Converting Decimals and Fractions

Converting Decimals to Fractions

• To convert a decimal to a fraction, write the decimal as a fraction with the decimal numerator and a denominator that is a power of 10 (e.g. 10, 100, 1000, etc.)
• For example:
  • 0.5 = 5/10 = 1/2
  • 0.25 = 25/100 = 1/4
  • 0.125 = 125/1000 = 1/8

Converting Fractions to Decimals

• To convert a fraction to a decimal, divide the numerator by the denominator
• For example:
  • 1/2 = 1 ÷ 2 = 0.5
  • 1/4 = 1 ÷ 4 = 0.25
  • 1/8 = 1 ÷ 8 = 0.125

Equivalent Ratios

• Equivalent ratios are fractions that have the same value, but different numerators and denominators
• For example:
  • 1/2 = 2/4 = 3/6
  • 1/4 = 2/8 = 3/12

Simplifying Fractions

• To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD)
• For example:
  • 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
  • 12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4

Converting Decimals to Fractions

• Decimals can be converted to fractions by writing the decimal as a fraction with a numerator equal to the decimal and a denominator that is a power of 10.
• Examples of decimal to fraction conversions include 0.5 = 5/10 = 1/2, 0.25 = 25/100 = 1/4, and 0.125 = 125/1000 = 1/8.

Converting Fractions to Decimals

• Fractions can be converted to decimals by dividing the numerator by the denominator.
• Examples of fraction to decimal conversions include 1/2 = 1 ÷ 2 = 0.5, 1/4 = 1 ÷ 4 = 0.25, and 1/8 = 1 ÷ 8 = 0.125.

Equivalent Ratios

• Equivalent ratios are fractions that have the same value but different numerators and denominators.
• Examples of equivalent ratios include 1/2 = 2/4 = 3/6 and 1/4 = 2/8 = 3/12.

Simplifying Fractions

• Fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
• Examples of simplifying fractions include 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4 and 12/16 = (12 ÷ 4)/(16 ÷ 4) = 3/4.