Simplifying Fractions

Simplifying Fractions

  • When writing a fractional answer, the fraction should be reduced to lowest terms or simplified.
  • To simplify a fraction, divide out or cancel out any factors other than one that are common to both the numerator and denominator.

Example: 6/8

  • Both 6 and 8 are divisible by 2.
  • 6 = 2 \times 3
  • 8 = 2 \times 4
  • Cancel out the common factor of 2, leaving \frac{3}{4}.
  • \frac{6}{8} and \frac{3}{4} are equivalent fractions.
  • A fraction is simplified when the only common factor between the numerator and denominator is 1.

Using TI-83/84 Calculator to Simplify Fractions

  1. Enter the fraction as numerator ÷ denominator.
  2. Press the MATH key, then ENTER twice.

Examples

Example 1: 3/9

  • 3 = 3 \times 1
  • 9 = 3 \times 3
  • Divide out the common factor of 3.
  • Simplified fraction: \frac{1}{3}.

Example 2: 12/28

  • 12 = 4 \times 3
  • 28 = 4 \times 7
  • Divide out the common factor of 4.
  • Simplified fraction: \frac{3}{7}.
  • If you didn't recognize that 4 went into both of those and you just started with the 2, you could still get to \frac{3}{7} eventually as long as you're paying attention to what you have and going, okay. Yeah. It's still divisible by two. So as long as there's a number other than one that will divide evenly into both, then it's still reducible.

Alternative Approach for 12/28

  • Divide out a 2:
    • 12 = 2 \times 6
    • 28 = 2 \times 14
    • This yields \frac{6}{14}.
  • Both 6 and 14 are divisible by 2, so divide out another 2:
    • 6 = 2 \times 3
    • 14 = 2 \times 7
    • This simplifies to \frac{3}{7}.

Calculator Usage

  • Input 3 ÷ 9, then MATH, ENTER, ENTER to get \frac{1}{3}.
  • Input 12 ÷ 28, then MATH, ENTER, ENTER to get \frac{3}{7}.

Example 3: 105/150

  • Using the calculator: 105 ÷ 150, then MATH, ENTER, ENTER.
  • Simplified fraction: \frac{7}{10}.

Example 4: 192/246

  • Using the calculator: 192 ÷ 246, then MATH, ENTER, ENTER.
  • Simplified fraction: \frac{32}{41}.