DAV Class 7 Maths Chapter 1 Worksheet 3
Rational Numbers Worksheet 3
1. Write the following rational numbers in standard form.
(i) \( \displaystyle \frac{33}{77} \)
Solution
\[ \begin{align*} \frac{33 \div {\color{green} 11}}{77 \div {\color{green} 11}} &= \color{red} \frac{3}{7} \end{align*} \]
(ii) \( \displaystyle \frac{64}{-20} \)
Solution
\[ \begin{align*} \frac{64 \times {\color{green} (-1)}}{-20 \times {\color{green} (-1)}} &= \frac{-64}{20}\\ \\ \frac{-64 \div {\color{green} 4}}{20 \div {\color{green} 4}} &= \color{red} \frac{-16}{5} \end{align*} \]
(iii) \( \displaystyle \frac{-27}{-15} \)
Solution
\[ \begin{align*} \frac{-27 \times {\color{green} (-1)}}{-15 \times {\color{green} (-1)}} &= \frac{27}{15} \\ \\ \frac{27 \div {\color{green} 3}}{15 \div {\color{green} 3}} &= \color{red} \frac{9}{5} \end{align*} \]
(iv) \( \displaystyle \frac{-105}{98} \)
Solution
\[ \begin{align*} \frac{-105 \div {\color{green} 7}}{98 \div {\color{green} 7}} &= \color{red} \frac{-15}{14} \end{align*} \]
2. Find \( x \) such that the rational numbers in each of the following pairs, become equivalent.
(i) \( \displaystyle \frac{9}{-5} , \frac{x}{10} \)
Solution
\[ \begin{align*} \frac{9}{-5} &= \frac{x}{10} \\ \\ x \times (-5) & = {9 \times 10} \\ \\ x & = \frac{9 \times {\cancel{10}}^2}{{\cancel{-5}}_{-1}} \\ \\ x & = \frac{18}{-1} \\ \\ x &= \color{red} -18 \end{align*} \]
(ii) \( \displaystyle \frac{8}{7} , \frac{x}{-35} \)
Solution
\[ \begin{align*} \frac{8}{7} &= \frac{x}{-35} \\ \\ x \times 7 & = 8 \times (-35) \\ \\ x & = \frac{8 \times \cancel{(-35)}^{-5}}{\cancel7_1} \\ \\ x & = 8 \times (-5) \\ x & = \color{red} -40 \end{align*} \]
(iii) \( \displaystyle \frac{36}{x} , 2 \)
Solution
\[ \begin{align*} \frac{36}{x} &= \frac{2}{1} \\ \\ 2 \times x & = 36 \times 1 \\ \\ x & = \frac{\cancel{36}^{18}}{\cancel2_1} \\ \\ x & = \color{red} 18 \end{align*} \]
(iv) \( \displaystyle \frac{x}{6} , -13 \)
Solution
\[ \begin{align*} \frac{x}{6} &= \frac{-13}{1} \\ \\ {x \times 1} &= {6 \times (-13)} \\ x &= \color{red} -78 \end{align*} \]
3. Check whether the following rational numbers are in standard form. If not, write them in standard form.
(i) \( \displaystyle \frac{-3}{19} \)
Answer yes, its in standard form.
(ii) \( \displaystyle \frac{4}{-7} \)
Answer No
\[ \begin{align*} &= \frac{4 \times \color{green} (-1)}{-7 \times \color{green}(-1)} \\ \\ &= \frac{-4}{7} \end{align*} \]
(iii) \( \displaystyle \frac{14}{35} \)
Answer No
\[ \begin{align*} &= \frac{\cancel{14}^2}{\cancel{35}_5} \\ \\ &= \frac{2}{5} \end{align*} \]
(iv) \( \displaystyle \frac{8}{-72} \)
Answer No
\[ \begin{align*} &= \frac{8 \times \color{green} (-1)}{-72 \times \color{green} (-1)} \\ \\ &= \frac{\cancel{-8}^{-1}}{\cancel{72}_9} \\ \\ &= \frac{-1}{9} \end{align*} \]
4. Fill in the blanks.
(i) \( \displaystyle \frac{2}{7} = \frac{8}{\boxed{?}} = \frac{\boxed{?}}{-63} \)
\[ \begin{align*} \frac{2 \times \color{green}4}{7 \times \color{green}4} &= \frac{8}{\color{red} 28} \\ \\ \frac{2 \times \color{green} (-9)}{7 \times \color{green} (-9)} &= \frac{\color{red} -18}{-63} \end{align*} \]
Answer \( \displaystyle \frac{2}{7} = \frac{8}{\color{red}\boxed{28}} = \frac{\color{red}\boxed{-18}}{-63} \)
(ii) \( \displaystyle \frac{36}{\boxed{?}} = \frac{-4}{9} = \frac{-84}{\boxed{?}} \)
\[ \begin{align*} \frac{-4 \times \color{green} (-9)}{9 \times \color{green} (-9)} &= \frac{36}{\color{red} -81} \\ \\ \frac{-4 \times \color{green} 21}{9 \times \color{green} 21} &= \frac{-84}{\color{red} 189} \end{align*} \]
Answer \( \displaystyle \frac{36}{\color{red}\boxed{-81}} = \frac{-4}{9} = \frac{-84}{\color{red}\boxed{189}} \)
(iii) \( \displaystyle \frac{105}{\boxed{?}} = \frac{\boxed{?}}{-99} = \frac{-5}{-11} \)
\[ \begin{align*} \frac{-5 \times \color{green} (-21)}{-11 \times \color{green} (-21)} &= \frac{105}{\color{red} 231} \\ \\ \frac{-5 \times \color{green} 9}{-11 \times \color{green} 9} &= \frac{\color{red} -45}{-99} \end{align*} \]
Answer \( \displaystyle \frac{105}{\color{red}\boxed{231}} = \frac{\color{red}\boxed{-45}}{-99} = \frac{-5}{-11} \)