Adding and Subtracting Fractions with Unlike Denominators — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
To subtract 34 − 13, the LCD is 8 so the answer is 68 − 28 = 48.
Corrected: To subtract 34 − 13, the LCD is 12 so the answer is 912 − 412 = 512.
The corrected sentence is: "To subtract 34 − 13, the LCD is 12 so the answer is 912 − 412 = 512.". The original sentence "To subtract 34 − 13, the LCD is 8 so the answer is 68 − 28 = 48." contained an error that needed to be fixed.
2. Fix the sentence:
56 − 12 equals 44 because you subtract both the numerators and denominators.
Corrected: 56 − 12 equals 56 − 36 = 26, which simplifies to 13.
The corrected sentence is: "56 − 12 equals 56 − 36 = 26, which simplifies to 13.". The original sentence "56 − 12 equals 44 because you subtract both the numerators and denominators." contained an error that needed to be fixed.
3. Fix the sentence:
The difference of 78 − 14 is 58 because you subtract 1 from 7 and keep the 8.
Corrected: The difference of 78 − 14 is 78 − 28 = 58 after converting 14 to 28.
The corrected sentence is: "The difference of 78 − 14 is 78 − 28 = 58 after converting 14 to 28.". The original sentence "The difference of 78 − 14 is 58 because you subtract 1 from 7 and keep the 8." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The LCD of 56 and 14 is 12.
The LCD of 6 and 4 is 12 because 12 is the smallest number divisible by both 6 and 4 (6×2=12, 4×3=12).
2. 34 − 16 = 912 − 212 = 712.
Convert to LCD 12: 34 = 912 and 16 = 212. Then 912 − 212 = 712.
3. To subtract 23 − 15, rewrite 23 as 10 15 .
23 = 1015 because 2×5=10 and 3×5=15. So 1015 − 315 = 715.
4. 710 − 15 = 710 − 210 = 12 in simplest form.
15 = 210 using LCD 10. Then 710 − 210 = 510 = 12 in simplest form.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. What happens if you forget to find the LCD before subtracting fractions?
Sample answer: You get a wrong answer because you are subtracting parts of different sizes.
Subtracting fractions with unlike denominators without converting gives an incorrect result because the fractional parts represent different-sized pieces.
2. What is 56 − 19? Show your final answer in simplest form.
Sample answer: The answer is 1318 because 1518 − 218 = 1318.
LCD of 6 and 9 is 18. Rename: 56 = 1518, 19 = 218. Difference = 1518 − 218 = 1318. Already in simplest form.