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

This answer key shows every step for the 20 fraction problems: the least common denominator, the renamed fractions, the calculation, and the simplified answer in bold. Use it to find the exact step where a mistake happened, such as forgetting to regroup.
Grade 5 · Common Core State Standards: 5.NF.A.1, 5.NF.A.2
Exercise 1 – Halves and fourths
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: \(\frac{2}{4} + \frac{1}{4} = \frac{3}{4}\).
\(\frac{3}{4}\)
Exercise 2 – Thirds and sixths
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: \(\frac{3}{6} = \frac{1}{2}\).
\(\frac{1}{2}\)
Exercise 3 – Fifths and halves
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: \(\frac{4}{10} + \frac{5}{10} = \frac{9}{10}\).
\(\frac{9}{10}\)
Exercise 4 – Fourths minus thirds
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: \(\frac{9}{12} – \frac{4}{12} = \frac{5}{12}\).
\(\frac{5}{12}\)
Exercise 5 – Sixths minus fourths
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: \(\frac{10}{12} – \frac{3}{12} = \frac{7}{12}\).
\(\frac{7}{12}\)
Exercise 6 – Sum greater than 1
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: \(\frac{17}{12} = 1\frac{5}{12}\).
\(1\frac{5}{12}\)
Exercise 7 – Eighths minus sixths
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: \(\frac{21}{24} – \frac{4}{24} = \frac{17}{24}\).
\(\frac{17}{24}\)
Exercise 8 – Tenths and fifteenths
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: \(\frac{9}{30} + \frac{8}{30} = \frac{17}{30}\).
\(\frac{17}{30}\)
Exercise 9 – Add mixed numbers
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: \(1\frac{3}{6} + 2\frac{2}{6} = 3\frac{5}{6}\).
\(3\frac{5}{6}\)
Exercise 10 – Regroup the fraction sum
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: \(3\frac{19}{12} = 4\frac{7}{12}\).
\(4\frac{7}{12}\)
Exercise 11 – Subtract with regrouping
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: \(3\frac{8}{6} – 1\frac{3}{6} = 2\frac{5}{6}\).
\(2\frac{5}{6}\)
Exercise 12 – Harder regrouping
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: \(4\frac{15}{12} – 2\frac{8}{12} = 2\frac{7}{12}\).
\(2\frac{7}{12}\)
Exercise 13 – Estimate, then add
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.
Exercise 14 – Missing number
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: \(\frac{7}{10} – \frac{4}{10} = \frac{3}{10}\).
\(\frac{3}{10}\)
Exercise 15 – Pizza for two meals
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.
Exercise 16 – Weekend hike
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.
Exercise 17 – Ribbon left over
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.
Exercise 18 – Will it fit?
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.
Exercise 19 – Practice time
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.
Exercise 20 – Apple pie and sauce
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.
All Grade 5 chapters: Grade 5 math.
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