# The Basics of Fractions

Fractions represent parts of a whole — that is, quantities that fall between the whole numbers. Probably the most commonly used fraction is 1/2, which is *one-half.* When you cut a cake into two pieces and take one for yourself, you get 1/2 of the cake —hope you're hungry!

When you slice yourself a fraction of a cake, that fraction contains two numbers, and each number tells you something different:

The top number — called the

*numerator*— tells you the number of*shaded*slices.The bottom number — called the

*denominator*— tells you the*total*number of slices.

When the numerator of a fraction is less than the denominator, that fraction is a *proper fraction.* If the numerator is greater than the denominator, that fraction is an *improper fraction.* You can convert improper fractions into mixed numbers.

Some fractions can be easily written as whole numbers:

When a fraction's denominator is 1, that fraction is equal to its numerator.

When a fraction's numerator and denominator are the same, that fraction is equal to 1. (This idea is important when you want to change the terms of a fraction.)

When you reverse the order of the numerator and denominator in a fraction, the result is the *reciprocal* of that fraction. You use reciprocals to divide by fractions.

## Sample questions

For each cake pictured below, identify the fraction of the cake that’s shaded.

Put the number of shaded slices over the number of total slices in each cake:

**a.****b.****c.****d.**What’s the reciprocal of each of the following fractions?

**a.****b.****c.****d.**To find the reciprocal, switch around the numerator and the denominator:

**a.****The reciprocal is****b.****The reciprocal is****c.****The reciprocal is****d.****The reciprocal is**

## Practice questions

For each cake pictured, identify the fraction of the cake that’s shaded.

Which of the following fractions are proper? Which are improper?

**a.****b.****c.****d.**Rewrite each of the following fractions as a whole number:

**a.****b.****c.****d.**Find the reciprocal of the following fractions:

**a.****b.****c.****d.**

Following are the answers to the practice questions:

Identify the fraction of the cake that’s shaded.

**a.****You have 1 shaded slice and 3 slices in total, so it’s****b.****You have 3 shaded slices and 4 slices in total, so it’s****c.****You have 5 shaded slices and 6 slices in total, so it’s****d.****You have 7 shaded slices and 12 slices in total, so it’s**Which of the following fractions are proper? Which are improper?

**a.****The numerator (3) is greater than the denominator (2), so****this fraction****is an****improper fraction.****b.****The numerator (8) is less than the denominator (9), so****this fraction****is a****proper fraction.****c.****The numerator (20) is less than the denominator (23), so****this fraction****is a****proper fraction.****d.****The numerator (75) is greater than the denominator (51), so****this fraction****is an****improper fraction.**Rewrite each of the following fractions as a whole number.

**a.****The numerator and denominator are the same, so****b.****The denominator is 1, so****c.****The numerator and denominator are the same, so****d.****The denominator is 1, so**Find the reciprocal of the following fractions by switching the numerator and denominator.

**a.****The reciprocal is****b.****The reciprocal is****c.****The reciprocal is****d.****The reciprocal is**