Class 7 Rational Numbers Exercise 4.3

\begin{array}{l} \text {Q1. Determine whether the following rational numbers are in the lowest form or not: } \\ \text {(i) } \quad \frac{65}{84} \quad \text {(ii) } \quad \frac{-15}{32} \quad \text {(iii) } \quad \frac{24}{128} \quad \text {(iv) } \quad \frac{-56}{-32} \end{array}\begin{array}{l} \text {Sol. } \\ \text {(i) HCF of 65 and 84 is 1. } \\ \therefore \frac{65}{84} \text {is already in its lowest form. } \\ \\\text {(ii) HCF of -15 and 32 is 1. } \\ \therefore \frac{-15}{32} \text {is already in its lowest form. } \\ \\\text {(iii) HCF of 24 and 128 is not 1. Therefore, given rational number is not in its simplest form. } \\ \\\text {(iv) HCF of 56 and 32 is 8. Therefore, given rational number is not in its simplest form. } \\ \\ \end{array}\begin{array}{l} \text {Q2. Express each of the following rational numbers to the lowest form: } \\ \text {(i) } \quad \frac{4}{22} \quad \text {(ii) } \quad \frac{-36}{180} \quad \text {(iii) } \quad \frac{132}{-428} \quad \text {(iv) } \quad \frac{-32}{-56} \end{array}\begin{array}{l} \text {Sol. } \\ \text {(i) HCF of 4 and 22 is 2. Therefore, dividing the fraction by 2, we get } \\ \frac{4 \div 2}{22 \div 2} = \frac{2}{11} \\ \\\text {(ii) HCF of 36 and 180 is 36. Therefore, dividing the fraction by 36, we get } \\ \frac{-36 \div 36}{180 \div 36} = \frac{-1}{5} \\ \\\text {(iii) HCF of 132 and 428 is 4. Therefore, dividing the fraction by 4, we get } \\ \frac{132 \div 4}{-428 \div 4 } = \frac{33}{-107} \\ \\\text {(iv) HCF of 32 and 56 is 8. Therefore, dividing the fraction by 8, we get } \\ \frac{-32 \div 8}{-56 \div 8} = \frac{-4}{-7}= \frac{4}{7}\end{array}\begin{array}{l} \text {Q3. Fill in the blanks: } \\ \text {(i) } \quad \frac{-5}{7}=\frac{\dots}{35}=\frac{\dots}{49} \\ \text {(ii) } \quad \frac{-4}{-9}=\frac{\dots}{18}=\frac{12}{\dots} \\ \text {(iii) } \quad \frac{6}{-13}=\frac{-12}{\ldots}=\frac{24}{\ldots .} \\ \text { (iv) } \quad \frac{-6}{\dots}=\frac{3}{11}=\frac{\dots}{-55} \end{array}\begin{array}{l} \text {Sol. } \\ \text {(i) } \quad \frac{-5}{7} = \frac{-5 \times 5}{7 \times 5}=\frac{-25}{35} \\ \text {Also, } \frac{-5}{7} \frac{-5 \times 7}{7 \times 7}=\frac{-35}{49} \\ \therefore \quad \frac{-5}{7}=\frac{-25}{35}=\frac{-35}{49} \\ \\\text {(ii) } \quad \frac{-4}{-9}= \frac{-4 \times-2}{-9 \times-2}=\frac{8}{18} \\ \text {Also } \frac{-4}{-9} = \frac{-4 \times-3}{-9 \times-3}=\frac{12}{27} \therefore \quad \frac{-4}{-9}=\frac{8}{18}=\frac{12}{27} \\ \\\text {(iii) } \quad \frac{6}{-13}=\frac{6 \times-2}{-13 \times-2}=\frac{-12}{26} \text {Also, } \quad \frac{6}{-13}=\frac{6 \times 4}{-13 \times 4}=\frac{24}{-52} \\\therefore \quad \frac{6}{-13}=\frac{-12}{26}=\frac{24}{-52} \\ \\\text {(iv) } \quad \frac{3}{11} = \frac{3 \times -2}{11 \times -2}=\frac{-6}{-22} \\ \\ \text {Also, } \quad \frac{3}{11}= \frac{3 \times -5}{11 \times -5}=\frac{-15}{-55} \\\therefore \quad\frac{-6}{-22}=\frac{3}{11}=\frac{-15}{-55} \\ \end{array}