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:
To find an equivalent fraction for 56, multiply only the numerator by 3 to get 156.
Corrected: To find an equivalent fraction for 56, multiply both the numerator and denominator by 3 to get 1518.
The corrected sentence is: "To find an equivalent fraction for 56, multiply both the numerator and denominator by 3 to get 1518." The error was only multiplied numerator: the original sentence "To find an equivalent fraction for 56, multiply only the numerator by 3 to get 156." needed to be fixed.
2. Fix the sentence:
47 is greater than 57 because 4 comes before 5.
Corrected: 47 is less than 57 because 4 sevenths is fewer than 5 sevenths.
The corrected sentence is: "47 is less than 57 because 4 sevenths is fewer than 5 sevenths." The error was reversed comparison with same denominator: the original sentence "47 is greater than 57 because 4 comes before 5." needed to be fixed.
3. Fix the sentence:
915 simplified is 33 because you divide 9 by 3 and 15 by 5.
Corrected: 915 simplified is 35 because you divide both 9 and 15 by 3.
The corrected sentence is: "915 simplified is 35 because you divide both 9 and 15 by 3." The error was used different divisors for numerator and denominator: the original sentence "915 simplified is 33 because you divide 9 by 3 and 15 by 5." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. 25 = 6 15 .
Since 5 × 3 = 15, multiply the numerator 2 by 3 as well: 2 × 3 = 6, so 25 = 615.
2. 1218 in simplest form is 23.
The GCF of 12 and 18 is 6. Divide both: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 23.
3. To compare 23 and 35, a common denominator you could use is 15.
The LCM of 3 and 5 is 15, so 15 works as a common denominator: 23 = 1015 and 35 = 915.
4. 48 = 1 2 .
Divide both parts of 48 by 4: 4 ÷ 4 = 1 and 8 ÷ 4 = 2, so 48 = 12.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. Explain why 34 and 68 are equivalent fractions.
Sample answer: If you multiply 34 by 22, you get 68. Since you multiplied both the numerator and denominator by the same number, the value stays the same.
A good answer includes: If you multiply 34 by 22, you get 68. Since you multiplied both the numerator and denominator by the same number, the value stays the same.
2. Is 512 greater than or less than 12? How do you know?
Sample answer: 512 is less than 12 because 12 equals 612, and 512 is less than 612.
A good answer includes: 512 is less than 12 because 12 equals 612, and 512 is less than 612.