5th Grade Adding and Subtracting Fractions with Unlike Denominators Quiz: 10 Questions with Explanations Home 5th Grade Math Worksheets, Lessons and Tests (Free PDF) 5th Grade Adding and Subtracting Fractions with Unlike Denominators Quiz: 10 Questions with Explanations
Answer these 10 multiple-choice questions on adding and subtracting fractions with unlike denominators. Each question has one correct answer. Find a common denominator first, then read the explanation to learn from any mistake.
Grade 5 · Common Core State Standards: 5.NF.A.1, 5.NF.A.2
Question 1 The bars show two fractions. What is their sum?
1/2 1/4 The bars show one half and one fourth. 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.
Question 2 Find \(\frac{2}{3} + \frac{1}{6}\).
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.
Question 3 Find \(\frac{3}{4} - \frac{1}{6}\).
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.
Question 4 Find \(1\frac{1}{2} + 2\frac{1}{4}\).
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.
Question 5 Find \(7\frac{1}{5} - 3\frac{1}{2}\).
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.
Question 6 Use the number line to choose the best estimate of \(\frac{5}{8} + \frac{4}{9}\).
0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1 5/8 4/9 Where do the fractions sit? A About 1/2B About 1C About 2D About 1 1/25/8 is a little more than 1/2 and 4/9 is a little less than 1/2. Two halves make about 1.
Question 7 Sofia ran \(\frac{3}{4}\) mile and then \(\frac{5}{6}\) mile. How far did she run in all?
3/4 mi 5/6 mi Total = ? Sofia's run. A \(\frac{8}{10}\) mileB \(1\frac{1}{12}\) milesC \(\frac{19}{24}\) mileD \(1\frac{7}{12}\) miles9/12 + 10/12 = 19/12 = 1 7/12. Adding the numerators and denominators gives 8/10, which is too small.
Question 8 Liam has \(4\frac{1}{2}\) cups of flour and uses \(1\frac{2}{3}\) cups. How much flour is left?
A \(3\frac{1}{6}\) cupsB \(2\frac{1}{6}\) cupsC \(2\frac{5}{6}\) cupsD \(3\frac{5}{6}\) cups4 3/6 - 1 4/6: regroup to 3 9/6 - 1 4/6 = 2 5/6.
Question 9 Which number makes this true? \(\frac{2}{3} + ? = 1\frac{1}{4}\)
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.
Question 10 Ethan walks \(\frac{1}{2}\) mile to school and \(\frac{3}{10}\) mile to the park. How much farther is the school?
A \(\frac{1}{10}\) mileB \(\frac{1}{5}\) mileC \(\frac{4}{5}\) mileD \(\frac{3}{10}\) mile5/10 - 3/10 = 2/10, which simplifies to 1/5. Adding gives 4/5, which is the wrong operation.
Remember
Fractions must have the same denominator before they can be added or subtracted.
The least common denominator is the smallest number both denominators divide into.
Only the numerators are added or subtracted. The denominator stays the same.
To subtract mixed numbers, regroup one whole as a fraction when needed.
Benchmarks 0, 1/2, and 1 help check that an answer makes sense.
All Grade 5 chapters: Grade 5 math .
Place Value and Powers of Ten Test with Point Values
