Students fix three simplification and equivalence errors — 4/10 simplified to 2/10, 5/8 called less than 3/8, and an incorrect multiplier creating a non-equivalent fraction. Part B has four fill-in-the-blank questions about simplifying 6/9, completing 3/4 = 6/__, and identifying the benchmark closest to 5/12. Part C has two short-answer questions about lowest terms and whether 7/10 is closer to 1/2 or 1.
Benchmark fraction reasoning gives students a quick estimation tool before they apply the formal comparison process.
Style:
Equivalent Fractions & Comparing
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
410 in simplest form is 210.
Rewrite: 410 in simplest form is 25 because you divide both parts by 2.
2. Fix the sentence:
58 is less than 38.
Rewrite: 58 is greater than 38 because 5 eighths is more than 3 eighths.
3. Fix the sentence:
23 = 612 because you multiply 2 by 3 and 3 by 4.
Rewrite: 23 = 69 because you multiply both the numerator and denominator by 3.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 69 in simplest form is 23.
2. 34 = 6 8 .
3. The benchmark fraction closest to 512 is 12.
4. 1015 in simplest form is 23.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How do you simplify a fraction to its lowest terms?
Divide both the numerator and the denominator by their greatest common factor.
2. Is 710 closer to 12 or to 1? Explain.
710 is closer to 12 than to 1, but actually 710 = 0.7 and 12 = 0.5, so it is closer to 12 by 0.2 vs 0.3 from 1.
Equivalent Fractions & Comparing
★ Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1) Fix the sentence:
4/10 in simplest form is 2/10.
Rewrite: 4/10 in simplest form is 2/5 because you divide both parts by 2.
2) Fix the sentence:
5/8 is less than 3/8.
Rewrite: 5/8 is greater than 3/8 because 5 eighths is more than 3 eighths.
3) Fix the sentence:
2/3 = 6/12 because you multiply 2 by 3 and 3 by 4.
Rewrite: 2/3 = 6/9 because you multiply both the numerator and denominator by 3.
★ Part B: Fill in the Blank
Write the missing word or number on each line.
1) 6/9 in simplest form is 2/3.
2) 3/4 = 6/8.
3) The benchmark fraction closest to 5/12 is 1/2.
4) 10/15 in simplest form is 2/3.
★ Part C: Short Answer
Answer each question in one or two complete sentences.
1) How do you simplify a fraction to its lowest terms?
Divide both the numerator and the denominator by their greatest common factor.
2) Is 7/10 closer to 1/2 or to 1? Explain.
7/10 is closer to 1/2 than to 1, but actually 7/10 = 0.7 and 1/2 = 0.5, so it is closer to 1/2 by 0.2 vs 0.3 from 1.
Ready to Practice?
Complete each section carefully.
9 Questions
15-20 minutes
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