Class 6 Ratio, Proportion and Unitary Method Exercise 9.2

\begin{array}{l} \text {Q1. Which ratio is larger in the following pairs? } \\ \text {(i) } \quad 3: 4 \text { or } 9: 16 \\ \text {(ii) } \quad 15: 16 \text { or } 24: 25 \\ \text {(iii) } \quad 4: 7 \text { or } 5: 8 \\ \text {(iv) } \quad 9: 20 \text { or } 8: 13 \\ \text {(v) } \quad 1: 2 \text { or } 13: 27 \\ \\\text {Sol. (i) } \quad 3: 4 = \frac {3}{4} \text { or } 9: 16 = \frac {9}{16} \\\text {LCM of 4 and 16 is 16 } \\ \text {to compare, we need to make denominator of each fraction equal to 16 } \\ \therefore \frac {3}{4} =\frac {3 \times 4}{4 \times 4} = \frac {12}{16} \\\text {Clearly, } 12 \gt 9 \\ \therefore \frac {12}{16} \gt \frac {9}{16} \\ \Rightarrow \frac {3}{4} \gt \frac {9}{16} \\ \Rightarrow 3 : 4 \gt 9 :16 \\ \\\text {(ii) } \quad 15: 16 = \frac {15}{16} \text { or } 24: 25 = \frac {24}{25} \\\text {LCM of 16 and 25 is 400 } \\ \text {To compare, we need to make denominator of each fraction equal to 400 } \\ \therefore \frac {15}{16} =\frac {15 \times 25}{16 \times 25} = \frac {375}{400} \\ \text {And } \frac {24}{25} =\frac {24 \times 16}{25 \times 16} = \frac {384}{400} \\\text {Clearly, } 384 \gt 375 \\ \therefore \frac {384}{400} \gt \frac {375}{400} \\ \Rightarrow \frac {24}{25} \gt \frac {15}{16} \\ \Rightarrow 24 : 25 \gt 15 : 16 \\ \\\text {(iii) } \quad 4: 7 = \frac {4}{7} \text { or } 5: 8= \frac {5}{8} \\\text {LCM of 7 and 8 is 56 } \\ \text {To compare, we need to make denominator of each fraction equal to 56 } \\ \therefore \frac {4}{7} =\frac {4 \times 8}{7 \times 8} = \frac {28}{56} \\ \text {And } \frac {5}{8} =\frac {5 \times 7}{8 \times 7} = \frac {35}{56} \\\text {Clearly, } 35 \gt 28 \\ \therefore \frac {35}{56} \gt \frac {28}{56} \\ \Rightarrow \frac {5}{8} \gt \frac {4}{7} \\ \Rightarrow 5 : 8 \gt 4 : 7 \\ \\\text {(iv) } \quad 9: 20 = \frac {9}{20} \text { or } 8: 13 = \frac {8}{13} \\\text {LCM of 20 and 13 is 260 } \\ \text {To compare, we need to make denominator of each fraction equal to 260 } \\ \therefore \frac {9}{20} =\frac {9 \times 13}{20 \times 13} = \frac {117}{260} \\ \text {And } \frac {8}{13} =\frac {8 \times 20}{13 \times 20} = \frac {160}{260} \\\text {Clearly, } 160 \gt 117 \\ \therefore \frac {160}{260} \gt \frac {117}{260} \\ \Rightarrow \frac {8}{13} \gt \frac {9}{20} \\ \Rightarrow 8 : 13 \gt 9 : 20 \\ \\\text {(v) } \quad 1: 2 = \frac {1}{2} \text { or } 13: 27 = \frac {13}{27} \\\text {LCM of 2 and 27 is 54 } \\ \text {To compare, we need to make denominator of each fraction equal to 54 } \\ \therefore \frac {1}{2} =\frac {1 \times 27}{2 \times 27} = \frac {27}{54} \\ \text {And } \frac {13}{27} =\frac {13 \times 2}{27 \times 2} = \frac {26}{54} \\\text {Clearly, } 27 \gt 26 \\ \therefore \frac {27}{54} \gt \frac {26}{54} \\ \Rightarrow \frac {1}{2} \gt \frac {13}{27} \\ \Rightarrow 1 : 2 \gt 13 : 27 \\ \\\text {Q2. Give two equivalent ratios of 6: 8 } \\ \\\text {Sol. Given ratio } 6: 8 = \frac {6}{8} \\\frac {6}{8} = \frac {6 \times 2}{8 \times 2} = \frac {12}{16} \\ \text {Also, } \frac {6}{8} = \frac {6 \times 3}{8 \times 3} = \frac {18}{24} \\\text {Hence, } \frac {12}{16} \text { and } \frac {18}{24} \text { are ratios equivalent to the ratio } \frac {6}{8} \\ \\\text {Q3. Fill in the following blanks: } \\\frac{12}{20}=\frac{\square}{5}=\frac{9}{\square} \\ \\\text {Sol. Given that } \frac{12}{20}=\frac{\square}{5}=\frac{9}{\square} \\\text {Now, } \frac{12}{20}=\frac{12 \div 4}{20 \div 4} = \frac {3}{5} \\ \text {Hence, the first missing number is 3} \\ \\\frac {3}{5} = \frac {3 \times 3}{5 \times 3} = \frac {9}{15} \\\text {Hence, the second missing number is 15} \\ \\\end{array}