5th Grade Fractions as Division Worksheet Solutions (PDF)
This fractions as division answers for 5th Grade covers fractions as division (Common Core 5.NF.B.3), with a free PDF to print.
This answer key gives a full worked solution for each of the 20 problems. Every solution shows the division, the fraction, and the mixed number, with the final answer in bold. Compare each step with the student paper to find where a mistake started.
Grade 5 · Common Core State Standards: 5.NF.B.3
Fractions as division answers: exercises 1 to 10
Exercise 1 – Half of a share
A fraction bar means division, so \(1 \div 2 = \frac{1}{2}\).
\(\frac{1}{2}\)
Exercise 2 – Three fifths
A fraction bar means division, so \(3 \div 5 = \frac{3}{5}\).
\(\frac{3}{5}\)
Exercise 3 – Fraction to division
The numerator is divided by the denominator.
\(\frac{4}{9} = 4 \div 9\)
4 shared equally among 9 people gives each person \(\frac{4}{9}\).
Exercise 4 – Seven eighths
A fraction bar means division, so \(7 \div 8 = \frac{7}{8}\).
\(\frac{7}{8}\)
Exercise 5 – Sandwiches for three
Division problem: \(2 \div 3\).
A fraction bar means division, so \(2 \div 3 = \frac{2}{3}\).
\(\frac{2}{3}\)
Each friend gets \(\frac{2}{3}\) of a sandwich.
Exercise 6 – Improper fraction
A fraction bar means division, so \(5 \div 4 = \frac{5}{4}\).
4 goes into 5 exactly 1 times with 1 left over. The 1 left over is split into 4 equal parts, which is \(\frac{1}{4}\) of a whole.
\(\frac{5}{4} = 1\frac{1}{4}\).
\(1\frac{1}{4}\)
Exercise 7 – Nine halves
A fraction bar means division, so \(9 \div 2 = \frac{9}{2}\).
2 goes into 9 exactly 4 times with 1 left over. The 1 left over is split into 2 equal parts, which is \(\frac{1}{2}\) of a whole.
\(\frac{9}{2} = 4\frac{1}{2}\).
\(4\frac{1}{2}\)
Exercise 8 – Eleven thirds
A fraction bar means division, so \(11 \div 3 = \frac{11}{3}\).
3 goes into 11 exactly 3 times with 2 left over. The 2 left over is split into 3 equal parts, which is \(\frac{2}{3}\) of a whole.
\(\frac{11}{3} = 3\frac{2}{3}\).
\(3\frac{2}{3}\)
Exercise 9 – Thirteen fifths
A fraction bar means division, so \(13 \div 5 = \frac{13}{5}\).
5 goes into 13 exactly 2 times with 3 left over. The 3 left over is split into 5 equal parts, which is \(\frac{3}{5}\) of a whole.
\(\frac{13}{5} = 2\frac{3}{5}\).
\(2\frac{3}{5}\)
Exercise 10 – Between two whole numbers
A fraction bar means division, so \(17 \div 6 = \frac{17}{6}\).
6 goes into 17 exactly 2 times with 5 left over. The 5 left over is split into 6 equal parts, which is \(\frac{5}{6}\) of a whole.
\(\frac{17}{6} = 2\frac{5}{6}\).
\(2\frac{5}{6}\)
The quotient is between 2 and 3.
Exercises 11 and up
Exercise 11 – Compare two quotients
\(7 \div 4 = \frac{7}{4} = 1\frac{3}{4}\).
\(9 \div 6 = \frac{9}{6} = 1\frac{3}{6} = 1\frac{1}{2}\).
Compare \(1\frac{3}{4}\) and \(1\frac{1}{2}\): \(\frac{3}{4} > \frac{1}{2}\).
\(7 \div 4\) is greater.
Exercise 12 – Missing number
The fraction \(\frac{3}{5}\) means \(3 \div 5\).
