(a) Which of these is a rational number between 2 and 3: 1827,73,103,52

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(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:
:
(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}

.

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