Write fractions in the lowest terms

key notes:

Definition of Lowest Terms:

  • A fraction is in lowest terms (or simplest form) when the numerator and denominator have no common factors other than 1. In other words, the greatest common divisor (GCD) of the numerator and denominator is 1.

Steps to Simplify a Fraction:

  • Step 1: Find the greatest common divisor (GCD) or greatest common factor (GCF) of the numerator and denominator.
  • Step 2: Divide both the numerator and the denominator by the GCD/GCF.
  • Step 3: The resulting fraction is the simplest form.

Example 1:

  • Fraction: 4/8
  • GCD of 4 and 8 is 4.
  • Divide both by 4:
    4 ÷ 4 = 1, 8 ÷ 4 = 2
  • Simplified fraction: 1/2

Example 2:

  • Fraction: 15/25
  • GCD of 15 and 25 is 5.
  • Divide both by 5:
    15 ÷ 5 = 3, 25 ÷ 5 = 5
  • Simplified fraction: 3/5

Tip for Finding the GCD:

  • List the factors of the numerator and denominator.
  • Choose the largest factor common to both.

Prime Factorization Method:

  • Break down both the numerator and denominator into prime factors.
  • Cancel out common prime factors to simplify the fraction.

Fraction Example Using Prime Factorization:

  • Fraction: 18/24
  • Prime factors of 18: 2 × 3 × 3
  • Prime factors of 24: 2 × 2 × 2 × 3
  • Cancel out the common factors of 2 and 3:
    18 ÷ 6 = 3, 24 ÷ 6 = 4
  • Simplified fraction: 3/4

Importance of Simplifying Fractions:

  • Simplifying fractions makes calculations easier, especially in addition, subtraction, multiplication, and division.
  • It helps in comparing fractions and understanding their values more clearly.

Practice Example:

  • Fraction: 28/42
  • Find the GCD of 28 and 42 (GCD = 14).
  • Divide both by 14:
    28 ÷ 14 = 2, 42 ÷ 14 = 3
  • Simplified fraction: 2/3

Learn with an example

Write 5/8 in the lowest terms.

Find the largest number that divides both the numerator and the denominator. The largest number that divides both 5 and 8 is 1. This fraction is already written in lowest terms.

Write 4/6 in the lowest terms.

Find the largest number that divides both the numerator and the denominator. The largest number that divides both 4 and 6 is 2. Divide the numerator and denominator by 2.

4 ÷ 2 = 2

6 ÷ 2 = 3

4/6 written in lowest terms is 2/3.

Write 3/6 in the lowest terms.

Find the largest number that divides both the numerator and the denominator. The largest number that divides both 3 and 6 is 3. Divide the numerator and denominator by 3.

3 ÷ 3 = 1

6 ÷ 3 = 2

3/6 written in lowest terms is 1/2.

Let’s practice!

Let’s practice!