5th Grade Fractions as Division Lesson (Free PDF)
A fraction is a division problem: the numerator divided by the denominator. So 3/4 means 3 divided by 4, which is how much each person gets when 3 items are shared equally by 4 people. When the numerator is larger, the quotient is a mixed number: 7 divided by 3 is 7/3, or 2 1/3.
Grade 5 · Common Core State Standards: 5.NF.B.3
- 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.
What does a fraction mean as division?
A fraction tells how many equal parts are shared. It also tells a division problem. The top number is what gets shared. The bottom number is how many equal groups share it. Four friends share 3 bars equally. Each friend gets \(3 \div 4\)\( = \frac{3}{4}\) of a bar.
How do you share whole objects equally?
- Write the division problem. The amount to share goes first.
- Write the quotient as a fraction: the amount shared is the numerator, and the number of groups is the denominator.
- If the numerator is greater than the denominator, rewrite the fraction as a mixed number.
- Simplify if you can.
- Check that the answer makes sense with a picture.
Worked example: Share 7 squares of chocolate among 3 people. \(7 \div 3\) means 7 shared in 3 equal groups. Each person gets 2 whole squares. The 1 square left over is cut into 3 equal pieces, and each person gets 1 piece. So each person gets \(2\frac{1}{3}\) squares.
How do you write a quotient as a mixed number?
Divide the numbers. The quotient is the whole number part. The remainder becomes the numerator, and the divisor stays the denominator. For example, \(7 \div 3 = 2 \text{ R } 1\), so \(\frac{7}{3} = 2\frac{1}{3}\). On a number line, 7/3 is the point that lies between 2 and 3.
Why can a quotient be greater than 1?
When the amount shared is greater than the number of groups, every group gets more than 1 whole. Eleven shared by 4 gives \(\frac{11}{4} = 2\frac{3}{4}\). Each part is between 2 and 3.
| Division | Fraction | Mixed number |
|---|---|---|
| \(1 \div 2\) | \(\frac{1}{2}\) | less than 1 |
| \(5 \div 4\) | \(\frac{5}{4}\) | \(1\frac{1}{4}\) |
| \(9 \div 2\) | \(\frac{9}{2}\) | \(4\frac{1}{2}\) |
| \(10 \div 3\) | \(\frac{10}{3}\) | \(3\frac{1}{3}\) |
Questions about fractions as division
Why is 3 divided by 4 the same as the fraction 3/4?
If 3 bars are shared among 4 friends, each friend gets one fourth of each bar. That makes 3 fourths, or 3/4. So 3 divided by 4 equals 3/4.
Which number is the numerator when I write a division as a fraction?
The number being divided, called the dividend, is the numerator. The number you divide by, called the divisor, is the denominator. For 5 divided by 8, write 5/8.
How do I turn a quotient like 7 divided by 3 into a mixed number?
Divide to get a whole number and a remainder: 7 divided by 3 is 2 remainder 1. Write the remainder over the divisor as the fraction part. The answer is 2 1/3.
Can a quotient be a fraction greater than 1?
Yes. When the number being shared is larger than the number of groups, each group gets more than one whole. For example, 5 divided by 4 is 5/4, which is 1 1/4.
What happens when the division comes out even?
The quotient is a whole number. For example, 12 divided by 4 is 3, and 12/4 is just another way to write 3.
All Grade 5 chapters: Grade 5 math.
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