4th Grade Adding and Subtracting Fractions and Mixed Numbers Worksheet Solutions (PDF)
Grade 4 · Common Core State Standards: 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d
Exercise 1 – Add eighths
Add the numerators and keep the denominator: \(2 + 3 = 5\).
Answer: \(\frac{5}{8}\).
Exercise 2 – Add tenths
\(4 + 5 = 9\), and the denominator stays 10.
Answer: \(\frac{9}{10}\).
Exercise 3 – Subtract twelfths
\(7 – 2 = 5\).
Answer: \(\frac{5}{12}\).
Exercise 4 – Subtract tenths
\(9 – 4 = 5\), so the answer is \(\frac{5}{10}\), which equals \(\frac{1}{2}\).
Answer: \(\frac{5}{10}\).
Exercise 5 – Unit fractions
A unit fraction has numerator 1. Three fourths is 3 pieces of \(\frac{1}{4}\).
Answer: \(\frac{3}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}\).
Exercise 6 – Decompose five sixths
Split 5 into two numbers: 1 + 4 and 2 + 3.
Answer: \(\frac{5}{6} = \frac{1}{6} + \frac{4}{6}\) and \(\frac{5}{6} = \frac{2}{6} + \frac{3}{6}\).
Exercise 7 – Sum greater than 1
\(5 + 6 = 11\), so the sum is \(\frac{11}{8}\).
\(11 \div 8 = 1\) remainder 3, so \(\frac{11}{8}\) = \(1\frac{3}{8}\).
Answer: \(1\frac{3}{8}\).
Exercise 8 – Mixed number to fraction
\(2 = \frac{6}{3}\), so \(\frac{6}{3} + \frac{1}{3} = \frac{7}{3}\).
Answer: \(\frac{7}{3}\).
Exercise 9 – Fraction to mixed number
\(11 \div 4 = 2\) remainder 3.
Answer: \(2\frac{3}{4}\).
Exercise 10 – Add mixed numbers
Wholes: \(1 + 2 = 3\). Fractions: \(\frac{2}{5} + \frac{1}{5} = \frac{3}{5}\).
Answer: \(3\frac{3}{5}\).
Exercise 11 – Regroup after adding
Wholes: \(3 + 1 = 4\). Fractions: \(\frac{5}{6} + \frac{4}{6} = \frac{9}{6} = 1\frac{3}{6}\).
\(4 + 1\frac{3}{6} = 5\frac{3}{6}\).
Answer: \(5\frac{3}{6}\).
Exercise 12 – Subtract mixed numbers
Wholes: \(4 – 2 = 2\). Fractions: \(\frac{7}{8} – \frac{3}{8} = \frac{4}{8}\).
Answer: \(2\frac{4}{8}\).
Exercise 13 – Subtract with regrouping
\(5\frac{1}{4} = \frac{21}{4}\) and \(2\frac{3}{4} = \frac{11}{4}\).
\(\frac{21}{4} – \frac{11}{4} = \frac{10}{4} = 2\frac{2}{4}\).
Answer: \(2\frac{2}{4}\).
Exercise 14 – Whole minus mixed
\(6 = \frac{30}{5}\) and \(2\frac{3}{5} = \frac{13}{5}\).
\(\frac{30}{5} – \frac{13}{5} = \frac{17}{5} = 3\frac{2}{5}\).
Answer: \(3\frac{2}{5}\).
Exercise 15 – Weekend runs
\(\frac{3}{8} + \frac{4}{8} = \frac{7}{8}\).
Answer: \(\frac{7}{8}\) mile.
Exercise 16 – Pizza left
The whole pizza is \(\frac{12}{12}\). \(\frac{12}{12} – \frac{5}{12} = \frac{7}{12}\).
Answer: \(\frac{7}{12}\) of the pizza.
Exercise 17 – Two boards
Wholes: \(2 + 1 = 3\). Fractions: \(\frac{3}{10} + \frac{8}{10} = \frac{11}{10} = 1\frac{1}{10}\).
\(3 + 1\frac{1}{10} = 4\frac{1}{10}\).
Answer: \(4\frac{1}{10}\) feet.
Exercise 18 – Flour left
\(4\frac{1}{3} = \frac{13}{3}\) and \(1\frac{2}{3} = \frac{5}{3}\).
\(\frac{13}{3} – \frac{5}{3} = \frac{8}{3} = 2\frac{2}{3}\).
Answer: \(2\frac{2}{3}\) cups.
Exercise 19 – Ethan's walk
Wholes: \(1 + 2 + 1 = 4\). Fractions: \(\frac{1}{4} + \frac{2}{4} + \frac{3}{4} = \frac{6}{4} = 1\frac{2}{4}\).
\(4 + 1\frac{2}{4} = 5\frac{2}{4}\).
Answer: \(5\frac{2}{4}\) miles.
Exercise 20 – Ribbon
Used: wholes \(1 + 2 = 3\), fractions \(\frac{3}{8} + \frac{4}{8} = \frac{7}{8}\), so \(3\frac{7}{8}\) yards.
Left: \(5 = \frac{40}{8}\) and \(3\frac{7}{8} = \frac{31}{8}\), so \(\frac{40}{8} – \frac{31}{8} = \frac{9}{8} = 1\frac{1}{8}\).
Answer: \(1\frac{1}{8}\) yards.
All Grade 4 chapters: Grade 4 math.
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