Adding and Subtracting Fractions with Unlike Denominators — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. What is 323 + 258 expressed as a mixed number in simplest form?
A) 6724
B) 53124
C) 5711
D) 613
The LCD of 3 and 8 is 24. Convert to 31624 + 21524, then add whole numbers (3 + 2 = 5) and fractions (1624 + 1524 = 3124 = 1724), giving 5 + 1724 = 6724.
2. A student wrote: 415 − 134 = 3420 − 11520 = 2920. Which part has an error?
A) The LCD should be 9, not 20
B) 420 should be regrouped as 2420 before subtracting
C) 1520 is the wrong conversion for 34
D) No step has an error
After converting to twentieths, 420 is smaller than 1520, so the student needed to borrow 1 whole (2020) from the 3 to make it 22420, then subtract 1520 to get 2920. The student skipped the regrouping step.
3. What is 79 + 512 expressed in simplest form?
A) 4336
B) 1736
C) 1221
D) 43
The LCD of 9 and 12 is 36. Rewrite as 2836 + 1536 = 4336, which converts to the mixed number 1736 since 43 divided by 36 is 1 remainder 7.
4. To find 616 − 4710, what is the LCD and the regrouped form of 616?
A) LCD = 30, regroup as 53530
B) LCD = 60, regroup as 57060
C) LCD = 30, regroup as 6530
D) LCD = 16, regroup as 51716
The LCD of 6 and 10 is 30. Converting 16 gives 530, which is less than 2130 (from 710), so borrow 1 whole (3030) from 6 to get 53530.
Part B: Fill in the Blank
Write the correct answer on each line.
1. 514 + 323 = 5312 + 3812 = 81112 in simplest form.
The LCD of 4 and 3 is 12. Add 5312 + 3812: whole numbers give 8, fractions give 1112. Since 11 and 12 share no factors, 81112 is already simplest.
2. 913 − 456 = 886 − 456 = 412 in simplest form.
Convert 13 to 26. Since 26 < 56, borrow 1 (= 66) from 9 to get 886. Then 886 − 456 = 436, which simplifies to 412.
3. The LCD of 4, 5, and 10 is 20.
The multiples of 4 include 20, the multiples of 5 include 20, and 10 divides into 20 evenly, so 20 is the smallest number all three denominators share.
4. 34 + 25 − 110 = 1520 + 820 − 220 = 1120 as a mixed number.
Using the LCD of 20, compute 1520 + 820 − 220 = 2120. Since 2120 is improper, convert to 1120.
5. 1018 − 635 = 10540 − 62440 = 32140 in simplest form.
The LCD of 8 and 5 is 40. Since 540 < 2440, borrow 1 (= 4040) from 10 to get 94540. Then 94540 − 62440 = 32140, which is already in simplest form.