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:
49 + 16 = 818 + 318 = 1118, and 1118 simplifies to 12.
Corrected: 49 + 16 = 818 + 318 = 1118, and 1118 is already in simplest form.
The addition 818 + 318 = 1118 is correct, but 1118 does not simplify to 12. Since 11 is prime and does not divide evenly into 18, 1118 is already in simplest form.
2. Fix the sentence:
To subtract 58 − 16, you can use any denominator, so 516 − 116 = 416.
Corrected: To subtract 58 − 16, use the LCD of 24 to get 1524 − 424 = 1124.
You must use the LCD, not just any denominator. The LCD of 8 and 6 is 24, so 58 becomes 1524 and 16 becomes 424, giving 1524 − 424 = 1124.
3. Fix the sentence:
The sum 13 + 29 = 39 + 29 = 59, and this equals 12 in simplest form.
Corrected: The sum 13 + 29 = 39 + 29 = 59, and 59 is already in simplest form.
The math 13 = 39 and 39 + 29 = 59 is correct, but 59 does not equal 12. Since 5 and 9 share no common factors, 59 is already in simplest form.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. The LCD of 15 and 17 is 35.
Since 5 and 7 are both prime and share no common factors, their LCD is simply 5 times 7, which equals 35.
2. 310 + 14 = 620 + 520 = 1120.
With the LCD of 20, multiply 310 by 22 to get 620 and 14 by 55 to get 520. Adding the numerators gives 6 + 5 = 11, so the answer is 1120.
3. To add 16 + 38, rewrite 16 as 4 24 .
The LCD of 6 and 8 is 24. To convert 16, multiply by 44 because 24 divided by 6 is 4, making the numerator 1 times 4 = 4.
4. 56 − 34 = 1012 − 912 = 112 in simplest form.
Converting to the LCD of 12 gives 1012 − 912 = 112. Since 1 and 12 share no common factor besides 1, the answer is already in simplest form.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How can you tell whether a fraction answer needs to be simplified?
Sample answer: Check if the numerator and denominator share a common factor greater than 1. If they do, divide both by that factor.
A good answer includes: Check if the numerator and denominator share a common factor greater than 1. If they do, divide both by that factor.
2. What is 710 − 215? Show your work and simplify if possible.
Sample answer: The LCD is 30. Rewrite as 2130 − 430 = 1730. The answer is 1730.
A good answer includes: The LCD is 30. Rewrite as 2130 − 430 = 1730. The answer is 1730.