5th Grade Adding and Subtracting Fractions with Unlike Denominators Worksheet Solutions (PDF)

The least common denominator of 2 and 4 is 4.

Rename the fractions: \(\frac{1}{2} = \frac{2}{4}\) and \(\frac{1}{4} = \frac{1}{4}\).

Add: \(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).

\(\frac{3}{4}\)

The least common denominator of 3 and 6 is 6.

Rename the fractions: \(\frac{1}{3} = \frac{2}{6}\) and \(\frac{1}{6} = \frac{1}{6}\).

Add: \(\frac{2}{6} + \frac{1}{6} = \frac{3}{6}\).

Simplify: \(\frac{3}{6} = \frac{1}{2}\).

\(\frac{1}{2}\)

The least common denominator of 5 and 2 is 10.

Rename the fractions: \(\frac{2}{5} = \frac{4}{10}\) and \(\frac{1}{2} = \frac{5}{10}\).

Add: \(\frac{4}{10} + \frac{5}{10} = \frac{9}{10}\).

\(\frac{9}{10}\)

The least common denominator of 4 and 3 is 12.

Rename the fractions: \(\frac{3}{4} = \frac{9}{12}\) and \(\frac{1}{3} = \frac{4}{12}\).

Subtract: \(\frac{9}{12} – \frac{4}{12} = \frac{5}{12}\).

\(\frac{5}{12}\)

The least common denominator of 6 and 4 is 12.

Rename the fractions: \(\frac{5}{6} = \frac{10}{12}\) and \(\frac{1}{4} = \frac{3}{12}\).

Subtract: \(\frac{10}{12} – \frac{3}{12} = \frac{7}{12}\).

\(\frac{7}{12}\)

The least common denominator of 3 and 4 is 12.

Rename the fractions: \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{3}{4} = \frac{9}{12}\).

Add: \(\frac{8}{12} + \frac{9}{12} = \frac{17}{12}\).

Simplify: \(\frac{17}{12} = 1\frac{5}{12}\).

\(1\frac{5}{12}\)

The least common denominator of 8 and 6 is 24.

Rename the fractions: \(\frac{7}{8} = \frac{21}{24}\) and \(\frac{1}{6} = \frac{4}{24}\).

Subtract: \(\frac{21}{24} – \frac{4}{24} = \frac{17}{24}\).

\(\frac{17}{24}\)

The least common denominator of 10 and 15 is 30.

Rename the fractions: \(\frac{3}{10} = \frac{9}{30}\) and \(\frac{4}{15} = \frac{8}{30}\).

Add: \(\frac{9}{30} + \frac{8}{30} = \frac{17}{30}\).

\(\frac{17}{30}\)

The least common denominator of 2 and 3 is 6.

Rename the fractions: \(1\frac{1}{2} = 1\frac{3}{6}\) and \(2\frac{1}{3} = 2\frac{2}{6}\).

Add: \(1\frac{3}{6} + 2\frac{2}{6} = 3\frac{5}{6}\).

\(3\frac{5}{6}\)

The least common denominator of 4 and 6 is 12.

Rename the fractions: \(2\frac{3}{4} = 2\frac{9}{12}\) and \(1\frac{5}{6} = 1\frac{10}{12}\).

Add: \(2\frac{9}{12} + 1\frac{10}{12} = 3\frac{19}{12}\).

Simplify: \(3\frac{19}{12} = 4\frac{7}{12}\).

\(4\frac{7}{12}\)

The least common denominator of 3 and 2 is 6.

Rename the fractions: \(4\frac{1}{3} = 4\frac{2}{6}\) and \(1\frac{1}{2} = 1\frac{3}{6}\).

The first fraction is smaller than the second, so regroup 1 whole as \(\frac{6}{6}\): \(4\frac{2}{6} = 3\frac{8}{6}\).

Subtract: \(3\frac{8}{6} – 1\frac{3}{6} = 2\frac{5}{6}\).

\(2\frac{5}{6}\)

The least common denominator of 4 and 3 is 12.

Rename the fractions: \(5\frac{1}{4} = 5\frac{3}{12}\) and \(2\frac{2}{3} = 2\frac{8}{12}\).

The first fraction is smaller than the second, so regroup 1 whole as \(\frac{12}{12}\): \(5\frac{3}{12} = 4\frac{15}{12}\).

Subtract: \(4\frac{15}{12} – 2\frac{8}{12} = 2\frac{7}{12}\).

\(2\frac{7}{12}\)

Estimate: \(\frac{5}{6}\) is close to 1 and \(\frac{3}{5}\) is close to \(\frac{1}{2}\), so the sum is about \(1\frac{1}{2}\).

