Adding and Subtracting Fractions: practice solutions, Grade 4 – download the PDF

1 Unit fractions ★★★

a) \(\dfrac{5}{8}=\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{8}+\dfrac{1}{8}\), five copies of \(\dfrac{1}{8}\).

b) For example \(\dfrac{5}{8}=\dfrac{2}{8}+\dfrac{3}{8}\) and \(\dfrac{5}{8}=\dfrac{4}{8}+\dfrac{1}{8}\). Any two numerators that add to 5 work.

2 Adding like fractions ★★★

Add the numerators and keep the denominator.

a) \(\dfrac{7}{10}\) b) \(\dfrac{7}{9}\) c) \(\dfrac{5}{6}\) d) \(\dfrac{8}{12}\)

3 Subtracting like fractions ★★★

Subtract the numerators and keep the denominator.

a) \(\dfrac{4}{8}\) b) \(\dfrac{3}{10}\) c) \(\dfrac{4}{6}\) d) \(\dfrac{7}{12}\)

4 Improper fractions to mixed numbers ★★★

Divide the numerator by the denominator.

a) \(7\div4=1\) r 3, so \(1\dfrac{3}{4}\).

b) \(11\div5=2\) r 1, so \(2\dfrac{1}{5}\).

c) \(9\div2=4\) r 1, so \(4\dfrac{1}{2}\).

d) \(10\div3=3\) r 1, so \(3\dfrac{1}{3}\).

5 Mixed numbers to improper fractions ★★★

Multiply the whole number by the denominator, then add the numerator.

a) \(1\times3+2=5\), so \(\dfrac{5}{3}\).

b) \(2\times4+1=9\), so \(\dfrac{9}{4}\).

c) \(3\times5+3=18\), so \(\dfrac{18}{5}\).

d) \(2\times6+5=17\), so \(\dfrac{17}{6}\).

6 Pizza party ★★★

a) \(\dfrac{2}{8}+\dfrac{3}{8}=\dfrac{5}{8}\). They ate \(\dfrac{5}{8}\) of the pizza.

b) The whole pizza is \(\dfrac{8}{8}\), so \(\dfrac{8}{8}-\dfrac{5}{8}=\dfrac{3}{8}\). \(\dfrac{3}{8}\) of the pizza is left.

7 True or false? ★★★

a) False. The denominator stays 5: \(\dfrac{3}{5}+\dfrac{2}{5}=\dfrac{5}{5}=1\).

b) True. Four copies of \(\dfrac{1}{7}\) make \(\dfrac{4}{7}\).

c) True. Six sixths make one whole.

8 Missing numbers ★★★

a) \(8-4=4\), so \(\dfrac{4}{9}\).

b) \(11-5=6\), so \(\dfrac{6}{12}\).

c) \(1=\dfrac{7}{7}\) and \(7-3=4\), so \(\dfrac{4}{7}\).

d) \(1=\dfrac{8}{8}\) and \(8-3=5\), so \(\dfrac{5}{8}\).

9 Adding mixed numbers ★★★

a) Wholes \(2+1=3\), fractions \(\dfrac{3}{5}\). Answer \(3\dfrac{3}{5}\).

b) \(5\) and \(\dfrac{7}{8}\). Answer \(5\dfrac{7}{8}\).

c) Wholes \(3\), fractions \(\dfrac{8}{6}=1\dfrac{2}{6}\). Answer \(4\dfrac{2}{6}\).

d) Wholes \(5\), fractions \(\dfrac{13}{10}=1\dfrac{3}{10}\). Answer \(6\dfrac{3}{10}\).

10 Subtracting mixed numbers ★★★

a) \(3\dfrac{4}{7}\).

b) \(3\dfrac{2}{9}\).

c) Write \(6=5\dfrac{4}{4}\). Then \(5\dfrac{4}{4}-2\dfrac{1}{4}=3\dfrac{3}{4}\).

d) Regroup: \(5\dfrac{1}{5}=4\dfrac{6}{5}\). Then \(4\dfrac{6}{5}-2\dfrac{3}{5}=2\dfrac{3}{5}\).

11 Whole number times a fraction ★★★

a) \(\dfrac{6}{5}=1\dfrac{1}{5}\).

b) \(\dfrac{12}{8}=1\dfrac{4}{8}\).

c) \(\dfrac{5}{6}\).

d) \(\dfrac{12}{3}=4\).

