Adding and Subtracting Fractions and Mixed Numbers: Grade 4 Math Worksheet Answer Key – PDF Download

Grade 4 Adding Worksheet Answer Key: problems 1–5

Problem 1: Unit fractions in a bar

Each shaded part is \(\frac{1}{6}\), and there are 4 of them.

Answer: \(\frac{4}{6}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)

Problem 2: Three ways to split seven eighths

Split the 7 eighths into two groups. Possible answers:

1. \(\frac{7}{8}=\frac{1}{8}+\frac{6}{8}\)
2. \(\frac{7}{8}=\frac{2}{8}+\frac{5}{8}\)
3. \(\frac{7}{8}=\frac{3}{8}+\frac{4}{8}\)

Any pair of numerators that adds to 7 is correct.

Problem 3: Missing part

1. \(5 – 2 = 3\), so \(\frac{5}{10}=\frac{2}{10}+\frac{3}{10}\)
2. \(9 – 4 = 5\), so \(\frac{9}{12}=\frac{5}{12}+\frac{4}{12}\)

Problem 4: Add like fractions

1. \(1 + 2 = 3\), so \(\frac{1}{5}+\frac{2}{5}=\frac{3}{5}\)
2. \(3 + 4 = 7\), so \(\frac{3}{8}+\frac{4}{8}=\frac{7}{8}\)
3. \(5 + 4 = 9\), so \(\frac{5}{12}+\frac{4}{12}=\frac{9}{12}\)
4. \(20 + 35 = 55\), so \(\frac{20}{100}+\frac{35}{100}=\frac{55}{100}\)

Problem 5: Add with a model

The green part is \(\frac{3}{10}\) and the pink part is \(\frac{4}{10}\). Together, 7 of the 10 parts are shaded.

Answer: \(\frac{3}{10}+\frac{4}{10}=\frac{7}{10}\)

Grade 4 Adding Worksheet Answer Key: problems 6–10

Problem 6: Subtract like fractions

1. \(5 – 2 = 3\), so \(\frac{5}{6}-\frac{2}{6}=\frac{3}{6}\)
2. \(9 – 4 = 5\), so \(\frac{9}{10}-\frac{4}{10}=\frac{5}{10}\)
3. \(11 – 5 = 6\), so \(\frac{11}{12}-\frac{5}{12}=\frac{6}{12}\)
4. \(8 – 3 = 5\), so \(\frac{8}{8}-\frac{3}{8}=\frac{5}{8}\)

Problem 7: Subtract with a model

Five parts are shaded and 2 are crossed out, leaving 3 parts.

Answer: \(\frac{5}{8}-\frac{2}{8}=\frac{3}{8}\)

Problem 8: Find the unknown

1. \(6 – 2 = 4\): \(\frac{4}{7}\)
2. \(8 – 3 = 5\): \(\frac{5}{10}\)
3. \(9 – 4 = 5\): \(\frac{5}{12}\)
4. \(2 + 3 = 5\): \(\frac{5}{8}\)

Problem 9: Make one whole

One whole is the same as \(\frac{5}{5}\), \(\frac{8}{8}\), or \(\frac{12}{12}\).

1. \(\frac{5}{5}-\frac{3}{5}=\frac{2}{5}\): \(\frac{2}{5}\)
2. \(\frac{8}{8}-\frac{3}{8}=\frac{5}{8}\): \(\frac{5}{8}\)
3. \(\frac{12}{12}-\frac{7}{12}=\frac{5}{12}\): \(\frac{5}{12}\)

Problem 10: Whole numbers as fractions

1. \(1 \times 6 = 6\): \(1=\frac{6}{6}\)
2. \(2 \times 3 = 6\): \(2=\frac{6}{3}\)
3. \(3 \times 4 = 12\): \(3=\frac{12}{4}\)

Grade 4 Adding Worksheet Answer Key: problems 11–15

Problem 11: Mixed number as a fraction

Each whole is \(\frac{4}{4}\), so two wholes are 8 fourths. Add 1 more fourth: 9 fourths.