The least common denominator of 6 and 5 is 30.

Rename the fractions: \(\frac{5}{6} = \frac{25}{30}\) and \(\frac{3}{5} = \frac{18}{30}\).

Add: \(\frac{25}{30} + \frac{18}{30} = \frac{43}{30}\).

Simplify: \(\frac{43}{30} = 1\frac{13}{30}\).

\(1\frac{13}{30}\)

The exact sum is close to the estimate.

Subtract to find the missing part: \(\frac{7}{10} – \frac{2}{5}\).

The least common denominator of 10 and 5 is 10.

Rename the fractions: \(\frac{7}{10} = \frac{7}{10}\) and \(\frac{2}{5} = \frac{4}{10}\).

Subtract: \(\frac{7}{10} – \frac{4}{10} = \frac{3}{10}\).

\(\frac{3}{10}\)

The least common denominator of 4 and 8 is 8.

Rename the fractions: \(\frac{1}{4} = \frac{2}{8}\) and \(\frac{3}{8} = \frac{3}{8}\).

Add: \(\frac{2}{8} + \frac{3}{8} = \frac{5}{8}\).

\(\frac{5}{8}\)

Maya ate \(\frac{5}{8}\) of the pizza.

The least common denominator of 2 and 4 is 4.

Rename the fractions: \(2\frac{1}{2} = 2\frac{2}{4}\) and \(1\frac{3}{4} = 1\frac{3}{4}\).

Add: \(2\frac{2}{4} + 1\frac{3}{4} = 3\frac{5}{4}\).

Simplify: \(3\frac{5}{4} = 4\frac{1}{4}\).

\(4\frac{1}{4}\)

Jamal hiked \(4\frac{1}{4}\) miles.

The least common denominator of 3 and 4 is 12.

Rename the fractions: \(3\frac{2}{3} = 3\frac{8}{12}\) and \(1\frac{3}{4} = 1\frac{9}{12}\).

The first fraction is smaller than the second, so regroup 1 whole as \(\frac{12}{12}\): \(3\frac{8}{12} = 2\frac{20}{12}\).

Subtract: \(2\frac{20}{12} – 1\frac{9}{12} = 1\frac{11}{12}\).

\(1\frac{11}{12}\)

Sofia has \(1\frac{11}{12}\) yards left.

Total in the bowl:

The least common denominator of 3 and 4 is 12.

Rename the fractions: \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{3}{4} = \frac{9}{12}\).

Add: \(\frac{8}{12} + \frac{9}{12} = \frac{17}{12}\).

Simplify: \(\frac{17}{12} = 1\frac{5}{12}\).

\(1\frac{5}{12}\)

Room left: \(2 – 1\frac{5}{12}\).

Rename 2 as \(1\frac{12}{12}\): \(1\frac{12}{12} – 1\frac{5}{12} = \frac{7}{12}\).

Yes, it fits. There is \(\frac{7}{12}\) cup of room left.

The LCD of 2, 4, and 3 is 12.

\(1\frac{1}{2} = 1\frac{6}{12}\), \(\frac{3}{4} = \frac{9}{12}\), \(2\frac{1}{3} = 2\frac{4}{12}\).

Add the wholes: \(1 + 2 = 3\). Add the fractions: \(\frac{6}{12} + \frac{9}{12} + \frac{4}{12} = \frac{19}{12} = 1\frac{7}{12}\).

Total: \(3 + 1\frac{7}{12} = 4\frac{7}{12}\) hours.

More than 4 hours: \(4\frac{7}{12} – 4 = \frac{7}{12}\) hour.

The total is \(4\frac{7}{12}\) hours, which is \(\frac{7}{12}\) hour more than 4 hours.

First find the apples used:

The least common denominator of 4 and 6 is 12.

Rename the fractions: \(2\frac{1}{4} = 2\frac{3}{12}\) and \(1\frac{5}{6} = 1\frac{10}{12}\).

Add: \(2\frac{3}{12} + 1\frac{10}{12} = 3\frac{13}{12}\).

Simplify: \(3\frac{13}{12} = 4\frac{1}{12}\).

\(4\frac{1}{12}\)

Now subtract from the amount Diego has:

The least common denominator of 2 and 12 is 12.

Rename the fractions: \(5\frac{1}{2} = 5\frac{6}{12}\) and \(4\frac{1}{12} = 4\frac{1}{12}\).

Subtract: \(5\frac{6}{12} – 4\frac{1}{12} = 1\frac{5}{12}\).

\(1\frac{5}{12}\)

Diego has \(1\frac{5}{12}\) pounds of apples left.