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:
810 and 35 are not equivalent because they have different denominators.
Corrected: 810 and 35 are not equivalent because 810 simplifies to 45, not 35.
The corrected sentence is: "810 and 35 are not equivalent because 810 simplifies to 45, not 35." The error was wrong reason for non-equivalence: the original sentence "810 and 35 are not equivalent because they have different denominators." needed to be fixed.
2. Fix the sentence:
13 is greater than 12 because 3 is greater than 2.
Corrected: 13 is less than 12 because when the numerator is the same, the fraction with the smaller denominator is larger.
The corrected sentence is: "13 is less than 12 because when the numerator is the same, the fraction with the smaller denominator is larger." The error was confused larger denominator with larger fraction: the original sentence "13 is greater than 12 because 3 is greater than 2." needed to be fixed.
3. Fix the sentence:
An equivalent fraction for 37 is 914.
Corrected: An equivalent fraction for 37 is 921 because you multiply both 3 and 7 by 3.
The corrected sentence is: "An equivalent fraction for 37 is 921 because you multiply both 3 and 7 by 3." The error was multiplied numerator by 3 but denominator by 2: the original sentence "An equivalent fraction for 37 is 914." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 38 = 9 24 .
The numerator went from 3 to 9 (×3), so multiply the denominator by 3 too: 8 × 3 = 24.
2. 1421 in simplest form is 23.
The GCF of 14 and 21 is 7. Divide both: 14 ÷ 7 = 2 and 21 ÷ 7 = 3, so 1421 = 23.
3. The GCF of 6 and 9 is 3.
The factors of 6 are 1, 2, 3, 6 and the factors of 9 are 1, 3, 9. The largest factor they share is 3.
4. 56 = 15 18 .
Since 6 × 3 = 18, multiply the numerator by 3 as well: 5 × 3 = 15, so 56 = 1518.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. How can you tell which is greater, 25 or 310, without a calculator?
Sample answer: Rewrite 25 as 410. Since 410 is greater than 310, the fraction 25 is greater.
A good answer includes: Rewrite 25 as 410. Since 410 is greater than 310, the fraction 25 is greater.
2. Why does dividing both parts of a fraction by the same number give an equivalent fraction?
Sample answer: Dividing the numerator and denominator by the same number is the same as dividing by 1, so the fraction keeps the same value.
A good answer includes: Dividing the numerator and denominator by the same number is the same as dividing by 1, so the fraction keeps the same value.