Question

(a) Which of these is a rational number between 2 and 3:

$\frac{18}{27},\frac{7}{3},\frac{10}{3},\frac{5}{2}$

(b) Find one rational number that lies between $\frac{7}{8}$ and $\frac{1}{2}$. What is its reciprocal?

[3 MARKS]

Answer 1

(a) Steps: 1 Mark
Result: 1 Mark
(b) Answer: 1 Mark


(a) Simplified form of the numbers:

$\frac{18}{27}=\frac{2}{3}$

$\frac{7}{3}=2\frac{1}{3}$

$\frac{10}{3}=3\frac{1}{3}$

$\frac{5}{2}=2\frac{1}{2}$

The rational numbers between 2 and 3 are $\frac{7}{3}$ and $\frac{5}{2}$.

(b) Rational number that will lie between $\frac{7}{8}$ and $\frac{1}{2}$ is their average.

$\frac{\frac{7}{8}+\frac{1}{2}}{2}=\frac{\frac{11}{8}}{2}=\frac{11}{16}$

Its reciprocal is $\frac{16}{11}$.