The missing number is \(3\).
Exercise 13 – Simplify the share
A fraction bar means division, so \(8 \div 12 = \frac{8}{12}\).
Simplify by dividing the top and bottom by 4: \(\frac{8}{12} = \frac{2}{3}\).
\(\frac{2}{3}\)
Exercise 14 – Fifteen sixths
A fraction bar means division, so \(15 \div 6 = \frac{15}{6}\).
6 goes into 15 exactly 2 times with 3 left over. The 3 left over is split into 6 equal parts, which is \(\frac{3}{6}\) of a whole.
\(\frac{15}{6} = 2\frac{3}{6}\).
Simplify: \(2\frac{3}{6} = 2\frac{1}{2}\).
\(2\frac{1}{2}\)
Exercise 15 – Trail mix
A fraction bar means division, so \(4 \div 5 = \frac{4}{5}\).
\(\frac{4}{5}\)
Each friend gets \(\frac{4}{5}\) pound.
Exercise 16 – Pizza for the team
A fraction bar means division, so \(3 \div 8 = \frac{3}{8}\).
\(\frac{3}{8}\)
Each player gets one slice from each pizza, so each player gets 3 slices out of 8.
Each player gets \(\frac{3}{8}\) of a pizza.
Exercise 17 – Ribbon pieces
A fraction bar means division, so \(17 \div 4 = \frac{17}{4}\).
4 goes into 17 exactly 4 times with 1 left over. The 1 left over is split into 4 equal parts, which is \(\frac{1}{4}\) of a whole.
\(\frac{17}{4} = 4\frac{1}{4}\).
\(4\frac{1}{4}\)
Each piece is \(4\frac{1}{4}\) feet long.
Exercise 18 – Bags of apples
A fraction bar means division, so \(25 \div 6 = \frac{25}{6}\).
6 goes into 25 exactly 4 times with 1 left over. The 1 left over is split into 6 equal parts, which is \(\frac{1}{6}\) of a whole.
\(\frac{25}{6} = 4\frac{1}{6}\).
\(4\frac{1}{6}\)
\(4\frac{1}{6}\) is between 4 and 5.
Each bag holds \(4\frac{1}{6}\) pounds, and yes, that is between 4 and 5 pounds.
Exercise 19 – Juice at recess
A fraction bar means division, so \(9 \div 12 = \frac{9}{12}\).
Simplify by dividing the top and bottom by 3: \(\frac{9}{12} = \frac{3}{4}\).
\(\frac{3}{4}\)
Each small cup gets \(\frac{3}{4}\) cup of juice.
Exercise 20 – Clay for art class
First find each group’s share.
A fraction bar means division, so \(22 \div 8 = \frac{22}{8}\).
8 goes into 22 exactly 2 times with 6 left over. The 6 left over is split into 8 equal parts, which is \(\frac{6}{8}\) of a whole.
\(\frac{22}{8} = 2\frac{6}{8}\).
Simplify: \(2\frac{6}{8} = 2\frac{3}{4}\).
\(2\frac{3}{4}\)
Now subtract what was used: \(2\frac{3}{4} – 1\frac{1}{4} = 1\frac{2}{4} = 1\frac{1}{2}\).
Each group has \(1\frac{1}{2}\) pounds of clay left.
Key facts behind this fractions as division answers
- The fraction a/b means a divided by b.
- The numerator is the amount shared. The denominator is the number of equal groups.
- If a is less than b, the quotient is less than 1.
- If a is greater than b, write the quotient as a mixed number: whole part plus remainder over divisor.
- Check with a picture or a number line.
How to use this fractions as division answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
Download the fractions as division answers as a PDF with the button below and keep it with your notes.
Download the fractions as division answers as a PDF with the button below and keep it with your notes.
Download the fractions as division answers as a PDF with the button below and keep it with your notes.
Download the fractions as division answers as a PDF with the button below and keep it with your notes.
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