If P = 96/ (95 × 97), Q = 97/ (96 × 98) and R = 1/97, then which of the following is TRUE?
R < Q < P
Rewrite using \((n-1)(n+1)=n^2-1\): \(P=\tfrac{96}{96^2-1}\), \(Q=\tfrac{97}{97^2-1}\).
P vs Q: The function \(f(x)=\tfrac{x}{x^2-1}\) decreases for \(x>1\), so \(P>Q\).
Q vs R: \(Q=\tfrac{97}{97^2-1}>\tfrac{97}{97^2}=\tfrac{1}{97}=R\).
Therefore R < Q < P.
Similar Questions
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
If the sum of two positive numbers is 65 and the square root of their product is 26, then the sum of their reciprocals is:
The value of \(9 \div [\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}\div(\frac{3}{4}-\frac{1}{3})\;of\;\frac{2}{9}]\) is:
Three fractions x, y and z are such that x > y > z. When the smallest of them is divided by the greatest, the result is \({\frac{9}{16}}\) , which exceeds y by 0.0625. If x + y + z = \(2{\frac{3}{12}}\) , then what is the value of x + z?
- The value of \(\frac{46+\frac{3}{4} \ \text{of}\ 32-6}{37-\frac{3}{4} \ \text{of}\ (34+6)}\) is:
The value of \(\frac{52-1170\div26+13\times2}{2+1\frac{1}{8}\ \rm of\ 2-1\frac{1}{4}}\) is:
The value of 25 ÷ 15 of 4 × [4 ÷ 5 × (9 - 7)] - (20 ÷ 5 of 9) is:
Let a, b and c be the fractions such that a < b < c. If c is divided by a, the result is 5/2, which exceeds b by 7/4, If \(a + b + c = 1\frac{{11}}{{12}},\) then (c – a) will be equal to:
The sum of three numbers is 2, the 1st number is 1/2 times the 2nd number andthe 3rd number is 1/4 times the 2nd number. The 2nd number is
Which of the following is correct?
Important Questions from Fractions
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?
