Grade: Grade 3 Subject: Mathematics Unit: Fractions Introduction SAT: Algebra ACT: Math

Fractions Basics

Fractions are everywhere! When you share a pizza, cut a sandwich in half, or eat part of a chocolate bar, you're using fractions. Let's learn how fractions work!

What is a Fraction?

A Fraction is Part of a Whole!

When we divide something into equal parts and take some of those parts, we're working with fractions. A fraction tells us how many parts we have out of how many total equal parts.

🍕 Think About Pizza!

Imagine a pizza cut into 4 equal slices. If you eat 1 slice, you've eaten one fourth (or one quarter) of the pizza.

You ate 1 out of 4 slices

That's the fraction 1/4 (one fourth)!

Key Idea: For something to be a fraction, all the parts must be equal in size! If a pizza is cut into unequal pieces, we can't use fractions to describe them easily.

Parts of a Fraction

Every fraction has two numbers - one on top and one on bottom. Let's learn what they mean!

3 4
3 = Numerator
^
How many parts we HAVE (the top number)
4 = Denominator
v
How many EQUAL parts in the whole (the bottom number)

🧠 Remember It This Way!

  • Denominator is DOWN at the bottom - both start with "D"!
  • Numerator is the Number of parts you have - both start with "N"!

In the fraction 3/4:

3 = We have 3 parts (numerator)

4 = The whole has 4 equal parts (denominator)

We have 3 out of 4 equal parts!

See Fractions with Pictures

Click on the bars and circles below to see how fractions work!

Fraction Bar: Click to fill or empty parts!

This bar is divided into 4 equal parts. Click each part to fill it in.

0/4

Click the parts to shade them!

Fraction Circle: Click the slices!

This circle is divided into 8 equal parts. Click to fill slices.

0/8

Click the slices to shade them!

Unit Fractions

A unit fraction is a special fraction where the numerator is always 1. It represents ONE part of a whole.

Unit Fractions Have 1 on Top!

1/2, 1/3, 1/4, 1/5, 1/6... These are all unit fractions because they show ONE equal part.

1/2
One Half
1/3
One Third
1/4
One Fourth
1/6
One Sixth
1/8
One Eighth
Notice Something? The bigger the denominator, the SMALLER each piece is! 1/8 is smaller than 1/4 because when you cut something into 8 pieces, each piece is smaller than if you cut it into 4 pieces.

Build Your Own Fraction

Use the controls below to create different fractions and see what they look like!

Fraction Builder

1/4

One fourth - 1 out of 4 equal parts

Fractions in Real Life

Fractions are all around us! Here are some examples:

🍕
Sharing Food

Split a pizza into 8 slices and take 3 - that's 3/8 of the pizza!

Telling Time

Half past (1/2 hour) and quarter past (1/4 hour) use fractions!

📏
Measuring

A ruler shows inches divided into halves, fourths, and eighths.

🥧
Recipes

Recipes use fractions like 1/2 cup of sugar or 3/4 teaspoon of salt.

💰
Money

A quarter is 1/4 of a dollar, and two quarters is 1/2 (or 2/4) of a dollar!

Sports

Games have halves (1/2) or quarters (1/4) like football and basketball!

Worked Examples

📝 Example 1: Reading a Fraction

What does the fraction 2/3 mean?

Step 1: Look at the denominator (bottom number): 3

This tells us the whole is divided into 3 equal parts.

Step 2: Look at the numerator (top number): 2

This tells us we have 2 of those parts.

Answer: 2/3 means 2 out of 3 equal parts!

📝 Example 2: Writing a Fraction

A candy bar is divided into 6 equal pieces. Emma ate 4 pieces. What fraction did Emma eat?

Step 1: Find the total equal parts: 6 pieces

The denominator is 6.

Step 2: Find how many parts Emma has: 4 pieces

The numerator is 4.

Answer: Emma ate 4/6 of the candy bar!

📝 Example 3: Identifying a Fraction from a Picture

What fraction is shaded?

Step 1: Count total parts: 5 parts

Step 2: Count shaded parts: 3 parts

Answer: 3/5 (three fifths) is shaded!

Practice Problems

Test your knowledge! Click the correct answer for each question.

Problem 1: What is the numerator in the fraction 5/8?

Problem 2: What is the denominator in the fraction 3/4?

Problem 3: A pie is cut into 6 equal slices. You eat 2 slices. What fraction did you eat?

Problem 4: Which of these is a unit fraction?

Problem 5: Look at this fraction bar. What fraction is shaded?

Fraction Match Game

Can you identify the fraction shown? Click the correct answer!

What fraction is shown?

Score: 0 / 0

Check Your Understanding

What does the numerator of a fraction tell us?

What does the denominator of a fraction tell us?

Which fraction shows 5 out of 8 equal parts?

What We Learned

🧩

Fractions

Fractions show parts of a whole that is divided into equal pieces.

🔢

Numerator

The top number - how many parts we HAVE.

📊

Denominator

The bottom number - how many TOTAL equal parts.

1️

Unit Fractions

Fractions with 1 on top (1/2, 1/3, 1/4...).

Keep Practicing! The more you work with fractions, the easier they become. Look for fractions in your everyday life - when you share snacks, tell time, or measure things!

Next Steps

  • Practice identifying fractions in pictures and real life
  • Make sure you can tell the numerator from the denominator
  • Try drawing your own fraction bars and circles
  • When you're ready, move on to learn about Comparing Fractions!