12 Flour for cookies ★★★

\(3\times\dfrac{3}{4}=\dfrac{9}{4}=2\dfrac{1}{4}\).

You need \(2\dfrac{1}{4}\) cups of flour.

13 A day on the trail ★★★

Wholes: \(2+1=3\). Fractions: \(\dfrac{3}{10}+\dfrac{8}{10}=\dfrac{11}{10}=1\dfrac{1}{10}\).

Total: \(3+1\dfrac{1}{10}=4\dfrac{1}{10}\). The hiker walked \(4\dfrac{1}{10}\) miles (about 6.6 kilometers).

14 Find the mistake ★★★

a) Sam added the denominators too. The parts are still ninths, so the denominator must stay 9.

b) \(\dfrac{4}{9}+\dfrac{3}{9}=\dfrac{7}{9}\).

15 Many ways to break up a number ★★★

a) \(2\dfrac{3}{4}=2+\dfrac{3}{4}\).

b) \(2\dfrac{3}{4}=\dfrac{11}{4}\). Two ways: \(\dfrac{5}{4}+\dfrac{6}{4}\) and \(\dfrac{8}{4}+\dfrac{3}{4}\). Any numerators that add to 11 work.

c) \(2\dfrac{3}{4}=\dfrac{11}{4}=11\times\dfrac{1}{4}\).

16 The rain barrel ★★★

a) Wholes \(2+1=3\); fractions \(\dfrac{3}{4}+\dfrac{2}{4}=\dfrac{5}{4}=1\dfrac{1}{4}\). Total \(4\dfrac{1}{4}\) gallons.

b) \(8\dfrac{1}{4}-4\dfrac{1}{4}=4\). The barrel has 4 gallons left (about 15 liters).

17 Shelves ★★★

a) \(7\times\dfrac{3}{4}=\dfrac{21}{4}=5\dfrac{1}{4}\) yards.

b) \(6=5\dfrac{4}{4}\), and \(5\dfrac{4}{4}-5\dfrac{1}{4}=\dfrac{3}{4}\). Yes, the plank is long enough and \(\dfrac{3}{4}\) yard is left over.

18 Who ran farther? ★★★

Dana: \(4\times\dfrac{3}{5}=\dfrac{12}{5}=2\dfrac{2}{5}\) miles.

Eli ran \(2\dfrac{4}{5}\) miles and \(2\dfrac{4}{5}-2\dfrac{2}{5}=\dfrac{2}{5}\).

Eli ran farther, by \(\dfrac{2}{5}\) mile.

19 Reading a number line ★★★

a) A is at \(1\dfrac{1}{4}=\dfrac{5}{4}\), B is at \(2\dfrac{1}{4}=\dfrac{9}{4}\), C is at \(2\dfrac{3}{4}=\dfrac{11}{4}\).

b) \(\dfrac{9}{4}-\dfrac{5}{4}=\dfrac{4}{4}=1\). A and B are 1 unit apart.

\(\dfrac{11}{4}-\dfrac{9}{4}=\dfrac{2}{4}\). B and C are \(\dfrac{2}{4}\) of a unit apart.

20 Mystery number ★★★

Work backward by adding: \(1\dfrac{4}{6}+1\dfrac{5}{6}\). Wholes \(1+1=2\); fractions \(\dfrac{4}{6}+\dfrac{5}{6}=\dfrac{9}{6}=1\dfrac{3}{6}\).

Total \(3\dfrac{3}{6}\), which is between 3 and 4. Check: \(3\dfrac{3}{6}-1\dfrac{5}{6}=2\dfrac{9}{6}-1\dfrac{5}{6}=1\dfrac{4}{6}\). I am \(3\dfrac{3}{6}\).

21 Is it 15 eighteenths? ★★★

a) The parts are still sixths. Multiplying by a whole number counts more sixths, it does not change their size, so the denominator stays 6. Also \(\dfrac{15}{18}\) is less than 1, but 3 groups of \(\dfrac{5}{6}\) are clearly more than 2 wholes.

b) \(3\times\dfrac{5}{6}=\dfrac{15}{6}=2\dfrac{3}{6}\).