5th Grade Adding and Subtracting Fractions with Unlike Denominators Quiz: 10 Questions with Explanations

A \(\frac{2}{6}\)B \(\frac{2}{4}\)C \(\frac{3}{4}\)D \(\frac{1}{8}\)

One half is 2/4, and 2/4 + 1/4 = 3/4. Adding numerators and denominators gives 2/6, which is a common mistake.

A \(\frac{5}{6}\)B \(\frac{3}{9}\)C \(\frac{3}{6}\)D \(\frac{2}{18}\)

Rename 2/3 as 4/6, then 4/6 + 1/6 = 5/6. Adding 2 + 1 over 3 + 6 is wrong.

A \(\frac{5}{12}\)B \(\frac{11}{12}\)C \(\frac{2}{12}\)D \(\frac{7}{12}\)

The LCD is 12: 9/12 – 2/12 = 7/12. A typical mistake is renaming 1/6 as 4/12 instead of 2/12.

A \(3\frac{3}{4}\)B \(3\frac{2}{6}\)C \(3\frac{1}{4}\)D \(4\frac{1}{4}\)

Rename 1/2 as 2/4. Then 1 + 2 = 3 and 2/4 + 1/4 = 3/4.

A \(3\frac{7}{10}\)B \(4\frac{3}{10}\)C \(3\frac{3}{10}\)D \(4\frac{7}{10}\)

Rename with tenths: 7 2/10 – 3 5/10. Regroup: 6 12/10 – 3 5/10 = 3 7/10. Subtracting the smaller fraction from the larger gives 4 3/10, which is wrong.

A About 1/2B About 1C About 2D About 1 1/2

5/8 is a little more than 1/2 and 4/9 is a little less than 1/2. Two halves make about 1.

A \(\frac{8}{10}\) mileB \(1\frac{1}{12}\) milesC \(\frac{19}{24}\) mileD \(1\frac{7}{12}\) miles

9/12 + 10/12 = 19/12 = 1 7/12. Adding the numerators and denominators gives 8/10, which is too small.

A \(3\frac{1}{6}\) cupsB \(2\frac{1}{6}\) cupsC \(2\frac{5}{6}\) cupsD \(3\frac{5}{6}\) cups

4 3/6 – 1 4/6: regroup to 3 9/6 – 1 4/6 = 2 5/6.

A \(\frac{5}{12}\)B \(\frac{7}{12}\)C \(\frac{11}{12}\)D \(\frac{1}{12}\)

1 1/4 is 15/12 and 2/3 is 8/12. Then 15/12 – 8/12 = 7/12.

A \(\frac{1}{10}\) mileB \(\frac{1}{5}\) mileC \(\frac{4}{5}\) mileD \(\frac{3}{10}\) mile

5/10 – 3/10 = 2/10, which simplifies to 1/5. Adding gives 4/5, which is the wrong operation.