Unit 5 — Fractions

Welcome back!

Until now, we have mostly worked with whole numbers.

Sometimes, however, a whole object is divided into equal parts.

Fractions help us describe those parts.

You use fractions every day, whether you are sharing a pizza, measuring ingredients, or telling time.

What Is a Fraction?

A fraction represents one or more equal parts of a whole.

For example:

If a pie is divided into 4 equal pieces and you eat 1 piece, you have eaten:

1/4

The whole pie has been divided into four equal parts.

Numerator and Denominator

Every fraction has two numbers.

The top number is the numerator.

It tells how many parts we have.

The bottom number is the denominator.

It tells how many equal parts make the whole.

Example:

3/5

Numerator:

3

Denominator:

5

This means:

3 of 5 equal parts.

Fractions Must Be Equal Parts

Fractions only work when the whole is divided into equal-sized pieces.

If one piece is larger than another, the pieces are not equal, and they do not represent correct fractions.

Equal parts are one of the most important ideas in working with fractions.

Comparing Fractions

Fractions can be compared.

Suppose we compare:

1/2

and

1/4

If two identical pizzas are used:

One-half is larger than one-fourth.

The fewer equal pieces a whole is divided into, the larger each piece becomes.

Fractions on a Number Line

Fractions can also be placed on a number line.

For example:

0 —— 1/4 —— 2/4 —— 3/4 —— 1

A number line shows that fractions are numbers, just like whole numbers.

They tell us where a value belongs between 0 and 1, or beyond.

Fractions in Everyday Life

Fractions appear in many situations.

Examples include:

• measuring ingredients
• sharing food
• dividing time
• measuring distance
• building projects
• music
• sports

Learning fractions helps us solve practical problems.

Activity

Find five examples of fractions around your home or classroom.

Examples might include:

• a measuring cup
• a clock
• a pizza
• a chocolate bar
• a ruler

Write the fraction you observe and explain what it represents.

Practice

Answer these questions.

What does the numerator tell us?

What does the denominator tell us?

Why must fractions represent equal parts?

Which is larger:

1/2 or 1/4?

Name three everyday uses for fractions.

Review

Today you learned:

• fractions describe equal parts of a whole
• every fraction has a numerator and denominator
• equal parts are essential
• fractions can be compared
• fractions can be placed on a number line
• fractions are useful in everyday life

Fractions help us describe quantities that are smaller than whole numbers while remaining precise and easy to understand.

Looking Ahead

Next we will explore measurement and geometry.

You will discover how mathematicians measure length, area, perimeter, angles, and shapes to better understand the world around us.