Math Worksheets · Free 13-page pack
Free Comparing Fractions Worksheets PDF
For grades 3-4, this 13-page PDF has six comparison worksheets and an answer key. Students decide which fraction is greater or whether the amounts match by considering the fractions' sizes. The pairs include halves, thirds, fourths, fifths, sixths, sevenths, and eighths.
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Practice this skill on screen30 questions in three levels (easy, medium, hard) with instant feedback. Nothing to install.Get the whole set: 8 packs in one zipFractions worksheet packs. Grades 1–5: identify, compare, add, subtract and simplify fractions. US Letter PDFs with answer keys, 509 KB.
What this printable is for
This comparison pack has 13 pages. The cover opens six practice pages; the key is on pages 8-13. Pages 2, 3, and 7 each present 8 fraction pairs and a Name and Date line. Their denominators range from 2 to 8. Students place a comparison sign between each pair. The other practice pages follow that format for comparing fraction sizes.
Comparing the amounts fractions name
A fraction comparison asks which amount is larger, even when the pieces are described in different ways. If denominators match, compare the numerators because each counted part has the same size. With different denominators, reason about the amount: use a familiar benchmark such as one half, make equivalent forms, or compare on a common-sized model. The digits alone do not tell the whole story because the denominator changes the size of each part.
A useful question is, “How much of the same whole does each fraction cover?” Children can place both quantities on equal-length strips, or reason from one half and one whole. For example, 2/3 is more than 2/5: the same two parts are larger when a whole is split into thirds than when it is split into fifths. The comparison sign should point toward the smaller amount and open toward the larger one.
Worked example 1
Compare 5/7 and 2/6.
Since 5/7 is more than one half and 2/6 is one third, the first amount is larger. A common-size drawing also shows five sevenths covering more than two sixths.
Answer: 5/7 > 2/6
Worked example 2
Compare 2/3 and 2/5.
Both fractions count two parts. Thirds are larger pieces than fifths when the wholes match, so two thirds covers more than two fifths.
Answer: 2/3 > 2/5
Worked example 3
Compare 3/6 and 2/4.
Each fraction names one half: divide numerator and denominator of 3/6 by 3, and of 2/4 by 2. The amounts are equal.
Answer: 3/6 = 2/4
How to teach it with this pack
Use equal length strips
Draw two same-length bars and divide each according to a fraction's denominator. Shade the numerator's number of parts in each bar, then compare the shaded lengths. Equal whole lengths matter: otherwise the visual comparison can be misleading. Ask the learner to explain which bar covers more before adding a sign.
Anchor to one half
Sort fractions as below, equal to, or above one half. For 2/6, notice that half of six parts is three, so two sixths is below one half. Then compare it with a fraction known to be above half, such as 5/7. The benchmark gives a reason for the order.
Read the sign as a mouth
Once the amounts are compared, say the full statement aloud: “five sevenths is greater than two sixths.” The open side of > faces the larger amount. Have the student point to that amount first, then draw the sign, avoiding a memorized direction with no quantity attached.
Test equal values
When two fractions may name the same amount, look for a shared benchmark or equivalent form. For 3/6 and 2/4, both reduce to one half. Ask the child to justify an equality sign with the matching amount, rather than assuming different numerals must mean different sizes.
Best uses for this template
Ideas for using this page
Sort a small set
Choose several fractions from the same range and ask learners to order them. Their explanations reveal whether they attend to the size of each part as well as the number of parts.
Practice comparison notation
A page of pairs gives students repeated opportunities to choose a comparison sign. Ask them to read each completed statement aloud to connect notation and meaning.
Discuss a disagreement
When two students choose different signs, invite each to draw the fractions using equal-length wholes. The model gives the discussion a common reference point. Ask them to defend the sign from the quantities.
Mistakes to watch for
Choosing 2/6 as greater than 5/7 because 6 is smaller than 7.
Compare each amount with one half: 2/6 is one third, below half, while 5/7 is above half. A benchmark helps show why the larger denominator alone does not decide the result.
Writing 2/3 < 2/5 because the numerators are both 2 and 3 is smaller than 5.
Keep the whole the same and compare piece sizes. Thirds are larger than fifths, so two thirds covers more than two fifths. Draw equal-length bars if the order is hard to see.
Putting > between 3/6 and 2/4 even though both amounts are one half.
Rename each fraction as halves by dividing top and bottom by the same number. Both become 1/2, so use an equals sign. Different-looking numerals can describe the same amount.
Reversing the sign and writing 2/6 > 5/7 after deciding 5/7 is larger.
Read the statement from left to right and let the open side face the larger value. Since 2/6 is smaller, write 2/6 < 5/7; say “less than” aloud to check the direction.
Quick answers
How do you compare fractions with different denominators?
Think about the amounts represented, not just the printed digits. One approach is to compare both fractions with a benchmark such as one half. Another is to rewrite them with a common denominator or draw equal-length strips. For instance, 2/3 exceeds 2/5 because thirds are larger parts than fifths of the same whole.
How to teach comparing fractions using a number line or model?
Draw two equal-length bars, or mark a number line from zero to one. Split the same whole into the number of parts named by each denominator, then locate how many parts the numerator counts. Students can see which endpoint lies farther right or which shaded bar covers more, and explain the comparison in words.
Can you share a few comparing fractions problems?
Try 5/7 versus 2/6, 2/3 versus 2/5, and 3/6 versus 2/4. The first pair can be judged around one half, the second has equal numerators but differently sized parts, and the last pair has equal values. Ask the learner to choose <, >, or = and give a reason for each choice.
What is included in this comparing fractions worksheet pack?
There are 13 pages altogether: a cover, six comparison sheets, and the key on pages 8-13. Students compare 8 pairs on each of practice pages 2, 3, and 7; each page has a Name/Date line. Denominators range from 2 to 8. The key gives a comparison sign for every pair.
Is this comparing fractions worksheet pack free?
Yes. Downloading costs nothing and requires no registration. This pack comes as a US Letter PDF only; no A4 or PNG version exists. The comparison answer key appears on pages 8-13 in the same file as the six student sheets.
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