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

Problem 12: Rename mixed numbers

1. \(3 \times 5 + 3 = 18\): \(3\frac{3}{5}=\frac{18}{5}\)
2. \(2 \times 6 + 5 = 17\): \(2\frac{5}{6}=\frac{17}{6}\)
3. \(4 \times 8 + 7 = 39\): \(4\frac{7}{8}=\frac{39}{8}\)
4. \(1 \times 12 + 9 = 21\): \(1\frac{9}{12}=\frac{21}{12}\)

Problem 13: Rename fractions as mixed numbers

1. \(7 : 4 = 1\) with remainder 3: \(\frac{7}{4}=1\frac{3}{4}\)
2. \(11 : 5 = 2\) with remainder 1: \(\frac{11}{5}=2\frac{1}{5}\)
3. \(17 : 6 = 2\) with remainder 5: \(\frac{17}{6}=2\frac{5}{6}\)
4. \(25 : 8 = 3\) with remainder 1: \(\frac{25}{8}=3\frac{1}{8}\)

Problem 14: Add mixed numbers

1. Wholes: \(1 + 2 = 3\). Fractions: \(\frac{2}{5}+\frac{1}{5}=\frac{3}{5}\). \(1\frac{2}{5}+2\frac{1}{5}=3\frac{3}{5}\)
2. Wholes: \(3 + 2 = 5\). Fractions: \(\frac{1}{8}+\frac{4}{8}=\frac{5}{8}\). \(3\frac{1}{8}+2\frac{4}{8}=5\frac{5}{8}\)
3. Wholes: \(4 + 1 = 5\). Fractions: \(\frac{3}{10}+\frac{5}{10}=\frac{8}{10}\). \(4\frac{3}{10}+1\frac{5}{10}=5\frac{8}{10}\)

Problem 15: Add mixed numbers and rename

1. Wholes: \(2 + 1 = 3\). Fractions: \(\frac{3}{4}+\frac{3}{4}=\frac{6}{4}=1\frac{2}{4}\). Then \(3 + 1\frac{2}{4} = 4\frac{2}{4}\). \(2\frac{3}{4}+1\frac{3}{4}=4\frac{2}{4}\)
2. Wholes: \(1 + 2 = 3\). Fractions: \(\frac{5}{6}+\frac{4}{6}=\frac{9}{6}=1\frac{3}{6}\). Then \(3 + 1\frac{3}{6} = 4\frac{3}{6}\). \(1\frac{5}{6}+2\frac{4}{6}=4\frac{3}{6}\)
3. Wholes: \(3 + 2 = 5\). Fractions: \(\frac{7}{8}+\frac{5}{8}=\frac{12}{8}=1\frac{4}{8}\). Then \(5 + 1\frac{4}{8} = 6\frac{4}{8}\). \(3\frac{7}{8}+2\frac{5}{8}=6\frac{4}{8}\)

Grade 4 Adding Worksheet Answer Key: problems 16–20

Problem 16: Subtract mixed numbers

1. Wholes: \(4 – 1 = 3\). Fractions: \(\frac{5}{6}-\frac{2}{6}=\frac{3}{6}\). \(4\frac{5}{6}-1\frac{2}{6}=3\frac{3}{6}\)
2. Wholes: \(6 – 2 = 4\). Fractions: \(\frac{7}{8}-\frac{3}{8}=\frac{4}{8}\). \(6\frac{7}{8}-2\frac{3}{8}=4\frac{4}{8}\)
3. Wholes: \(5 – 3 = 2\). Fractions: \(\frac{9}{10}-\frac{4}{10}=\frac{5}{10}\). \(5\frac{9}{10}-3\frac{4}{10}=2\frac{5}{10}\)

