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

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

Date _________________________________

Name ________________________________

Grade ________________________________

Score _________________________________

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)

Source: https://class.ronliskey.com/study/mathematics-7/7-2-sb-study-guide-rational-numbers/