For example, in the fraction ¼, 1 is the numerator. The fraction indicates one part of a whole that has four parts.

For example, in the fraction ¼, 4 is the denominator. This whole has been divided into four equal parts.

Some examples of improper fractions: 10/3, 9/4, 15/3, 25/5.

To simplify an improper fraction, first divide the numerator by the denominator. For example, for the fraction 10/3, divide 10 by 3. 3 goes into 10 three times (3 x 3 = 9), but there will be a remainder of 1. Write the remainder as a fraction of the original denominator. With a remainder of 1 the fraction of the mixed number will be 1/3. The mixed number of 10/3 is 31/3. Note, not all improper fractions will be mixed numbers; some will simplify into whole numbers. For example: 25/5 simplifies to 5.

Do you ever help your parents with baking? Measuring cups use fractions. A recipe may call for ¼ teaspoon of vanilla or 2/3 of a cup of flour. Pay attention throughout your day and see how many times you use fractions without even realizing it.

The circle itself is not a fraction. It represents the whole number one.

If you shade one part of the circle, you will have shaded ½ of the circle. The other half remains untouched.

If you shade one piece of the circle, you would have ¼ of the circle shaded. If you shade two pieces of the circle, you would have 2/4 of the circle shaded. Note that 2/4 simplifies to ½. You can also see this visually because you have shaded half of the circle even though it is divided into 4 parts.

Continue shading parts and writing the fraction that represents the shaded area. Remember, for a circle divided into eight parts, the denominator will always be 8; only the numerator will change to represent the shaded regions.

An example of three equivalent fractions: 1/2, 5/10, 10/20

Compare the diagrams of each fraction and see if they match. A diagram of 1/2, 5/10, and 10/20 will have identical shaded regions and therefore are all equivalent fractions. Note: For numbers with large denominators, it will be a bit more difficult to draw pictures.

For example: 1/2 is in its simplest form, but 5/10 and 10/20 can be simplified further. 5/10 can be divided by 5 to simplify to 1/2. 10/20 can be divided by 10 to simplify to 1/2.

For example: set 10/20 = 1/2. Cross multiply: 2 x 10 = 20 x 1. 20 = 20; therefore, the fractions are equivalent. Another example: 5/10 = 1/2. Cross multiply: 5 x 2 = 10 x 1. 10 = 10; therefore, the fractions are equivalent.