Comparing Fractions Worksheet
Compare fractions using equal parts, benchmarks, and common denominators. Choose three practice levels with worked examples and explained answers.
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Comparing fractions
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Compare fractions that refer to the same-sized whole and justify each comparison.
Grade 5 review of prerequisite fraction comparison. Each comparison uses the same-sized whole. Supported practice uses common denominators; standard and challenge practice use equivalent fractions and reasoning.
Supported practice
Example: 2/7 < 5/7. Both wholes are split into seven equal parts, and two of those parts are fewer than five.
1. Fill in <, >, or =: 3/8 5/8. Explain using the number of eighths.
2. Fill in <, >, or =: 7/10 4/10.
3. Fill in <, >, or =: 2/6 2/6.
4. Place 1/5, 4/5, and 2/5 in order from least to greatest.
Supported answers
1. 3/8 < 5/8. Three eighths are fewer than five eighths.
2. 7/10 > 4/10. Seven tenths are more than four tenths.
3. 2/6 = 2/6. Both fractions describe two sixths of the same-sized whole.
4. 1/5, 2/5, 4/5. Compare the numerators because each part is one fifth.
Standard practice
Example: Compare 2/3 and 3/4. Use twelfths: 2/3 = 8/12 and 3/4 = 9/12, so 2/3 < 3/4.
1. Compare 3/4 and 5/8 using a common denominator.
2. Compare 2/3 and 3/5 using a common denominator.
3. Compare 4/6 and 2/3. Explain.
4. Place 1/2, 5/6, and 2/3 in order from least to greatest.
Standard answers
1. 3/4 = 6/8, so 3/4 > 5/8.
2. 2/3 = 10/15 and 3/5 = 9/15, so 2/3 > 3/5.
3. 4/6 = 2/3. Dividing the numerator and denominator of 4/6 by 2 gives 2/3.
4. 1/2, 2/3, 5/6. In sixths, these are 3/6, 4/6, and 5/6.
Challenge practice
Example: 7/8 is 1/8 below 1, while 5/6 is 1/6 below 1. Since 1/8 < 1/6, 7/8 is closer to 1 and is the greater fraction.
1. Compare 5/6 and 7/9. Give exact equivalent fractions to justify your answer.
2. Leo says 3/8 > 3/5 because 8 > 5. Explain why this is incorrect.
3. Write a fraction strictly between 1/2 and 2/3. Prove it using twelfths.
4. Sam ate 3/4 of a small pizza. Ana ate 2/3 of a large pizza. Can the fractions alone tell who ate more pizza? Explain.
Challenge answers
1. 5/6 = 15/18 and 7/9 = 14/18, so 5/6 > 7/9.
2. With the same whole, an eighth is smaller than a fifth. Three eighths are smaller than three fifths, so 3/8 < 3/5.
3. 7/12 is one answer: 1/2 = 6/12 < 7/12 < 8/12 = 2/3. Other correct fractions are possible.
4. No. The wholes have different sizes. Although 3/4 > 2/3 as numbers, the pizza sizes are needed to compare the amounts eaten.