Comparing Fractions — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
In Grade 3, I said 1/4 is greater than 1/3 because 4 is bigger than 3.
Corrected: In Grade 3, 1/3 is greater than 1/4 because thirds are bigger pieces than fourths.
When the whole is cut into 3 parts, each part is larger than when it is cut into 4 parts, so 1/3 > 1/4.
2. Fix the sentence:
In Grade 3, I wrote 1/5 is greater than 1/2 because 5 is more than 2.
Corrected: In Grade 3, 1/2 is greater than 1/5 because halves are bigger pieces than fifths.
Same numerator means we take one piece from each; halves are larger pieces than fifths, so 1/2 > 1/5.
3. Fix the sentence:
In Grade 3, I said 2/8 equals 2/3 because both numerators are 2.
Corrected: In Grade 3, 2/3 is greater than 2/8 because thirds are bigger pieces than eighths.
Two bigger pieces are more than two smaller pieces, so 2/3 > 2/8.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In Grade 3, between 1/3 and 1/4, the greater fraction is 1/3.
Thirds are larger than fourths, so 1/3 > 1/4.
2. In Grade 3, between 1/2 and 1/5, the smaller fraction is 1/5.
Fifths are smaller pieces than halves, so 1/5 < 1/2.
3. In Grade 3, 2/3 compared to 2/8 is greater because thirds are bigger than eighths.
Two thirds cover more of the whole than two eighths, so 2/3 > 2/8.
4. In Grade 3, with the same numerator 3, the greater fraction between 3/4 and 3/6 is 3/4.
Three bigger pieces (fourths) cover more than three smaller pieces (sixths), so 3/4 > 3/6.
Part C: True or False?
Read each statement. Circle True or False.
1. In Grade 3, when two fractions have the same numerator, the one with the smaller denominator is greater.
True False
Fewer equal parts in the whole make each part larger, so the fraction names more of the whole.
2. In Grade 3, 1/8 is greater than 1/2 because 8 is bigger than 2.
True False
Halves are much bigger pieces than eighths, so 1/2 > 1/8.
3. In Grade 3, 2/5 is greater than 2/10 because fifths are bigger pieces than tenths.
True False
Two fifths cover more of the whole than two tenths, since fifths are larger pieces.