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 13 + 14, you add the numerators and the denominators to get 27.
Corrected: To add 13 + 14, you find a common denominator of 12 and get 412 + 312 = 712.
The corrected sentence is: "To add 13 + 14, you find a common denominator of 12 and get 412 + 312 = 712.". The original sentence "To add 13 + 14, you add the numerators and the denominators to get 27." contained an error that needed to be fixed.
2. Fix the sentence:
The sum of 25 + 13 is 315 because 2 + 1 = 3 and the LCD is 15.
Corrected: The sum of 25 + 13 is 1115 because 615 + 515 = 1115.
The corrected sentence is: "The sum of 25 + 13 is 1115 because 615 + 515 = 1115.". The original sentence "The sum of 25 + 13 is 315 because 2 + 1 = 3 and the LCD is 15." contained an error that needed to be fixed.
3. Fix the sentence:
When you add 12 + 16, the answer is 46 which simplifies to 24.
Corrected: When you add 12 + 16, the answer is 46 which simplifies to 23.
The corrected sentence is: "When you add 12 + 16, the answer is 46 which simplifies to 23.". The original sentence "When you add 12 + 16, the answer is 46 which simplifies to 24." 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 least common denominator of 14 and 16 is 12.
The LCD of 4 and 6 is 12 because 12 is the smallest number that both 4 and 6 divide into evenly (4×3=12, 6×2=12).
2. 13 + 15 = 515 + 315 = 815.
Convert both fractions to LCD 15: 13 = 515 and 15 = 315. Then 515 + 315 = 815.
3. To add 38 + 14, rewrite 14 as 2 8 .
14 = 28 because 1×2=2 and 4×2=8. So 38 + 28 = 58.
4. 25 + 110 = 410 + 110 = 12 in simplest form.
410 + 110 = 510, which simplifies to 12 by dividing both numerator and denominator by 5.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why you need a common denominator before adding fractions.
Sample answer: Fractions must have the same denominator so the parts are equal sizes and can be combined.
The denominator tells you the size of each fractional part. You must have equal-size parts before you can combine them by adding numerators.
2. What is 14 + 23? Show your final answer in simplest form.
Sample answer: The answer is 1112 because 312 + 812 = 1112.
LCD of 4 and 3 is 12. Rename: 14 = 312, 23 = 812. Sum = 312 + 812 = 1112. Already in simplest form.