Not So Impossible Improper Fractions!

Lesson Plan - Get It!

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• Are you ready?

Begin with the video below on changing an improper fraction into a mixed number.

Begin by learning how to change an improper fraction into a mixed number.

Improper Fractions Are Top-Heavy Fractions

You already know what many fractions look like.

A proper fraction has a numerator that is less than the denominator.

Examples:

The numerator is smaller than the denominator, so each fraction is less than 1 whole.

An improper fraction is different.

An improper fraction has a numerator that is greater than or equal to the denominator.

Examples:

These fractions may look a little top-heavy because the top number is just as big as, or bigger than, the bottom number. That means the fraction is equal to 1 whole or more than 1 whole.

Look at this improper fraction.

This means 6 halves.

Since 2 halves make 1 whole, you can group the 6 halves like this:

2 halves = 1 whole

2 halves = 1 whole

2 halves = 1 whole

So, ⁶/₂ = 3 wholes.

Now look at this one.

This means 7 halves.

Group the halves into wholes.

2 halves = 1 whole

2 halves = 1 whole

2 halves = 1 whole

That uses 6 halves.

There is 1 half left over.

So, ⁷/₂ = 3 ¹/₂.

You just changed an improper fraction into a mixed number!

A mixed number has a whole number and a fraction together.

Examples:

The Fast Way: Divide

Drawing pictures works, but division is faster.

To change an improper fraction into a mixed number, divide the numerator by the denominator.

Try this example.

Step 1: Divide the numerator by the denominator.

7 divided by 2 = 3 remainder 1

Step 2: The answer, 3, becomes the whole number.

Step 3: The remainder, 1, becomes the new numerator.

Step 4: The denominator stays the same.

Here is another example.

Step 1: Divide.

14 divided by 5 = 2 remainder 4

Step 2: The whole number is 2.

Step 3: The remainder is 4, so 4 becomes the numerator.

Step 4: Keep the denominator, 5.

One more? Of course. Fractions like attention.

18 divided by 7 = 2 remainder 4

When you convert an improper fraction to a mixed number, the value does not change. You are just writing the same amount in a new way.

Answer the following questions.

• What are three ways fractions can be shown?
• What is the numerator? What does it represent?
• What is the denominator? What does it represent?
• What is an improper fraction?
• What do you know about the value of an improper fraction?

Fractions can be shown as a picture, as a number, or on a number line.

The numerator is the top number in a fraction and tells how many parts there are. The denominator is the bottom number and tells how many equal parts the whole is divided into.

An improper fraction has a numerator that is greater than or equal to the denominator. If the numerator equals the denominator, the fraction equals 1 whole. If the numerator is greater than the denominator, the fraction is greater than 1.

Now, look more closely at the steps for converting an improper fraction to a mixed number and the visual representation of what the improper fraction and mixed number mean.

How ⁷/₄ Becomes 1 ³/₄

Start with this improper fraction.

This means 7 fourths.

Think about fourths as pieces of a whole. One whole has 4 fourths.

⁴/₄ = 1 whole

Now count 7 fourths.

1 fourth

2 fourths

3 fourths

4 fourths

That makes 1 whole.

Keep counting.

5 fourths

6 fourths

7 fourths

After you make 1 whole, there are 3 fourths left over.

So, ⁷/₄ is the same as:

That means:

1 whole + ³/₄

So:

Now use division to get the same answer.

7 divided by 4 = 1 remainder 3

The 1 tells you there is 1 whole.

The remainder, 3, tells you there are 3 parts left over.

The denominator stays 4 because the pieces are still fourths.

So:

Try another example.

This means 11 thirds.

Since 3 thirds make 1 whole, divide 11 by 3.

11 divided by 3 = 3 remainder 2

The 3 becomes the whole number.

The 2 becomes the numerator.

The denominator stays 3.

Check it with a quick meaning check:

3 wholes = 9 thirds

2 thirds left over = 2 thirds

9 thirds + 2 thirds = 11 thirds

Yes! The mixed number and improper fraction match.

Use this step-by-step process every time.

1. Divide the numerator by the denominator.
2. Write the quotient as the whole number.
3. Write the remainder as the numerator of the fraction.
4. Keep the same denominator.
5. Check that the mixed number makes sense.

Example:

17 divided by 5 = 3 remainder 2

Why? Because 3 wholes equals 15 fifths, and 2 fifths are left over.

Write out the steps for converting an improper fraction to a mixed number using the Improper Fractions to Mixed Numbers Flow Chart from Downloadable Resources in the right-hand sidebar.

Then, check your chart against the steps below and make any necessary corrections.

• Are you ready to create and convert some improper fractions on your own?

Move to the Got It? section!