Algebra Readiness 2.1 Simplify Fractions

Fractions that represent the same number are called equivalent fractions. The least common multiple of the denominators of two or more fractions is called the least common denominator (LCD). A fraction is in simplest form if its numerator and denominator have a greatest common factor of 1.

Example 1: Writing Equivalent Fractions Write two fractions that are equivalent to 6/9. Multiply or divide the numerator and denominator by the same nonzero number to find an equivalent fraction. 6 = 6 · 2 = 12 multiply numerator and =18denominator by 2. 6 = 6 ÷ 3 = 2divide numerator and denominator by 3.

You Try on your white boards: Write two fractions that are equivalent to the given fraction. 1) 6/10 12/20, 3/5 2) 12/16 ¾, 6/8 3) 4/5 8/10, 12/15 4) 32/54 16/27, 64/108

In order to compare two fractions you need to have a common denominator. The easiest way to do this is to cross multiply and compare the “new” numerators. Compare2/7 and 9/12. Cross multiply: 2 x 12 and 9 x 7 “new” numerators: 24 and 63, 24 < 63, So, 2/7< 9/12.

Example 2: Comparing Fractions Compare 3/4 and 7/15. Cross Multiply: 3 x 15 and 7 x 4 45 and > 28 So, 3/4 > 7/15.

You Try on Your White Boards: Copy and compare the fractions. 5) 3/11 and ¼ 12 and 11 3/11 > ¼ 6) 7/10 and 2/5 35 and 20 7/10 > 2/5 7) 4/21 and 8/ and 168 4/21 = 8/42 8) 3/22 and 4/7 21 and 88 3/22 < 4/7

Whenever you work with fractions they always need to be in simplest form. We must reduce the numerator and denominator by their greatest common factor (GCF).

Write 10/18 in simplest form. You can use a factor tree to find the GCF Λ Λ = 2·5 18 = 2·3·3 They both have one 2. So the GCF is 2. Divide the numerator and denominator by ÷ 2 =

Example 3: Simplifying Fractions 1) Write 12/14 in simplest form Λ Λ Λ = 2 · 2 · 3 14 = 2 · 7 They both have one 2. So the GCF is 2. Divide the top and bottom by ÷ 2 =

2) Write 9/16 in simplest form. 916 Λ Λ Λ 2 4 Λ = 3 · 3 16 = 2 · 2 · 2· 2 They do not have anything in common, so 9/16 is already in simplest form.

3) Write 18/24 in simplest form Λ Λ Λ Λ Λ = 2 · 3 · 3 24 = 2 · 2 · 2 · 3 They both have one 2 and one 3, so the GCF is 2 · 3 = 6 So, divide the top and bottom by ÷ 6 =

You try on your white board. 9) 15/18 5/6 10) 8/17 8/17 11) 20/25 4/5 12) 18/81 2/9