Comparing Fractions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. In Grade 3, 6/8 compared to 1/2 using the benchmark 4/8 gives 6/8 > 1/2.
6/8 has more eighths than 4/8, and 4/8 = 1/2, so 6/8 > 1/2.
2. In Grade 3, 2/10 compared to 1/2 using the benchmark 5/10 gives 2/10 < 1/2.
2/10 is fewer tenths than 5/10, and 5/10 = 1/2, so 2/10 < 1/2.
3. In Grade 3, 3/3 equals the benchmark 1 because all three thirds make one whole.
3 thirds cover the entire whole, so 3/3 = 1.
4. In Grade 3, 0/5 equals the benchmark 0 because zero fifths are shaded.
0/5 has zero pieces out of five, which equals 0.
5. In Grade 3, between 1/4 and 3/4, the fraction closer to 1/2 is 1/4.
1/4 is only 1/4 away from 2/4, while 3/4 is 1/4 away too, but 1/4 is less than 1/2 and 3/4 is more; both are equally close to 1/2, but 1/4 is the closer choice below 1/2.
6. In Grade 3, 5/6 is closer to the benchmark 1 than to 1/2.
5/6 sits just below 1, so it is closer to 1 than to 1/2.
7. In Grade 3, 2/6 equals 1/3 when simplified using a benchmark comparison to 1/3.
2/6 simplifies to 1/3 because both 2 and 6 share a factor of 2.
8. In Grade 3, compare 5/8 and 1/2 using 4/8: 5/8 > 1/2.
5/8 has one more eighth than 4/8, so 5/8 > 1/2.
9. In Grade 3, compare 3/4 and 3/10: 3/4 > 3/10.
Fourths are bigger pieces than tenths, so 3/4 > 3/10.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
In Grade 3, 1/12 is nearest to
→ 0
0
In Grade 3, 5/10 equals
→ 1/2
1/2
In Grade 3, 8/8 equals
→ 1
1
In Grade 3, 7/8 is nearest to
→ about 1 but not equal
about 1 but not equal
1/12 is tiny, so it is close to 0; 5/10 simplifies to 1/2; 8/8 is a whole, so it equals 1; 7/8 is only 1/8 from 1, so it is near but not equal to 1.