Students correct three addition errors — adding denominators to get 2/7, computing a wrong numerator with a correct LCD, and simplifying 4/6 as 2/4 instead of 2/3. Part B has four fill-in-the-blank questions about LCD, a 1/3 + 1/5 computation, and converting 1/4 to eighths. Part C has two short-answer questions about why a common denominator is needed and computing 1/4 + 2/3.
Correcting the add-the-denominators error targets the misunderstanding behind the majority of unlike-denominator fraction errors at Grade 5.
Style:
Adding and Subtracting Fractions with Unlike Denominators
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.
Rewrite: To add 13 + 14, you find a common denominator of 12 and get 412 + 312 = 712.
2. Fix the sentence:
The sum of 25 + 13 is 315 because 2 + 1 = 3 and the LCD is 15.
Rewrite: The sum of 25 + 13 is 1115 because 615 + 515 = 1115.
3. Fix the sentence:
When you add 12 + 16, the answer is 46 which simplifies to 24.
Rewrite: When you add 12 + 16, the answer is 46 which simplifies to 23.
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.
2. 13 + 15 = 515 + 315 = 815.
3. To add 38 + 14, rewrite 14 as 2 8 .
4. 25 + 110 = 410 + 110 = 12 in simplest form.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why you need a common denominator before adding fractions.
Fractions must have the same denominator so the parts are equal sizes and can be combined.
2. What is 14 + 23? Show your final answer in simplest form.
The answer is 1112 because 312 + 812 = 1112.
Adding and Subtracting Fractions with Unlike Denominators
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
To add 1/3 + 1/4, you add the numerators and the denominators to get 2/7.
Rewrite: To add 1/3 + 1/4, you find a common denominator of 12 and get 4/12 + 3/12 = 7/12.
2) Fix the sentence:
The sum of 2/5 + 1/3 is 3/15 because 2 + 1 = 3 and the LCD is 15.
Rewrite: The sum of 2/5 + 1/3 is 11/15 because 6/15 + 5/15 = 11/15.
3) Fix the sentence:
When you add 1/2 + 1/6, the answer is 4/6 which simplifies to 2/4.
Rewrite: When you add 1/2 + 1/6, the answer is 4/6 which simplifies to 2/3.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) The least common denominator of 1/4 and 1/6 is 12.
2) 1/3 + 1/5 = 5/15 + 3/15 = 8/15.
3) To add 3/8 + 1/4, rewrite 1/4 as 2/8.
4) 2/5 + 1/10 = 4/10 + 1/10 = 1/2 in simplest form.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) Explain why you need a common denominator before adding fractions.
Fractions must have the same denominator so the parts are equal sizes and can be combined.
2) What is 1/4 + 2/3? Show your final answer in simplest form.
The answer is 11/12 because 3/12 + 8/12 = 11/12.
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Complete each section carefully.
9 Questions
15-20 minutes
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