Equivalent Fractions and Comparing Fractions: Grade 4 Math Worksheet Answer Key – PDF Download

Grade 4 Equivalent Worksheet Answer Key: problems 1–5

Problem 1: Name the shaded parts

Bar A has 2 of 4 parts shaded: \(\frac{2}{4}\). Bar B has 4 of 8 parts shaded: \(\frac{4}{8}\). Both cover the same length of the bar.

Answer: \(\frac{2}{4}=\frac{4}{8}\)

Problem 2: Fill in the numerator

1. \(2 \times 3 = 6\), so multiply the numerator too: \(1 \times 3 = 3\). \(\frac{1}{2}=\frac{3}{6}\)
2. \(3 \times 4 = 12\), so multiply the numerator too: \(1 \times 4 = 4\). \(\frac{1}{3}=\frac{4}{12}\)
3. \(5 \times 2 = 10\), so multiply the numerator too: \(3 \times 2 = 6\). \(\frac{3}{5}=\frac{6}{10}\)
4. \(4 \times 2 = 8\), so multiply the numerator too: \(3 \times 2 = 6\). \(\frac{3}{4}=\frac{6}{8}\)

Problem 3: Tenths and hundredths

1. \(5 \times 2 = 10\) and \(2 \times 2 = 4\). \(\frac{2}{5}=\frac{4}{10}\)
2. \(10 \times 10 = 100\) and \(7 \times 10 = 70\). \(\frac{7}{10}=\frac{70}{100}\)
3. \(4 \times 25 = 100\) and \(1 \times 25 = 25\). \(\frac{1}{4}=\frac{25}{100}\)

Problem 4: Divide to get an equivalent fraction

1. Divide both by 2: \(6 : 2 = 3\) and \(8 : 2 = 4\). \(\frac{6}{8}=\frac{3}{4}\)
2. Divide both by 2: \(10 : 2 = 5\) and \(12 : 2 = 6\). \(\frac{10}{12}=\frac{5}{6}\)
3. Divide both by 2: \(4 : 2 = 2\) and \(10 : 2 = 5\). \(\frac{4}{10}=\frac{2}{5}\)
4. Divide both by 4: \(8 : 4 = 2\) and \(12 : 4 = 3\). \(\frac{8}{12}=\frac{2}{3}\)
5. Divide both by 50: \(50 : 50 = 1\) and \(100 : 50 = 2\). \(\frac{50}{100}=\frac{1}{2}\)

Problem 5: Area model of fifths

There are \(5 \times 3 = 15\) pieces in all. Shaded pieces: \(2 \times 3 = 6\).

Answer: \(\frac{2}{5}=\frac{6}{15}\)

Grade 4 Equivalent Worksheet Answer Key: problems 6–10

Problem 6: Number line in tenths

Divide the numerator and denominator of \(\frac{6}{10}\) by 2: \(6 : 2 = 3\) and \(10 : 2 = 5\).

Answer: \(\frac{6}{10}=\frac{3}{5}\)

Problem 7: Equivalent or not

1. \(4 \times 3 = 12\) and \(3 \times 3 = 9\). Yes.
2. \(5 \times 3 = 15\) but \(2 \times 3 = 6\), not 4. No.
3. \(6 \times 2 = 12\) and \(5 \times 2 = 10\). Yes.
4. \(3 \times 2 = 6\) but \(8 \times 2 = 16\), not 12. No.

Problem 8: Find the missing denominator

1. \(2 \times 4 = 8\), so multiply the denominator by 4 too: \(3 \times 4 = 12\). \(\frac{2}{3}=\frac{8}{12}\)
2. \(3 \times 3 = 9\), so multiply the denominator by 3 too: \(4 \times 3 = 12\). \(\frac{3}{4}=\frac{9}{12}\)
3. \(5 \times 4 = 20\), so multiply the denominator by 4 too: \(6 \times 4 = 24\). \(\frac{5}{6}=\frac{20}{24}\)
4. \(3 \times 4 = 12\), so multiply the denominator by 4 too: \(5 \times 4 = 20\). \(\frac{3}{5}=\frac{12}{20}\)

Problem 9: Three names for one third

\(1 \times 2 = 2\) and \(3 \times 2 = 6\). \(1 \times 3 = 3\) and \(3 \times 3 = 9\). \(1 \times 4 = 4\) and \(3 \times 4 = 12\).

Answer: \(\frac{1}{3}=\frac{2}{6}=\frac{3}{9}=\frac{4}{12}\)

Problem 10: Compare to one half

1. Half of 8 is 4. The numerator 3 is less than it. \(\frac{3}{8} < \frac{1}{2}\)
2. Half of 6 is 3. The numerator 5 is greater than it. \(\frac{5}{6} > \frac{1}{2}\)
3. Half of 8 is 4. The numerator 4 is equal to it. \(\frac{4}{8} = \frac{1}{2}\)
4. Half of 10 is 5. The numerator 4 is less than it. \(\frac{4}{10} < \frac{1}{2}\)
5. Half of 12 is 6. The numerator 7 is greater than it. \(\frac{7}{12} > \frac{1}{2}\)

Grade 4 Equivalent Worksheet Answer Key: problems 11–15

Problem 11: Same denominator

1. Same denominator, so compare the numerators 5 and 3. \(\frac{5}{8} > \frac{3}{8}\)
2. Same denominator, so compare the numerators 7 and 9. \(\frac{7}{12} < \frac{9}{12}\)
3. Same denominator, so compare the numerators 2 and 5. \(\frac{2}{6} < \frac{5}{6}\)

