Fractions Intro

A fraction names an equal part of a whole or a group.

Reading is good — doing is better. Practice Fractions intro as an interactive lesson.

Definition

A fraction is a number that shows how many equal parts you have out of a total number of equal parts. It is written with two numbers stacked, like 3/4, where the bottom number tells you how many equal parts the whole is split into, and the top number tells you how many of those parts you are talking about.

Remember the rule

Numerator over Denominator: TOP = parts you HAVE, BOTTOM = parts in the WHOLE.

Key words

Fraction: A number that shows a part of a whole, written as one number over another, like 1/2.
Numerator: The top number in a fraction. It tells how many parts you have.
Denominator: The bottom number in a fraction. It tells how many equal parts the whole is cut into.
Equal parts: Parts that are all exactly the same size, not bigger or smaller than each other.
Whole: The entire thing before it is split into parts, like a whole pizza or a whole candy bar.
Half: One of two equal parts of a whole, written as 1/2.
Unit fraction: A fraction where the numerator is 1, like 1/3 or 1/8. It names just one equal part.
Number line: A straight line with numbers on it that can be used to show where a fraction lives between 0 and 1.

Worked examples

A pizza is cut into 4 equal slices. You eat 1 slice. What fraction did you eat?

→ 1/4 (one-fourth) · The pizza has 4 equal parts (denominator = 4) and you ate 1 part (numerator = 1).

A chocolate bar is broken into 8 equal pieces. Your friend has 3 pieces. What fraction does your friend have?

→ 3/8 (three-eighths) · 8 equal pieces total, your friend holds 3 of them.

A circle is divided into 3 equal parts and 2 parts are colored red. Write the fraction that is colored.

→ 2/3 (two-thirds) · 3 equal parts total, 2 are colored, so the numerator is 2 and the denominator is 3.

A ribbon is cut into 6 equal pieces. One piece is used. What fraction of the ribbon is left?

→ 5/6 (five-sixths) · 6 pieces total minus 1 used leaves 5 pieces remaining.

Place 1/2 on a number line between 0 and 1.

→ Split the space between 0 and 1 into 2 equal parts. Mark the point right in the middle. That point is 1/2. · The denominator 2 tells you to make 2 equal jumps; the numerator 1 tells you to stop at the first jump.

A rectangle is split into 4 equal parts. All 4 parts are shaded. What fraction is shaded?

→ 4/4, which equals 1 whole. · When the numerator and denominator are the same, you have the whole thing.

Common mistakes

Mixing up the numerator and denominator — remember, the BOTTOM number tells the total parts, not the top.
Thinking fractions only work when the pieces look the same shape — the pieces must be equal in SIZE, even if they look different in shape.
Writing the fraction backwards, for example writing 4/1 instead of 1/4 for one-fourth.
Forgetting that all parts must be EQUAL — if the pieces are different sizes, you cannot write a fraction for them.
Thinking a bigger denominator always means a bigger fraction — 1/8 is actually smaller than 1/2 because the whole is cut into more pieces.

FAQs

Why is the bottom number called the denominator?

It comes from a word meaning 'name' — the denominator names what kind of parts we have, like fourths or eighths.

Can the numerator be bigger than the denominator?

Yes! That is called an improper fraction, like 5/4. In 3rd grade you will mostly see fractions where the numerator is smaller, but it is okay if it is equal or bigger too.

Does 2/4 and 1/2 mean the same thing?

Yes! If you cut something into 4 parts and take 2, that is the same amount as cutting it into 2 parts and taking 1. These are called equivalent fractions, and you will learn more about them soon.

How do I remember which number goes on top?

Think of it this way: you always ask HOW MANY do I have? That answer goes on top. Then ask HOW MANY total? That answer goes on the bottom.

Can a whole number be written as a fraction?

Yes! Any whole number can be written as a fraction with 1 on the bottom. For example, 3 = 3/1. Also, when the top and bottom are the same, like 4/4, that equals 1 whole.

Why do the parts have to be equal?

If the parts are not equal, the fraction does not make fair sense. Imagine splitting a cookie into one huge piece and one tiny piece — calling each piece one-half would not be fair or accurate.

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