Which one of the following fractions is greater than $\\frac{2}{7}$ and less than $\\frac{7}{9}$?<\/p>\n
[amp_mcq option1=”$\\frac{15}{19}$” option2=”$\\frac{11}{17}$” option3=”$\\frac{11}{14}$” option4=”$\\frac{17}{21}$” correct=”option2″]<\/p>\n
Let’s test option B, $\\frac{11}{17} \\approx 0.6471$. Which one of the following fractions is greater than $\\frac{2}{7}$ and less than $\\frac{7}{9}$? [amp_mcq option1=”$\\frac{15}{19}$” option2=”$\\frac{11}{17}$” option3=”$\\frac{11}{14}$” option4=”$\\frac{17}{21}$” correct=”option2″] This question was previously asked in UPSC CBI DSP LDCE – 2023 Download PDFAttempt Online To find the fraction greater than $\\frac{2}{7}$ and less than $\\frac{7}{9}$, we can compare each option with the given bounds. … <\/p>\n
\nIs $\\frac{11}{17} > \\frac{2}{7}$? Compare $11 \\times 7$ with $17 \\times 2$. $77 > 34$. Yes, $\\frac{11}{17} > \\frac{2}{7}$.
\nIs $\\frac{11}{17} < \\frac{7}{9}$? Compare $11 \\times 9$ with $17 \\times 7$. $99 < 119$. Yes, $\\frac{11}{17} < \\frac{7}{9}$.\nSince $\\frac{11}{17}$ satisfies both conditions, it is the correct answer.\n\nLet's quickly check other options:\nA) $\\frac{15}{19} \\approx 0.7895$. Is $\\frac{15}{19} < \\frac{7}{9}$? Compare $15 \\times 9 = 135$ with $19 \\times 7 = 133$. $135 > 133$, so $\\frac{15}{19} > \\frac{7}{9}$. Incorrect.
\nC) $\\frac{11}{14} \\approx 0.7857$. Is $\\frac{11}{14} < \\frac{7}{9}$? Compare $11 \\times 9 = 99$ with $14 \\times 7 = 98$. $99 > 98$, so $\\frac{11}{14} > \\frac{7}{9}$. Incorrect.
\nD) $\\frac{17}{21} \\approx 0.8095$. Is $\\frac{17}{21} < \\frac{7}{9}$? Compare $17 \\times 9 = 153$ with $21 \\times 7 = 147$. $153 > 147$, so $\\frac{17}{21} > \\frac{7}{9}$. Incorrect.
\n<\/section>\n
\n$\\frac{2}{7} \\approx 0.28$
\n$\\frac{7}{9} \\approx 0.78$
\nA) $\\frac{15}{19} \\approx \\frac{15}{20} = 0.75$. Closer check needed. (Actual: 0.789)
\nB) $\\frac{11}{17} \\approx \\frac{11}{16} = 0.6875$ or $\\frac{10}{16} = 0.625$. Looks promising. (Actual: 0.647)
\nC) $\\frac{11}{14} \\approx \\frac{11}{15} \\approx 0.73$. Closer check needed. (Actual: 0.786)
\nD) $\\frac{17}{21} \\approx \\frac{17}{20} = 0.85$. Too high. (Actual: 0.810)
\n<\/section>\n","protected":false},"excerpt":{"rendered":"