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 2/5 is greater than 3/5 because 2 comes first.
Corrected: In Grade 3, 3/5 is greater than 2/5 because 3 fifths is more than 2 fifths.
When denominators are equal, the fraction with the larger numerator names more equal pieces, so it is greater.
2. Fix the sentence:
In Grade 3, I wrote 4/8 is less than 6/8 because 4 is bigger.
Corrected: In Grade 3, 4/8 is less than 6/8 because 4 eighths is fewer pieces than 6 eighths.
Eighths are equal-size parts, so counting more of them gives a larger fraction; 6/8 has two more eighths than 4/8.
3. Fix the sentence:
In Grade 3, I said 5/6 equals 3/6 because both are sixths.
Corrected: In Grade 3, 5/6 is greater than 3/6 because 5 sixths is more pieces than 3 sixths.
Same denominator only tells us the pieces are the same size; the fraction with more of those pieces is greater, so 5/6 > 3/6.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In Grade 3, compare 3/5 and 2/5. The greater fraction is 3/5.
3 fifths is more pieces than 2 fifths, so 3/5 > 2/5.
2. In Grade 3, 4/8 and 6/8 have the same denominator. The smaller fraction is 4/8.
4 eighths is fewer than 6 eighths, so 4/8 < 6/8.
3. In Grade 3, using the fraction bar, 5/6 is greater than 3/6 because 5 pieces are more than 3 pieces.
With equal sixths, the bar with 5 shaded pieces is longer than the bar with 3 shaded pieces.
4. In Grade 3, 7/10 compared to 4/10 gives the symbol > between them.
7 tenths is more than 4 tenths, so we write 7/10 > 4/10.
Part C: True or False?
Read each statement. Circle True or False.
1. In Grade 3, when two fractions have the same denominator, the one with the greater numerator is greater.
True False
Equal denominators give equal-size parts, so more parts means a larger fraction.
2. In Grade 3, 2/6 is greater than 5/6 because 2 is a smaller number.
True False
Both are sixths, and 5 sixths is more pieces than 2 sixths, so 2/6 < 5/6.
3. In Grade 3, 4/9 equals 4/9 because the numerator and denominator match in both.
True False
When the numerator and denominator are the same in both fractions, the fractions name the same amount.