Step into the world of unlike denominators with three error-fix sentences that catch the classic traps: claiming the LCD of 2/5 + 1/4 is 10, subtracting both numerators and denominators in 3/8 - 1/6, and falsely simplifying 7/10 to 7/5. Then fill in the LCD of 1/3 and 1/8, finish 2/7 + 1/2 = 4/14 + 7/14, and rewrite 5/6 over an 18 denominator.
Two short-answer questions ask you to walk through 3/5 + 1/4 step by step and explain why the least common denominator beats any old common multiple. By the end, fifth graders will have nailed down the full LCD process and learned to spot denominator mistakes the moment they appear.
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 25 + 14, the LCD is 10 so the answer is 410 + 210 = 610.
Rewrite: To add 25 + 14, the LCD is 20 so the answer is 820 + 520 = 1320.
2. Fix the sentence:
38 − 16 equals 22, which is 1, because you subtract both the top and bottom numbers.
Rewrite: 38 − 16 = 924 − 424 = 524 after finding the LCD of 24.
3. Fix the sentence:
12 + 310 = 410 + 310 = 710, but 710 simplifies to 75.
Rewrite: 12 + 310 = 510 + 310 = 810, which simplifies to 45.
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.
2. 27 + 12 = 414 + 714 = 1114.
3. To subtract 56 − 19, rewrite 56 as 15 18 .
4. 34 − 28 = 68 − 28 = 12 in simplest form.
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.
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?
Using the LCD keeps the numbers smaller, making the math easier and reducing the need to simplify at the end.
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 2/5 + 1/4, the LCD is 10 so the answer is 4/10 + 2/10 = 6/10.
Rewrite: To add 2/5 + 1/4, the LCD is 20 so the answer is 8/20 + 5/20 = 13/20.
2) Fix the sentence:
3/8 − 1/6 equals 2/2, which is 1, because you subtract both the top and bottom numbers.
Rewrite: 3/8 − 1/6 = 9/24 − 4/24 = 5/24 after finding the LCD of 24.
3) Fix the sentence:
1/2 + 3/10 = 4/10 + 3/10 = 7/10, but 7/10 simplifies to 7/5.
Rewrite: 1/2 + 3/10 = 5/10 + 3/10 = 8/10, which simplifies to 4/5.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) The least common denominator of 1/3 and 1/8 is 24.
2) 2/7 + 1/2 = 4/14 + 7/14 = 11/14.
3) To subtract 5/6 − 1/9, rewrite 5/6 as 15/18.
4) 3/4 − 2/8 = 6/8 − 2/8 = 1/2 in simplest form.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) What is 3/5 + 1/4? Show each step and give your answer in simplest form.
The LCD is 20. Rewrite as 12/20 + 5/20 = 17/20. The answer is 17/20.
2) Why is the least common denominator usually better to use than any common denominator?
Using the LCD keeps the numbers smaller, making the math easier and reducing the need to simplify at the end.
Ready to Practice?
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9 Questions
15-20 minutes
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