A fraction represents equal parts of a whole. Halves divide into 2 equal parts; thirds into 3; fourths into 4. One half is one of two equal parts. Fractions require understanding that parts must be equal in size and knowing what the whole is.
You already know how to divide shapes into equal parts — that is exactly what a fraction uses. A fraction is a way of naming one or more equal pieces of a whole thing. When you cut a pizza into 2 equal pieces and take one piece, you have one-half, written 1/2. The bottom number (called the denominator) tells you how many equal pieces the whole was cut into. The top number (called the numerator) tells you how many of those pieces you are talking about.
Think about thirds: if you fold a piece of paper into 3 equal strips, each strip is one-third (1/3) of the paper. If you have 2 strips colored in, you have 2/3. The whole paper was split into 3 equal parts, and you are describing 2 of them. Fourths work the same way — cut something into 4 equal pieces and each piece is one-fourth (1/4), also called a quarter. You already use quarters every day when you think about coins!
The most important rule in fractions is that the parts must be equal in size. If you cut a brownie into 4 pieces but some are big and some are small, those are NOT fourths — they're just 4 pieces. Equal size is what makes a fraction fair and meaningful. If a friend says they got "half" of the sandwich but their half is twice as big as yours, something went wrong with the equal-parts rule.
One thing to notice: the more pieces you divide something into, the smaller each piece gets. One-half of a pie is bigger than one-third of the same pie, and one-third is bigger than one-fourth. This feels backward to some people because 4 is a bigger number than 2, but remember — a bigger denominator means the whole was cut into *more* pieces, so each piece is *smaller*. Keeping this in mind will help you as you learn to compare fractions later.