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

5th Grade math worksheet solutions: Adding and Subtracting Fractions with Unlike Denominators – Maths PDF

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Sommaire

This grade 5 add subtract fractions answers for 5th Grade covers adding and subtracting fractions with unlike denominators (Common Core 5.NF.A.1, 5.NF.A.2), with a free PDF to print.

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

Grade 5 add subtract fractions answers: exercises 1 to 10

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

Thirds become sixths: 2/6 + 1/6 = 3/6 = 1/2.

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

Landing point: 5/12.

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

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

Exercises 11 and up

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

Together: 2/8 + 3/8 = 5/8 of the pizza.

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.

Key facts behind this grade 5 add subtract fractions answers

Key facts

Fractions must have the same denominator before they can be added or subtracted.
The least common denominator is the smallest number both denominators divide into.
Only the numerators are added or subtracted. The denominator stays the same.
To subtract mixed numbers, regroup one whole as a fraction when needed.
Benchmarks 0, 1/2, and 1 help check that an answer makes sense.

How to use this grade 5 add subtract fractions answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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