Problem 12: Same numerator

1. Same numerator. Pieces of size 1/5 are bigger than pieces of size 1/8. \(\frac{3}{5} > \frac{3}{8}\)
2. Same numerator. Pieces of size 1/6 are bigger than pieces of size 1/10. \(\frac{4}{6} > \frac{4}{10}\)
3. Same numerator. Pieces of size 1/3 are bigger than pieces of size 1/4. \(\frac{2}{3} > \frac{2}{4}\)

Problem 13: Compare with bars

Cut both bars into tenths: \(\frac{1}{2}=\frac{5}{10}\) and \(\frac{3}{5}=\frac{6}{10}\).

Answer: \(\frac{1}{2} < \frac{3}{5}\)

Problem 14: Common denominators

1. \(\frac{3}{4}=\frac{9}{12}\) and \(\frac{5}{6}=\frac{10}{12}\). \(\frac{3}{4} < \frac{5}{6}\)
2. \(\frac{5}{8}=\frac{5}{8}\) and \(\frac{3}{4}=\frac{6}{8}\). \(\frac{5}{8} < \frac{3}{4}\)
3. \(\frac{7}{12}=\frac{7}{12}\) and \(\frac{2}{3}=\frac{8}{12}\). \(\frac{7}{12} < \frac{2}{3}\)

Problem 15: Order the fractions

1. Use denominator 8: \(\frac{3}{4}=\frac{6}{8}\), \(\frac{1}{2}=\frac{4}{8}\), \(\frac{5}{8}=\frac{5}{8}\). Order: \(\frac{1}{2} < \frac{5}{8} < \frac{3}{4}\)
2. Use denominator 12: \(\frac{2}{3}=\frac{8}{12}\), \(\frac{1}{6}=\frac{2}{12}\), \(\frac{5}{12}=\frac{5}{12}\). Order: \(\frac{1}{6} < \frac{5}{12} < \frac{2}{3}\)

Grade 4 Equivalent Worksheet Answer Key: problems 16–20

Problem 16: Points in tenths

1. A is \(\frac{2}{10}\), B is \(\frac{6}{10}\), and C is \(\frac{9}{10}\).
2. Divide by 2: \(\frac{2}{10}=\frac{1}{5}\).
3. One half is \(\frac{5}{10}\). B and C are to the right of it, so points B and C (\(\frac{6}{10}\) and \(\frac{9}{10}\)).

Problem 17: Compare using hundredths

1. \(\frac{3}{10}=\frac{30}{100}\). Since 30 is greater than 28, \(\frac{3}{10} > \frac{28}{100}\).
2. \(\frac{4}{5}=\frac{80}{100}\). Since 80 is greater than 75, \(\frac{4}{5} > \frac{75}{100}\).

Problem 18: Find the mistake

The denominator tells how many equal parts are in the whole. A whole cut into 4 parts has smaller parts than a whole cut into 3 parts. Check with a common denominator: \(\frac{1}{4}=\frac{3}{12}\) and \(\frac{1}{3}=\frac{4}{12}\).

Answer: \(\frac{1}{4} < \frac{1}{3}\)

Problem 19: Pizza night

Divide Maya’s fraction by 3: \(\frac{3}{6}=\frac{1}{2}\). Both ate half a pizza.

Answer: They ate the same amount.

Problem 20: Ribbon for crafts

Rewrite \(\frac{3}{4}\) with denominator 8: \(3 \times 2 = 6\) and \(4 \times 2 = 8\), so \(\frac{3}{4}=\frac{6}{8}\). Now compare \(\frac{5}{8} < \frac{6}{8}\).

Answer: Ethan has more ribbon.

Grade 4 Equivalent Worksheet Answer Key: problems 21–24

Problem 21: Homework progress

Use denominator 24: \(\frac{5}{8}=\frac{15}{24}\) and \(\frac{7}{12}=\frac{14}{24}\). Since \(\frac{15}{24} > \frac{14}{24}\), \(\frac{5}{8} > \frac{7}{12}\).

Answer: Ethan

Problem 22: Farmers market peaches

Half of 12 is 6, and 5 is less than 6, so \(\frac{5}{12} < \frac{1}{2}\). Check: \(\frac{1}{2}=\frac{6}{12}\) and 5 twelfths is less than 6 twelfths.

Answer: Liam

Problem 23: Dimes and pennies

Noah has \(\frac{7}{10}\) of a dollar. Diego has \(\frac{65}{100}\) of a dollar. Rewrite: \(\frac{7}{10}=\frac{70}{100}\). Since \(\frac{70}{100} > \frac{65}{100}\), Noah has \$0.70 and Diego has \$0.65.

Answer: Noah has more.

Problem 24: Trail run

The denominators 8, 3, and 12 all go into 24. \(\frac{5}{8}=\frac{15}{24}\), \(\frac{2}{3}=\frac{16}{24}\), \(\frac{7}{12}=\frac{14}{24}\).

Since 14 < 15 < 16, the order is Sofia, Jamal, Priya.

How to use this grade 4 equivalent worksheet answer key

Read this grade 4 equivalent worksheet answer key after trying each problem yourself, and redo any problem you missed.

See every chapter on the Grade 4 math page.