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 add 25 + 14, the LCD is 10 so the answer is 410 + 210 = 610.
Corrected: To add 25 + 14, the LCD is 20 so the answer is 820 + 520 = 1320.
The LCD of 5 and 4 is 20, not 10, because 20 is the smallest number both 5 and 4 divide into evenly. Multiplying 25 by 44 gives 820 and 14 by 55 gives 520, so the correct sum is 1320.
2. Fix the sentence:
38 − 16 equals 22, which is 1, because you subtract both the top and bottom numbers.
Corrected: 38 − 16 = 924 − 424 = 524 after finding the LCD of 24.
You cannot subtract numerators and denominators separately. The LCD of 8 and 6 is 24, so rewrite as 924 − 424 = 524.
3. Fix the sentence:
12 + 310 = 410 + 310 = 710, but 710 simplifies to 75.
Corrected: 12 + 310 = 510 + 310 = 810, which simplifies to 45.
12 equals 510 (multiply by 55), not 410. Adding 510 + 310 gives 810, which simplifies to 45 because both 8 and 10 are divisible by 2.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The least common denominator of 13 and 18 is 24.
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24 and the multiples of 8 are 8, 16, 24. The smallest number they share is 24, so the LCD is 24.
2. 27 + 12 = 414 + 714 = 1114.
With the LCD of 14, convert 27 to 414 and 12 to 714. Adding the numerators gives 4 + 7 = 11, so the sum is 1114.
3. To subtract 56 − 19, rewrite 56 as 15 18 .
Since the LCD of 6 and 9 is 18, multiply 56 by 33 to get 1518. The numerator becomes 15 because 5 times 3 equals 15.
4. 34 − 28 = 68 − 28 = 12 in simplest form.
Converting 34 to 68 and subtracting gives 68 − 28 = 48. Since 4 and 8 share a factor of 4, simplify to 12.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. What is 35 + 14? Show each step and give your answer in simplest form.
Sample answer: The LCD is 20. Rewrite as 1220 + 520 = 1720. The answer is 1720.
A good answer includes: The LCD is 20. Rewrite as 1220 + 520 = 1720. The answer is 1720.
2. Why is the least common denominator usually better to use than any common denominator?
Sample answer: Using the LCD keeps the numbers smaller, making the math easier and reducing the need to simplify at the end.
A good answer includes: Using the LCD keeps the numbers smaller, making the math easier and reducing the need to simplify at the end.