Equivalent Fractions & Comparing — Answer Key
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.
Corrected: 410 in simplest form is 25 because you divide both parts by 2.
The corrected sentence is: "410 in simplest form is 25 because you divide both parts by 2.". The original sentence "410 in simplest form is 210." contained an error that needed to be fixed.
2. Fix the sentence:
58 is less than 38.
Corrected: 58 is greater than 38 because 5 eighths is more than 3 eighths.
The corrected sentence is: "58 is greater than 38 because 5 eighths is more than 3 eighths.". The original sentence "58 is less than 38." contained an error that needed to be fixed.
3. Fix the sentence:
23 = 612 because you multiply 2 by 3 and 3 by 4.
Corrected: 23 = 69 because you multiply both the numerator and denominator by 3.
The corrected sentence is: "23 = 69 because you multiply both the numerator and denominator by 3.". The original sentence "23 = 612 because you multiply 2 by 3 and 3 by 4." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 69 in simplest form is 23.
GCF of 6 and 9 is 3. 6÷3=2, 9÷3=3. Simplest form: 23.
2. 34 = 6 8 .
34 × 22 = 68. Multiply numerator and denominator by 2.
3. The benchmark fraction closest to 512 is 12.
512 ≈ 0.417, and 12 = 0.5. It is closer to 12 than to 0 or 1.
4. 1015 in simplest form is 23.
GCF of 10 and 15 is 5. 10÷5=2, 15÷5=3. Simplest form: 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?
Sample answer: Divide both the numerator and the denominator by their greatest common factor.
Dividing by the GCF reduces a fraction to its simplest form in one step.
2. Is 710 closer to 12 or to 1? Explain.
Sample answer: 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.
710 = 0.7 is 0.3 away from 1 and 0.2 away from 12 — it is closer to 1.