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Given that $$0\lt p\lt q\lt r\lt s$$ and $$p, q, r, s$$ are integers, which of the following is the smallest?（ ）
A. $$\frac {p+q}{r+s}$$
B. $$\frac {p+s}{q+r}$$
C. $$\frac {q+s}{p+r}$$
D. $$\frac {r+s}{p+q}$$
Speed
00:00
06:52

## QuestionMathsClass 7

Given that $$0\lt p\lt q\lt r\lt s$$ and $$p, q, r, s$$ are integers, which of the following is the smallest?（ ）
A. $$\frac {p+q}{r+s}$$
B. $$\frac {p+s}{q+r}$$
C. $$\frac {q+s}{p+r}$$
D. $$\frac {r+s}{p+q}$$

A
4.6
4.6

## Solution

A fraction is relatively smaller if the difference between numerator and denominator is high.
$$0\lt p\lt q\lt r\lt s$$
$$\implies p,q$$ are the smallest and $$r,s$$ are the greatest among $$p,q,r,s$$
$$\implies$$ Difference between $$p+q$$ and $$r+s$$ is higher than any other combination, such that $$p+q$$ is very small in comparison with $$r+s$$.
Thus, $$\frac {p+q}{r+s}$$ is the smallest.