Adding and Subtracting Fractions with Unlike Denominators — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. What is 56 + 38 − 14 expressed in simplest form?
A) 2324
B) 710
C) 1924
D) 1112
LCD of 6, 8, and 4 is 24. 56=2024, 38=924, 14=624. So 2024+924−624=2324.
2. Maria ran 34 + 56 mi. Which LCD conversion is correct?
A) 912 + 1012
B) 310 + 510
C) 812 + 1012
D) 68 + 58
LCD of 4 and 6 is 12. 34=912 (×3) and 56=1012 (×2). So the correct conversion is 912 + 1012 = 1912 = 1712 miles.
3. Which step is WRONG? 23+49 → LCD=9 → 69+49 → 109 → 119
A) LCD=9 is wrong
B) 69 conversion is wrong
C) 109 is wrong
D) No step is wrong
All steps are correct. LCD of 3 and 9 is 9. 23 = 69. 69 + 49 = 109 = 119. The entire solution is accurate.
4. To subtract 712 − 29, you use LCD=36. What are the renamed fractions?
A) 2136 and 836
B) 1436 and 636
C) 736 and 236
D) 2836 and 836
LCD of 12 and 9 is 36. 712 = 2136 (×3) and 29 = 836 (×4). Difference = 2136 − 836 = 1336.
Part B: Fill in the Blank
Write the correct answer on each line.
1. 23 + 512 + 14 = 812 + 512 + 312 = 113 in simplest form.
LCD of 3, 12, and 4 is 12. 23=812, 512=512, 14=312. Sum=1612=43=113.
2. The LCD of 5, 6, and 10 is 30.
LCM(5,6)=30; 30 is also divisible by 10. So LCD of 5, 6, and 10 is 30.
3. 78 − 13 = 2124 − 824 = 1324 in simplest form.
LCD of 8 and 3 is 24. 78=2124, 13=824. Difference=1324. GCF(13,24)=1, already simplest.
4. If you add 49 + 23, the sum is 119 as a mixed number.
LCD of 9 and 3 is 9. 23=69. Sum=49+69=109=119.
5. 1115 − 25 = 1115 − 615 = 13 in simplest form.
25 = 615 using LCD 15. Then 1115 − 615 = 515 = 13 in simplest form.