Why Equal Parts Matter

Before we write any fraction symbols, we need one idea to be crystal clear: equal parts.

Imagine three friends find one whole sandwich. If they break it into pieces of different sizes, one person gets more than the others. That is not fair.

For sharing to be fair, every piece must be exactly the same size. That single idea is the foundation of every fraction you will ever use.

What “Equal” Really Means

Two parts are equal only when they cover exactly the same amount of the whole. “Almost the same” is not good enough.

• 2 equal parts → each is one-half
• 3 equal parts → each is one-third
• 4 equal parts → each is one-fourth

The more equal parts we make, the smaller each part becomes.

1. Exploring Equal Parts

Divide the whole into equal parts. Every slice must be the same size.

Checking for True Equality

Sometimes pieces look similar but are not equal. One piece might be slightly larger. That small difference matters.

What is a Unit Fraction?

A unit fraction is a fraction with 1 as the numerator. The most important ones for now are:

1/2   1/3   1/4   1/6   1/8

Every other fraction is made by repeating a unit fraction. 3/4 is simply three pieces of 1/4. 2/3 is two pieces of 1/3.

Build 3/4 of a Pizza

This pizza is divided into 4 equal slices. Each slice is 1/4. Click slices to shade them. Shade exactly 3 slices to make 3/4.

Seeing Unit Fractions Clearly

When a whole is divided into equal parts, one single part is the unit fraction for that whole.

• 2 equal parts → one part is 1/2
• 3 equal parts → one part is 1/3
• 4 equal parts → one part is 1/4

Lesson 2 Quiz — Unit Fractions

5 questions · 4 options each. Your percent score becomes XP.

A Fraction Is a Number

In Lessons 1 and 2 we treated fractions as parts of a whole — equal pieces of a pizza or equal groups of shells. That is important. Now we take the next step: we treat a fraction as a number that has a location on the number line.

The number line runs from 0 to 1 (and beyond). Every fraction between 0 and 1 has an exact place on that line.

How the Number Line Works with Fractions

Imagine the distance from 0 to 1 as one whole. If we divide that distance into 4 equal lengths, each length is 1/4.

• 0 is the start
• 1/4 is one jump of size 1/4 from 0
• 2/4 (same as 1/2) is two jumps
• 3/4 is three jumps
• 4/4 (same as 1) is four jumps — back to the whole

The same idea works for any unit fraction: 1/3, 1/6, 1/8, and so on.

Why the Number Line Matters

Being able to place a fraction on the number line is the bridge between “parts of a shape” and “fractions as numbers we can compare and later calculate with.”

If you only see fractions as pizza slices, later work gets harder. When you can also see them on the number line, you build a much stronger foundation for comparing fractions and understanding equivalence.

Interactive Number Line

The line below shows 0 to 1 divided into fourths. Click a mark to place Finn there. Try to place him at 3/4.

Lesson 3 Quiz — Number Line

5 questions. Your percent score becomes XP.

One idea

Two fractions can name the same amount even when they look different. That is called being equivalent.

See it with bars

Look at two bars that are the same length. The first is cut into 2 equal parts with 1 shaded. The second is cut into 4 equal parts with 2 shaded.

Build it

Shade parts on the bar to make a fraction equivalent to 1/2. Use 4 equal parts.

Lesson 4 Quiz — Equivalence

5 questions · 4 options. Score % becomes XP.

One idea

When two fractions have the same denominator, the one with the larger numerator is greater. More equal pieces means more of the whole.

Same-size pieces

Fourths are the same size as each other. So 3 fourths is more pizza than 1 fourth.

On the number line

Farther to the right means greater. 3/4 sits to the right of 1/4 on the line from 0 to 1.

Lesson 5 Quiz — Compare

5 questions · 4 options. Score % becomes XP.