5th Grade Fractions as Division Lesson: Notes and Examples (Free PDF)

$5th grade fractions as division lesson – Maths PDF$

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This 5th grade fractions as division lesson covers fractions as division (Common Core 5.NF.B.3), with a free PDF to print.

Key takeaway: This lesson helps fifth grade students see a fraction as a division and use that idea to share amounts equally.

Topic: Fractions as Division (5th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 5.NF.B.3
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

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.

This lesson helps fifth grade students see a fraction as a division and use that idea to share amounts equally. It shows that three wholes shared among four people gives each person three fourths, so a fraction bar means divide.

Students learn to write a division as a fraction, to write a fraction as a division, and to turn improper fractions into mixed numbers. They also place quotients on a number line and solve sharing stories. Also, plan about 20 minutes. Then, draw a bar or a set of pieces for each example and share them out.

Grade 5 · Common Core State Standards: 5.NF.B.3

Key facts in this 5th grade fractions as division lesson

Key facts

The fraction a/b means a divided by b.
Next, 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.
Then, 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.

Each of the 4 friends gets one fourth of every bar, which is 3 fourths in all.

Fractions and division

For whole numbers a and b (b is not 0), $\frac{a}{b} = a \div b$. The numerator is the dividend and the denominator is the divisor.

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.

Seven squares shared by 3 people: each person gets 2 whole squares and 1/3 of a square.

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.

Seven divided by 3 is the same point as 7/3 on the number line.

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.

Eleven shared into 4 equal parts: each part is 11/4, or 2 3/4.

Division	Fraction	Mixed number
$1 \div 2$	$\frac{1}{2}$	less than 1
$5 \div 4$	$\frac{5}{4}$	$1\frac{1}{4}$
$9 \div 2$	$\frac{9}{2}$	$4\frac{1}{2}$
$10 \div 3$	$\frac{10}{3}$	$3\frac{1}{3}$

5th grade fractions as division lesson: questions and answers

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.

Common mistakes with this 5th grade fractions as division lesson

Students put the divisor on top of the fraction. Instead, the amount being shared is the numerator, and the number of groups is the denominator.
Students write a quotient that is greater than one as a proper fraction. Also, if the amount is greater than the number of groups, the fraction is improper.
Students ignore the whole number when they write a mixed number. Instead, divide the numerator by the denominator and keep the quotient as the whole number.

How to study this chapter

Say the division in words, such as 3 shared among 4. Finally, the sentence tells you the numerator and the denominator.
Draw a model whenever a division has a smaller number first. Also, seeing the pieces makes the fraction clear.
Parents can share a sandwich or a bar of chocolate among family members and write the result as a fraction.

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