Ratios, Rates, and Fractions

• Ratio


  Comparison of two quantities that have the same units
• Ways to write a ratio

  • Fraction form
  • Word form
  • Colon form
• To figure out a ratio

  1. Write it in fraction form

  2. Simplify
• Rate


  Comparison of quantities that have different units
• Unit rate


  A rate with a denominator of 1
• Unit price


  A unit rate related to a price
• Whole number


  A number that isn't a fraction
• Numerator


  The top of a fraction
• Denominator


  The bottom of a fraction
• Improper fraction


  When the numerator is larger than the denominator
• Mixed number


  A fraction that includes a whole number
• Adding/subtracting fractions (same denominator)

  Add/subtract the numerators
• Adding/subtracting fractions with different denominators

  1. Find the least common denominator (LCD)

  2. Multiply the numerators and denominators by the denominator's factor pair number
• Simplifying fractions


  Find the greatest common factor of the numerator and denominator
• Multiplying fractions


  1. Multiply the numerators with each other

  2. Multiply the denominators with each other

  3. Simplify the answer by finding the GCF
• Dividing fractions


  1. Change the problem to multiplication and integrate the reciprocal

  2. Simplify the answer
• Changing a mixed number to an improper fraction

  1. Multiply the denominator by the whole number

  2. Add the numerator then write it over the denominator
• To perform operations involving a fraction/mixed number and whole number, give the whole number a denominator of one
• If the result of an operation that involves a fraction is an improper fraction, change it to a mixed number
• Reciprocal


  Flip the numerator and denominator of the second fraction
• Multiplying Mixed Numbers

  1. Convert them into improper fractions

  2. Multiply the numerators with each other and the denominators with each other

  3. Write as a mixed number and simplify
• Dividing Mixed Numbers

  1. Convert them into improper fractions

  2. Integrate the reciprocal and multiply

  3. Write as mixed number and simplify
• Adding Or Subtracting Mixed Numbers

  1. Convert them into improper fractions

  2. Find the least common denominator

  3. Multiply the numerators and denominators by the denominator's factor pair

  4. Add or subtract

  5. Write as a mixed number and simplify
• To find ratios


  Divide the numerator and denominator by the same number
• Equivalent ratios


  Ratios that when you simplify them equal the same thing
• Commonly used fractions are called benchmark fractions, like 1/2.