DAV Class 7 Maths Chapter 1 Worksheet 4
Rational Numbers Worksheet 4
1. Find the absolute value of the following rational numbers.
(i) \( \displaystyle \frac{1}{-5} \)
Answer Absolute value of \( \displaystyle \frac{1}{-5} \) is \( \displaystyle \left| \frac{1}{-5} \right| = \color{red} \frac{1}{5} \)
(ii) \( \displaystyle \frac{7}{9} \)
Answer Absolute value of \( \displaystyle \frac{7}{9} \) is \( \displaystyle \left| \frac{7}{9} \right| = \color{red} \frac{7}{9} \)
(iii) \( \displaystyle \frac{0}{-4} \)
Answer Absolute value of \( \displaystyle \frac{0}{-4} \) is \( \displaystyle \left| \frac{0}{-4} \right| = \color{red} \frac{0}{4} \implies 0\)
(iv) \( \displaystyle \frac{-3}{-2} \)
Answer Absolute value of \( \displaystyle \frac{-3}{-2} \) is \( \displaystyle \left| \frac{-3}{-2} \right| = \color{red} \frac{3}{2} \)
2. Compare the absolute values of the rational numbers in the following pairs.
(i) \( \displaystyle \frac{3}{-7} , \frac{-3}{7} \)
Answer
\[ \begin{align*} \text{Absolute value of } \frac{3}{-7} \text{ is } \left| \frac{3}{-7} \right| &= \frac{3}{7} \\ \\ \text{Absolute value of } \frac{-3}{7} \text{ is } \left| \frac{-3}{7} \right| &= \frac{3}{7} \\ \\ \frac{3}{7} &= \frac{3}{7} \\ \\ \color{red} \left| \frac{3}{-7} \right| &= \color{red} \left| \frac{-3}{7} \right| \end{align*} \]
(ii) \( \displaystyle \frac{-5}{7} , \frac{4}{3} \)
Answer
\[ \begin{align*} \text{Absolute value of } -\frac{5}{7}\text{ is } \left| \frac{-5}{7} \right| & = \frac{5}{7} \\ \text{Absolute value of } \frac{4}{3} \text{ is } \left| \frac{4}{3} \right| & = \frac{4}{3} \\\\ \frac{5}{7} \quad {\Huge \times} \quad &\frac{4}{3} \\ \\ 5 \times 3 \quad \text{and} \quad &4 \times 7 \\ 15 \quad < \quad &28 \\ \\ \color{red} \left| \frac{-5}{7} \right| < & \ \color{red} \left| \frac{4}{3} \right| \end{align*} \]
(iii) \( \displaystyle \frac{-4}{5} , -3 \)
Solution
\[ \begin{align*} \text{Absolute value of } \frac{-4}{5} \text{ is } \left| \frac{-4}{5} \right| &= \frac{4}{5} \\ \\ \text{Absolute value of } -3 \text{ is } \left| -3 \right| &= 3 \\ \\ \frac{4}{5} \quad {\Huge \times} \quad &\frac{3}{1} \\ \\ 4 \times 1 \quad \text{and} \quad & 3 \times 5 \\ 4 \quad < \quad & 15 \\ \\ \color{red} \left| \frac{-4}{5} \right| < & \ \color{red}\left| -3 \right| \end{align*} \]
3. Find all the rational numbers whose absolute value is-
(i) \( \displaystyle\frac{2}{5} \)
\[ \begin{align*} \text{Absolute value of } \left| \frac{2}{5} \right| &= \frac{2}{5} \\ \\ \text{Absolute value of } \left| \frac{-2}{5} \right| &= \frac{2}{5} \\ \\ \text{Absolute value of } \left| \frac{2}{-5} \right| &= \frac{2}{5} \\ \\ \text{Absolute value of } \left| \frac{-2}{-5} \right| &= \frac{2}{5} \\ \end{align*} \]
Answer \( \displaystyle \color{red}\frac{2}{5} , \color{red}\frac{-2}{5} \)
(ii) 0
Answer \( \color{red}0 \)
(iii) \( \displaystyle \frac{3}{4} \)
\[ \begin{align*} \text{Absolute value of } \left| \frac{3}{4} \right| &= \frac{3}{4} \\ \\ \text{Absolute value of } \left| \frac{-3}{4} \right| &= \frac{3}{4} \\ \\ \text{Absolute value of } \left| \frac{3}{-4} \right| &= \frac{3}{4} \\ \\ \text{Absolute value of } \left| \frac{-3}{-4} \right| &= \frac{3}{4} \\ \end{align*} \]
Answer \( \displaystyle \color{red}\frac{3}{4} , \color{red}\frac{-3}{4} \)