4th Grade Adding and Subtracting Fractions and Mixed Numbers Test Solutions and Scoring (PDF)
This grade 4 add subtract fractions test answers for 4th Grade covers adding and subtracting fractions and mixed numbers (Common Core 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d), with a free PDF to print.
Grade 4 · Common Core State Standards: 4.NF.B.3a, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.3d
Grade 4 add subtract fractions test answers: worked solutions
Question 1 – Like denominators [2 pts]
(a) \(3 + 6 = 9\). (b) \(11 – 4 = 7\).
(a) \(\frac{9}{10}\) (b) \(\frac{7}{12}\)
Scoring: 1 point for each correct answer; 0 points if the denominator is added.
Question 2 – Decompose [2 pts]
Split 7 into 3 + 4 and 5 + 2.
\(\frac{7}{8} = \frac{3}{8} + \frac{4}{8}\) and \(\frac{7}{8} = \frac{5}{8} + \frac{2}{8}\) (other correct splits are accepted)
Scoring: 1 point for each correct decomposition.
Question 3 – Mixed number picture [2 pts]
2 whole strips and 3 fifths: \(2\frac{3}{5}\).
\(2 = \frac{10}{5}\), and \(\frac{10}{5} + \frac{3}{5} = \frac{13}{5}\).
\(2\frac{3}{5}\) = \(\frac{13}{5}\)
Scoring: 1 point for the mixed number; 1 point for the improper fraction.
Question 4 – Convert [2 pts]
(a) \(17 \div 6 = 2\) remainder 5, so \(2\frac{5}{6}\).
(b) \(3 = \frac{6}{2}\), and \(\frac{6}{2} + \frac{1}{2} = \frac{7}{2}\).
(a) \(2\frac{5}{6}\) (b) \(\frac{7}{2}\)
Scoring: 1 point for each part.
Question 5 – Add mixed numbers [2 pts]
Wholes: \(2 + 3 = 5\). Fractions: \(\frac{5}{8} + \frac{6}{8} = \frac{11}{8} = 1\frac{3}{8}\).
\(5 + 1\frac{3}{8} = 6\frac{3}{8}\).
\(6\frac{3}{8}\)
Scoring: 1 point for adding the wholes and the fractions; 1 point for regrouping to the correct answer.
Question 6 – Subtract mixed numbers [2 pts]
\(6\frac{2}{5} = \frac{32}{5}\) and \(3\frac{4}{5} = \frac{19}{5}\).
\(\frac{32}{5} – \frac{19}{5} = \frac{13}{5} = 2\frac{3}{5}\).
\(2\frac{3}{5}\)
Scoring: 1 point for converting correctly; 1 point for the correct answer.
Question 7 – Hiking trail [3 pts]
(a) \(5\frac{2}{10} = \frac{52}{10}\) and \(2\frac{7}{10} = \frac{27}{10}\). \(\frac{52}{10} – \frac{27}{10} = \frac{25}{10} = 2\frac{5}{10}\).
(b) \(2\frac{5}{10} = \frac{25}{10}\) and \(1\frac{8}{10} = \frac{18}{10}\). \(\frac{25}{10} – \frac{18}{10} = \frac{7}{10}\).
(a) \(2\frac{5}{10}\) miles (b) \(\frac{7}{10}\) mile
Scoring: (a) 1 point for the method, 1 point for the answer; (b) 1 point.
Question 8 – Farmers market [3 pts]
(a) Wholes \(1 + 2 = 3\), fractions \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4} = 1\frac{1}{4}\), so \(4\frac{1}{4}\).
(b) \(4\frac{1}{4} + \frac{3}{4} = 4\frac{4}{4} = 5\).
(c) \(6 – 5 = 1\).
(a) \(4\frac{1}{4}\) lb (b) 5 lb (c) 1 lb
Scoring: 1 point for each part.
Question 9 – Mia's mistake [2 pts]
Mia added the denominators. The size of the parts (fifths) does not change when you add. Two fifths plus two fifths is four fifths.
\(\frac{2}{5} + \frac{2}{5} = \frac{4}{5}\)
Scoring: 1 point for the explanation; 1 point for the correct sum.
Total score
20 points
Key facts behind this grade 4 add subtract fractions test answers
- With like denominators, add or subtract the numerators and keep the denominator.
- A fraction can be decomposed in more than one way, such as 5/6 = 2/6 + 3/6.
- A mixed number such as 2 1/4 equals the improper fraction 9/4.
- To add mixed numbers, add the wholes and the fractions, then regroup when the fraction is greater than 1.
- To subtract mixed numbers, change them to improper fractions first.
How to use this grade 4 add subtract fractions test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
Download the grade 4 add subtract fractions test answers as a PDF with the button below and keep it with your notes.
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