Basic Fractions

Short Course

This is a short course (slide show) in the basic concepts of reducing fractions and calculating the lowest common denominator.

What is a Fraction?

Another way to look at a division problem with two integers (like we did in the previous unit), is to view it as a way of breaking a number into its parts. If you remember, division is repeated subtraction. So by repeatedly subtracting the divisor, we are also calculating how many groups there are in the dividend. We often write a division calculation as dividend / divisor (the “/” means divided by) or by writing this the ratio of the dividend to the divisor, . When we write the calculation with a horizontal bar, we call this a fraction.

The English word “fraction” comes from the Latin word “fractio”. The word “fractio” means “to divide” or “to break”. We use the word “fraction” when we want to divide or break something into its parts. Each part has the same size.

So if we have an object that is made of 8 parts (like a pizza that is cut into 8 slices) and we are going to eat 3 slices (we are hungry and its very good pizza), we would represent our share of the object (pizza) by dividing 3 by 8, we would write this calculation as 3 / 8. We could also call this calculation as a “ratio” of the two integers 3 and 8 and write it as . This ratio (division) of two integers is called fraction.

When we write it as a fraction, the top number of the ratio is called the numerator and the bottom number is called the denominator. In fact, any rational number can be written with a numerator and a denominator.

We can represent any integer as a rational number (as a ratio or fraction) by substituting the integer for the numerator and making the denominator equal to 1. For example, the integer 9 can be written a 9 divided by 1, 9 / 1, or . All three ways means the same thing, the integer 9.

However, in the world of rational numbers, one situation doesn’t make any sense. Using our example of a pizza, we said that we cut it into 8 equal parts (slices). But in the world of rational numbers (including ratios and fractions), can we ever have a situation where the object (in our case, the pizza) ever have 0 (zero) parts? Having 0 (zeros) parts (slices) doesn’t make any sense so we have a rule:

• The denominator of the fraction can never be equal to 0 (zero). This also means that division by 0 (zero) will not be allowed.

We will follow this rule with all fractions to avoid this difficult situation.

Reducing Fractions

Simplifying or reducing a fraction is essential to accurately calculating with fractions. Click on the Reducing Fractions link to learn/review this concept in detail.

Lowest Common Denominator

The final basic concept is how to find the Lowest Common Denominator when you add or subtract fractions. Click on the link for detailed information and examples.