Adding and Subtracting Fractions: math practice, Grade 5 – download the PDF

1 Missing numbers in equivalent fractions ★★★

Find the missing number in each equation.

1. \(\dfrac{3}{5} = \dfrac{?}{20}\)
2. \(\dfrac{7}{8} = \dfrac{21}{?}\)
3. \(\dfrac{4}{9} = \dfrac{?}{45}\)
4. \(\dfrac{10}{15} = \dfrac{2}{?}\)

2 Simplify the fractions ★★★

Write each fraction in simplest form.

1. \(\dfrac{12}{18}\)
2. \(\dfrac{15}{25}\)
3. \(\dfrac{18}{45}\)
4. \(\dfrac{28}{16}\)

3 Least common multiples ★★★

Find the least common multiple (LCM) of each pair.

1. \(4\) and \(6\)
2. \(3\) and \(8\)
3. \(6\) and \(9\)
4. \(5\) and \(10\)
5. \(12\) and \(8\)

4 Easy sums with one common denominator ★★★

Calculate. Write each answer in simplest form.

1. \(\dfrac{1}{4} + \dfrac{1}{2}\)
2. \(\dfrac{2}{3} + \dfrac{1}{6}\)
3. \(\dfrac{3}{10} + \dfrac{1}{5}\)

5 Easy differences ★★★

The bar below shows \(\dfrac{5}{6}\) with some parts crossed out.

1. What fraction of the bar is left after the crossed parts are removed?
2. Calculate \(\dfrac{7}{8} - \dfrac{1}{4}\).
3. Calculate \(\dfrac{9}{10} - \dfrac{2}{5}\).

6 True or false? ★★★

Say whether each statement is true or false, and justify your answer.

1. \(\dfrac{2}{3} = \dfrac{6}{9}\)
2. \(\dfrac{3}{4} = \dfrac{4}{5}\)
3. \(\dfrac{5}{10} = \dfrac{1}{2}\)
4. \(\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{2}{7}\)

7 Juice in the pitcher ★★★

Noah pours \(\dfrac{1}{2}\) liter of orange juice and \(\dfrac{1}{4}\) liter of apple juice into a pitcher. How many liters of juice are in the pitcher?

8 Which is greater? ★★★

Compare the fractions by rewriting them with a common denominator. Use \(<\), \(>\) or \(=\).

1. \(\dfrac{3}{4}\) and \(\dfrac{5}{8}\)
2. \(\dfrac{7}{10}\) and \(\dfrac{2}{3}\)

9 Sums with unlike denominators ★★★

Add. Write each answer as a mixed number.

1. \(\dfrac{2}{5} + \dfrac{3}{4}\)
2. \(\dfrac{5}{6} + \dfrac{3}{8}\)

10 Differences with unlike denominators ★★★

Subtract. Write each answer in simplest form.

1. \(\dfrac{7}{9} - \dfrac{1}{6}\)
2. \(\dfrac{11}{12} - \dfrac{3}{8}\)

11 Adding mixed numbers ★★★

Calculate.

1. \(2\dfrac{1}{3} + 1\dfrac{1}{2}\)
2. \(3\dfrac{3}{4} + 2\dfrac{2}{3}\)

12 Subtracting mixed numbers ★★★

Calculate.

1. \(5\dfrac{1}{2} - 2\dfrac{1}{3}\)
2. \(4\dfrac{1}{4} - 1\dfrac{2}{3}\)

13 A walk in the park ★★★

Leo walks \(\dfrac{3}{4}\) mile in the morning and \(\dfrac{2}{3}\) mile in the afternoon.

1. How many miles does he walk in all?
2. How much farther did he walk in the morning than in the afternoon?

14 Estimate first ★★★

For each calculation, estimate with the benchmarks \(0\), \(\dfrac{1}{2}\) and \(1\), then find the exact answer.

1. \(\dfrac{5}{8} + \dfrac{7}{12}\)
2. \(\dfrac{13}{15} - \dfrac{4}{9}\)

15 Three fractions ★★★

Calculate and simplify.

1. \(\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4}\)
2. \(\dfrac{3}{4} + \dfrac{5}{6} - \dfrac{1}{3}\)

16 Find the error ★★★

Sam wrote: \(\dfrac{2}{3} + \dfrac{3}{4} = \dfrac{5}{7}\).

1. Explain, using an estimate, how you can tell that his answer is wrong.
2. Explain his mistake and give the correct answer.

17 Ribbon cutting ★★★

A ribbon is \(5\dfrac{1}{4}\) feet long. Mia cuts off one piece that is \(1\dfrac{2}{3}\) feet long and another that is \(2\dfrac{1}{2}\) feet long. How much ribbon is left? Give the answer in feet and in inches (\(1\) foot \(= 12\) inches).

18 Missing fractions ★★★

Find the missing fraction.

1. \(\dfrac{3}{8} + \square = \dfrac{11}{12}\)
2. \(\square - \dfrac{2}{5} = \dfrac{1}{3}\)

19 The community garden ★★★

In a garden, tomatoes cover \(\dfrac{2}{5}\) of the area, peppers cover \(\dfrac{1}{4}\), and herbs cover the rest.

1. What fraction of the garden is covered by herbs?
2. The garden is \(40\) square feet. How many square feet are herbs?

20 Training plan ★★★

A runner wants to run \(7\) miles in three days. On Monday she runs \(2\dfrac{1}{3}\) miles and on Tuesday \(1\dfrac{3}{4}\) miles. How far must she run on Wednesday to reach her goal?

21 A pattern with differences ★★★

Calculate each difference, then look at the pattern.

1. \(\dfrac{1}{4} - \dfrac{1}{5}\)
2. \(\dfrac{1}{5} - \dfrac{1}{6}\)
3. Use (a) and (b) to find \(\dfrac{1}{20} + \dfrac{1}{30}\) without finding a new common denominator, then check by adding.