Dividing Unit Fractions and Whole Numbers

Lesson 1 of 2

In this lesson:

• Divide a unit fraction by a whole number
• Divide a whole number by a unit fraction
• Use visual models for both types

Goals for Today's Fraction Division Lesson

By the end of this lesson, you should be able to:

1. Split a unit fraction into equal parts and find the quotient
2. Count how many unit fractions fit into a whole number
3. Draw fraction bar models for both division types

Quick Review of Unit Fractions

You already know that a unit fraction has 1 as the numerator:

• , , , ...
• Each one represents one equal part of a whole

Today we explore: what happens when we divide these fractions?

Sharing a Fraction Among Groups

You have of a pizza. You share it equally among 4 friends.

• Question: How much of the whole pizza does each friend get?
• Predict: Will each piece be more or less than ?

Each friend gets a smaller piece — we are dividing!

Fraction Bar Shows One Third Divided by Four

Each small part is of the whole bar.

Solving One Third Divided by Four

Multiplication check:

The answer checks out — four copies of equal .

Another Example: One Half Divided by Three

• Start with of the whole
• Split that half into 3 equal parts
• Each part is of the whole

Check:

Quick Check: One Fourth Divided by Two

What is ?

• Picture a fraction bar with shaded
• Split that quarter into 2 equal parts
• How much of the whole is each part?

Think before the next slide...

The Pattern for Unit Fraction Divided by Whole

• (answer to the Quick Check)
• The denominator multiplies by the divisor
• Splitting into parts makes pieces times smaller

Practice: Unit Fraction Divided by Whole

Solve each problem. Draw a model and write a multiplication check.

Pause and try before the next slide.

Practice Answers: Unit Fraction Divided by Whole

Problem 1:

Check:

Problem 2:

Check:

Now Flip the Division Around

We just learned:

Now consider:

• These are NOT the same question!
• Different question → very different answer

Counting Fraction Pieces in Wholes

You have 4 feet of ribbon. Each bow needs foot.

• Question: How many bows can you make?
• Think: How many -size pieces fit in 4 wholes?

Each whole has 3 thirds, so 4 wholes have many thirds!

Four Wholes Divided Into Thirds

Count all the thirds: 4 × 3 = 12 pieces.

Solving Four Divided by One Third

Multiplication check:

The answer is bigger than 4 — and that is correct!

Why Dividing by a Fraction Gives More

"Dividing makes things bigger? That seems wrong!"

• With whole numbers: 12 ÷ 3 = 4 (smaller)
• With unit fractions: 4 ÷ = 12 (bigger!)

Why? Each whole contains multiple fraction pieces. More pieces means a larger count.

Another Example: Three Divided by One Half

• Each whole has 2 halves
• Three wholes have 3 × 2 = 6 halves

Check:

Quick Check: Five Divided by One Fourth

What is ?

• How many quarters fit in 5 wholes?
• Each whole has _____ quarters
• So 5 wholes have _____ quarters total

Think before the next slide...

The Pattern for Whole Divided by Unit Fraction

• (answer to the Quick Check)
• Multiply the whole number by the denominator
• The answer is always larger than the starting number

Practice: Whole Divided by Unit Fraction

Solve each problem. Draw a model and write a multiplication check.

Pause and try before the next slide.

Practice Answers: Whole Divided by Unit Fraction

Problem 1:

Check:

Problem 2:

Check:

Summary of Both Division Types

✓ Splitting a fraction gives a smaller result
✓ Counting fraction pieces gives a larger result
✓ Always verify: quotient × divisor = dividend

and are not the same!
Dividing by a unit fraction increases the result