Adding Fractions with Different Denominators

Adding Fractions with Different Denominators exercise

• Define the terms.

  Hints

  A denominator is part of a fraction.

  Look for common words on the left and right sides to help you make matches.

  Think of the word least as small, and the word greatest as large.

  Solution

  • The Lowest Common Multiple, or LCM is the smallest multiple shared by two or more numbers.
  • The Lowest Common Denominator, or LCD is the lowest number that can be used as the denominator for two or more fractions.
  • The Greatest Common Factor or GCF is the largest factor that all the numbers share.
  • The denominator is the number below the fraction bar.

• Sort the steps.

  Hints

  The numerator is the number above the fraction bar, and the denominator is the number below.

  Before adding fractions with unlike denominators, you need to find a common denominator using multiplication or division.
  Example: $\frac{1}{2}$ and $\frac{1}{4}$
  $\frac{1}{2}$ = $\frac{2}{4}$ if we multiply the numerator and denominator by 2.
  $\frac{2}{4}$ and $\frac{1}{4}$ have common denominators and can now be added together.

  Solution

  The steps to add fractions with unlike denominators are:
  1) Change fractions with unlike denominators to equivalent fractions with a common denominator. ($\frac{1}{12}$ + $\frac{1}{4}$ becomes $\frac{1}{12}$ + $\frac{3}{12}$)
  2) Bring the common denominator over to the solution side of the equation ($\frac{1}{12}$ + $\frac{3}{12}$ = $\frac{}{12}$)
  3) Add the numerators ($\frac{1}{12}$ + $\frac{3}{12}$ = $\frac{4}{12}$)
  4) Simplify the fraction if necessary ($\frac{4}{12}$ becomes $\frac{1}{3}$)

• Add fractions with unlike denominators.

  Hints

  Sometimes the lowest common denominator is already the denominator of one of the fractions in the equation.

  To find what $\frac{1}{5}$ is equivalent to, we need to multiply the numerator and denominator by 3.

  • 1 x 3 = numerator
  • 5 x 3 = denominator

  You have the solution for $\frac{3}{15}$ + $\frac{2}{15}$ = ? from step 3. Now divide both the numerator and denominator of this fraction by 5 to simplify.

  Solution

  STEP ONE
  $\frac{1}{5}$ = $\frac{3}{15}$
  Now we can add $\frac{3}{15}$ + $\frac{2}{15}$
  STEP TWO
  $\frac{3}{15}$ + $\frac{2}{15}$ = $\frac{}{15}$
  STEP THREE
  $\frac{3}{15}$ + $\frac{2}{15}$ = $\frac{5}{15}$
  STEP FOUR
  $\frac{5}{15}$ = $\frac{1}{3}$

• Solve the equations.

  Hints

  In order to add fractions with unlike denominators, first create equivalent fractions with the same denominator using multiplication or division.
  Example:
  $\frac{1}{5}$ + $\frac{2}{15}$
  $\frac{1}{5}$ = $\frac{3}{15}$
  $\frac{3}{15}$ and $\frac{2}{15}$ can be added together.

  Next, bring the common denominator over to the solution side of the equation and add the numerators together.
  Example:
  $\frac{3}{15}$ + $\frac{2}{15}$ = $\frac{5}{15}$

  Finally, look for a Greatest Common Factor, and simplify if possible.
  Example:
  $\frac{5}{15}$ can be simplified to $\frac{1}{3}$ by dividing the numerator and denominator by 5.

  One of the solutions must be simplified.

  Solution

  1) $\frac{3}{10}$ + $\frac{3}{5}$ = ?
  $\frac{3}{10}$ + $\frac{6}{10}$ = $\frac{9}{10}$

  2) $\frac{1}{4}$ + $\frac{1}{6}$ = ?
  $\frac{3}{12}$ + $\frac{2}{12}$ = $\frac{5}{12}$

  3) $\frac{1}{3}$ + $\frac{2}{9}$ = ?
  $\frac{3}{9}$ + $\frac{2}{9}$ = $\frac{5}{9}$

  4) $\frac{1}{10}$ + $\frac{3}{20}$ = ?
  $\frac{2}{20}$ + $\frac{3}{20}$ = $\frac{5}{20}$ = $\frac{1}{4}$

• Find the lowest common denominator.

  Hints

  The Lowest Common Denominator, or LCD, is the smallest number that can be used to make equal denominators in fractions.
  Example: The LCD for $\frac{1}{4}$ and $\frac{1}{5}$ is 20.

  Since all of the fractions have even numbers as denominators, the answer cannot be an odd number.

  Try multiplying the greatest denominator (8) by 2, and see if the other denominators can fit into the solution. If not, the answer must be a greater number.

  Solution

  • 4 x 6 = 24
  • 6 x 4 = 24
  • 8 x 3 = 24

  The lowest common denominator is 24.

• Solve the equations.

  Hints

  In order to add fractions with unlike denominators, first create equivalent fractions with the same denominator using multiplication or division.
  Example:
  $\frac{1}{5}$ + $\frac{2}{15}$
  $\frac{1}{5}$ = $\frac{3}{15}$
  $\frac{3}{15}$ and $\frac{2}{15}$ can be added together.

  Next, bring the common denominator over to the solution side of the equation and add the numerators together.
  Example:
  $\frac{3}{15}$ + $\frac{2}{15}$ = $\frac{5}{15}$

  Finally, look for a Greatest Common Factor, and simplify if possible.
  Example:
  $\frac{5}{15}$ can be simplified to $\frac{1}{3}$ by dividing the numerator and denominator by 5.

  Three of the solutions must be simplified.

  Solution

  1) $\frac{3}{9}$ + $\frac{1}{3}$ = ?
  $\frac{3}{9}$ + $\frac{3}{9}$ = $\frac{6}{9}$ = $\frac{2}{3}$

  2) $\frac{1}{6}$ + $\frac{2}{12}$ = ?
  $\frac{2}{12}$ + $\frac{2}{12}$ = $\frac{4}{12}$ = $\frac{1}{3}$

  3) $\frac{1}{8}$ + $\frac{3}{16}$ = ?
  $\frac{2}{16}$ + $\frac{3}{16}$ = $\frac{5}{16}$ This fraction cannot be further simplified.

  4) $\frac{1}{18}$ + $\frac{1}{6}$ = ?
  $\frac{1}{18}$ + $\frac{3}{18}$ = $\frac{4}{18}$ = $\frac{2}{9}$