Equivalent Fractions & Comparing — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The LCD of 4 and 6 is 12.
List multiples of 4 (4, 8, 12...) and 6 (6, 12...). The smallest shared multiple is 12, so the LCD is 12.
2. 34 = 9 12 and 56 = 10 12 , so 34 is less than 56.
Multiply 34 by 33 to get 912. Then 56 = 1012, so 34 (912) is less than 56 (1012).
3. 710 = 14 20 .
Since 10 × 2 = 20, multiply the numerator by 2 as well: 7 × 2 = 14, so 710 = 1420.
4. The mixed number 249 as an improper fraction is 229.
Multiply the whole number by the denominator and add the numerator: 2 × 9 + 4 = 22, so 249 = 229.
5. 1830 in simplest form is 35.
The GCF of 18 and 30 is 6. Divide both: 18 ÷ 6 = 3 and 30 ÷ 6 = 5, so 1830 = 35.
6. Put >, <, or = : 47 < 35.
Convert to LCD 35: 47 = 2035 and 35 = 2135. Since 20 < 21, 47 < 35.
7. The improper fraction 176 as a mixed number is 256.
Divide 17 by 6: 6 goes into 17 two times (12) with remainder 5, so 176 = 256.
8. The LCD of 9 and 12 is 36.
List multiples of 12 (12, 24, 36...) and 9 (9, 18, 27, 36...). The smallest they share is 36.
9. 2436 in simplest form is 23.
The GCF of 24 and 36 is 12. Divide both: 24 ÷ 12 = 2 and 36 ÷ 12 = 3, so 2436 = 23.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
513
→ 163
167
338
→ 278
256
227
→ 167
278
416
→ 256
163
Correct matches: 513 → 163; 338 → 278; 227 → 167; 416 → 256.