A fraction represents a part of a whole. It is written with two numbers: the numerator on top shows how many parts we have, and the denominator on the bottom shows how many equal parts the whole is divided into.
Let's look at one half. We take a circle and divide it into two equal parts. If we shade one of these parts, we have one half, written as one over two. The numerator is one because we shaded one part, and the denominator is two because the whole is divided into two equal parts.
Now let's visualize three quarters. We divide a circle into four equal parts by drawing two perpendicular lines. Then we shade three of these four parts. This gives us three quarters, written as three over four. The numerator is three because we shaded three parts, and the denominator is four because the circle is divided into four equal parts.
Fractions can be represented using any shape, not just circles. Here we use a rectangle divided into five equal parts. If we shade two of these five parts, we get two fifths, written as two over five. This shows that fractions are a flexible way to represent parts of any whole.
We can compare fractions by looking at their visual representations. Here we compare one half and one third. When we look at the shaded areas, we can see that one half is larger than one third. This is because when we divide something into fewer parts, each part is bigger. So one half is greater than one third.
Sometimes different fractions represent the same amount. These are called equivalent fractions. For example, one half is equivalent to two fourths. If we divide a circle in half and shade one part, we get the same amount as dividing it into four parts and shading two. Both fractions represent exactly the same portion of the whole.