Study Guides | rational numbers | Comparing, ordering, adding, subtracting rational numbers

Study Guide: Comparing, ordering, adding, subtracting rational numbers

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2-3. Adding or Subtracting Rational Numbers

Example 1: Adding Fractions

\begin{align} \frac{3}{7} + \frac{4}{7} &= \\[2ex] \frac{(3 + 4)}{7} &= \frac{7}{7} = 1 \end{align}

Example 2: Subtracting Fractions

\begin{align} \frac{8}{11} - \left \( -\frac{2}{11} \right \) &= \frac{8 - (-2)}{11} \\[2ex] &= \frac{10}{11} \\[2ex] \end{align}

  1. $ \frac{-8}{13} + \frac{2}{13} = $
  1. $ \frac{3}{5} - \frac{-4}{5} = $
  1. $ \frac{-2}{9} + \frac{-7}{9} = $
  1. $ \frac{-5}{12} - \frac{-7}{12} = $
  1. $ \frac{-9}{11} + \frac{10}{11} = $
  1. $ \frac{5}{13} - \frac{-7}{13} = $

2-3. Multiplying Rational Numbers

Example 3: Multiplying Fractions

\begin{align} 5 \left \( 3\frac{1}{4} \right \) &= \left \( \frac{5}{1} \right \) \left \( \frac{3(4)+1}{4} \right \) \\[2ex] &= \left \( \\frac{5}{1} \right \) \left \( \frac{13}{4} \right \) \\[2ex] &= \left \( \\frac{65}{4} \right \) \end{align}

  1. $ 3 \left \( -\frac{2}{5} \right \) = \left\( \frac{3}{1} \right\) \left \( -\frac{2}{5} \right \) = $
  1. $ 2 \left \( 3\frac{4}{5} \right \) = \left \( \frac{2}{1} \right \) \left \( \frac{19}{5} \right \) = $
  1. $ \frac{-2}{3} \left \( \frac{-4}{5} \right \) = $
  1. $ \frac{8}{11} \left \( \frac{-22}{4} \right \) = $
  1. $ 5\frac{1}{4} \left \( \frac{3}{7} \right \) = $
  1. $ 2\frac{1}{2} \left \( 1\frac{3}{10} \right \) = $
  1. $ 4\frac{7}{8} \left \( 2\frac{2}{3} \right \) = $
  1. $ -\frac{8}{9} \left \( \frac{7}{16} \right \) = $

Video: Irrational Numbers (6:40)

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