = 5, giving 56.
2. 912 − 512 = 412.
Both fractions share the denominator 12, so subtract just the numerators: 9 − 5 = 4, which gives 412.
3. 48 + 38 = 78.
The denominators are the same (8), so add the numerators: 4 + 3 = 7, making the answer 78.
4. 67 − 27 = 47.
When fractions have the same denominator, subtract the top numbers: 6 − 2 = 4, so the result is 47.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. If you solve 48 + 48, what is the answer and can it be simplified?
Sample answer: 48 + 48 = 88, which equals 1 whole. Since the numerator and denominator are the same, the fraction simplifies to 1.
Adding the numerators gives 4 + 4 = 8, so 48 + 48 = 88. When the numerator equals the denominator, the fraction equals exactly 1 whole.
2. Explain how to solve 710 − 310 step by step.
Sample answer: Subtract the numerators: 7 − 3 = 4. Keep the denominator 10. The answer is 410, which can be simplified to 25.
Keep the denominator 10 and subtract the numerators: 7 − 3 = 4, so the answer is 410. You can simplify by dividing both by 2 to get 25.