Dividing a Whole Number by Unit Fraction with Tiles

Typically, in about 5th grade in the US, students learn how to divide whole numbers by unit fractions like $ \boxed{ 3 \div \frac{1}{2} } $.

A unit fraction is just a fraction whose numerator is 1.

Examples of Unit Fractions non Examples of Unit Fractions
$$ \bf{\frac{ \red{1}}{2 } } $$ $$ \bf{ \frac{ 3}{2} } $$
$$ \bf{ \frac{ \red{1}}{5} } $$ $$ \bf{\frac{ 2 }{2}} $$

Ok, but what does this all mean ?

First, let's review dividing whole numbers by whole numbers. (We will soon see that dividing whole numbers by unit fractions has the same meaning.)

$$ 6 \div 3 $$ means : How many groups of 3 are in 6 . As you can see, there are 2 groups of 3 in 6 .

meaning of division


Now, let's look at whole by unit fraction

We can think of 2 divided by $$ \frac{1}{4} $$ as "How many $$ \frac{1}{4}$$ 's are in 2 ?

meaning of whole divided by unit fraction

Examples

Example 1
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Example 2
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Problem 1

What is $$ 3 \div \frac{1}{3} $$ ?

Practice problem on whole divided by unit fraction
Problem 2

What is $$ 4 \div \frac{1}{5} $$ ?

Practice problem on whole divided by unit fraction

back to 5th grade math lessons

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