Problem 17: Subtract with renaming

1. \(3\frac{1}{4}=\frac{13}{4}\) and \(1\frac{3}{4}=\frac{7}{4}\). \(13 – 7 = 6\). \(3\frac{1}{4}-1\frac{3}{4}=\frac{6}{4}=1\frac{2}{4}\)
2. \(5\frac{2}{6}=\frac{32}{6}\) and \(2\frac{5}{6}=\frac{17}{6}\). \(32 – 17 = 15\). \(5\frac{2}{6}-2\frac{5}{6}=\frac{15}{6}=2\frac{3}{6}\)
3. \(4\frac{1}{5}=\frac{21}{5}\) and \(1\frac{3}{5}=\frac{8}{5}\). \(21 – 8 = 13\). \(4\frac{1}{5}-1\frac{3}{5}=\frac{13}{5}=2\frac{3}{5}\)
4. \(6 =\frac{48}{8}\) and \(2\frac{3}{8}=\frac{19}{8}\). \(48 – 19 = 29\). \(6 -2\frac{3}{8}=\frac{29}{8}=3\frac{5}{8}\)

Problem 18: Jumps on a number line

The first jump ends at \(\frac{2}{6}\). The second jump adds 3 sixths: \(2 + 3 = 5\).

Answer: \(\frac{2}{6}+\frac{3}{6}=\frac{5}{6}\), so the jumps end at \(\frac{5}{6}\).

Problem 19: Find the mistake

Ethan added the denominators. The denominator names the size of the pieces (fifths), and adding does not change the size. Only the numerators are added: \(2 + 1 = 3\).

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

Problem 20: Peach crate

Sold: \(\frac{4}{12}+\frac{5}{12}=\frac{9}{12}\). Left: \(\frac{12}{12}-\frac{9}{12}=\frac{3}{12}\).

Answer: \(\frac{9}{12}\) sold and \(\frac{3}{12}\) left

Grade 4 Adding Worksheet Answer Key: problems 21–25

Problem 21: Hiking trail

Wholes: \(2 + 1 = 3\). Fractions: \(\frac{5}{6}+\frac{4}{6}=\frac{9}{6}=1\frac{3}{6}\). Then \(3 +1\frac{3}{6}=4\frac{3}{6}\).

Answer: \(4\frac{3}{6}\) miles

Problem 22: Ribbon left over

\(5\frac{1}{8}=\frac{41}{8}\) and \(2\frac{6}{8}=\frac{22}{8}\). Subtract: \(41 – 22 = 19\), so \(\frac{19}{8}\) = \(2\frac{3}{8}\).

Answer: \(2\frac{3}{8}\) yards

Problem 23: Pizza party

Eaten: \(\frac{2}{12}+\frac{5}{12}+\frac{3}{12}=\frac{10}{12}\). Left: \(\frac{12}{12}-\frac{10}{12}=\frac{2}{12}\).

Answer: \(\frac{10}{12}\) eaten and \(\frac{2}{12}\) left

Problem 24: Farmers market fruit

Total fruit: wholes \(3 + 2 = 5\); fractions \(\frac{3}{5}+\frac{4}{5}=\frac{7}{5}=1\frac{2}{5}\); total \(5 +1\frac{2}{5}=6\frac{2}{5}\) pounds.

Left after the pie: wholes \(6 – 1 = 5\); fractions \(\frac{2}{5}-\frac{1}{5}=\frac{1}{5}\).

Answer: \(5\frac{1}{5}\) pounds

Problem 25: Filling the water jug

First total: \(3\frac{1}{4}+2\frac{3}{4}=\frac{13}{4}+\frac{11}{4}=\frac{24}{4}= 6\) cups.

After pouring: \(6 =\frac{24}{4}\) and \(4\frac{2}{4}=\frac{18}{4}\). \(24 – 18 = 6\), so \(\frac{6}{4}\) = \(1\frac{2}{4}\).

Answer: \(1\frac{2}{4}\) cups

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