Part 1: Numbers

# 1.3: Simplifying fractions

Notes

In the following, “A/B” represents the fraction “A over B.” For example, “2/3” refers to the fraction “2 over 3” or “two-thirds.”

When reporting a fraction, we generally want to express the fraction in its simplest form (lowest terms). To simplify a fraction, find a whole number other than 1 that divides both the numerator (top number) and denominator (bottom number) evenly. In other words, find a common factor for the numerator and denominator. Then simply divide the numerator and denominator by this common factor to create an equivalent fraction. Repeat if necessary until there are no further common factors; the final fraction is in simplest form.

For example, to find the simplest form for 18/42:

• Divide each of 18 and 42 by 2: 18/42 = 9/21.
• Divide each of 9 and 21 by 3: 9/21 = 3/7.
• 3/7 is the simplest form since 3 and 7 have no common factors.
• Note that we could have done this in one step by dividing each of 18 and 42 by 6: 18/42 = 3/7.

The video below shows how to express a selection of fractions in simplest form.

Practice Exercises

Do the following exercises to practice expressing fractions in simplest form. Write the numerator and denominator of the fraction in simplest form in each box. For example, 63/84 has simplest form 3/4 (since 21 is a common factor of 63 and 84 and 63/21 = 3 and 84/21 = 4), so you would write 3 for the numerator and 4 for the denominator.