Unit 9 — Fractions and Decimals

Welcome back!

Many things in everyday life are not whole numbers.

We measure time, money, distance, weight, and food using parts of a whole.

Fractions and decimals help us describe these quantities accurately.

Today you will strengthen your understanding of fractions and learn how they connect to decimals.

Reviewing Fractions

A fraction represents part of a whole.

Example:

3/4

The numerator tells how many parts we have.

The denominator tells how many equal parts make up the whole.

In 3/4:

• Numerator = 3
• Denominator = 4

Equivalent Fractions

Different fractions can represent the same amount.

Examples:

• 1/2 = 2/4
• 2/3 = 4/6
• 3/5 = 6/10

Multiply or divide both the numerator and denominator by the same number to create equivalent fractions.

Equivalent fractions have the same value.

Comparing Fractions

Fractions can be compared using:

• common denominators
• benchmark fractions
• visual models
• number lines

Example:

3/8 < 5/8

because both fractions have the same denominator and 3 is less than 5.

Introducing Decimals

Decimals are another way to write parts of a whole.

Examples:

• 0.5 = 1/2
• 0.25 = 1/4
• 0.75 = 3/4

The decimal point separates whole numbers from fractional parts.

Place Value with Decimals

The first place to the right of the decimal point is the tenths place.

The second place is the hundredths place.

Example:

4.36

• 4 ones
• 3 tenths
• 6 hundredths

Understanding decimal place value helps us compare and calculate accurately.

Fractions, Decimals, and Money

Money provides a familiar example of decimals.

One dollar equals:

100 cents

Examples:

$0.25

equals:

25 cents

or

1/4 of a dollar.

Using money helps us understand decimal values in everyday life.

Solving Problems

Example:

Maria walked:

2.5 miles

on Monday and

1.75 miles

on Tuesday.

How many miles did she walk altogether?

Estimate first.

Then solve carefully.

Always check whether your answer makes sense.

Activity

Create a table showing ten fractions and their matching decimals.

Include drawings or number lines for each example.

Explain how you know each pair represents the same value.

Practice

Answer these questions.

What does the numerator represent?

What does the denominator represent?

What are equivalent fractions?

What is the tenths place?

How are decimals used when working with money?

Why is estimation helpful?

Review

Today you learned:

• fractions represent parts of a whole
• equivalent fractions have the same value
• decimals are another way to represent fractions
• decimal place value extends the base-ten system
• money uses decimals every day
• estimation helps verify answers

Fractions and decimals help us describe the world with greater precision.

Looking Ahead

Next we will explore measurement and geometry, learning how to measure length, area, volume, angles, and shapes while solving practical real-world problems.