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: $\frac{32}{41}$.