Question

Find four rational numbers between $ \dfrac{2}{7} $ and $ \dfrac{3}{4} $ .

Answer 1

Hint: To find required four rational numbers between $ \dfrac{2}{7} $ and $ \dfrac{3}{4} $ , first we will write LCM (least common multiple) of $ 7 $ and $ 4 $ . Then, we will rewrite the given numbers such that the denominator becomes equal.

Complete step-by-step answer:
In the given problem, to find required four rational numbers between $ \dfrac{2}{7} $ and $ \dfrac{3}{4} $ , let us write the LCM (least common multiple) of $ 7 $ and $ 4 $ . LCM of $ 7 $ and $ 4 $ is $ 28 $ . Now we will rewrite the given numbers such that the denominator becomes $ 28 $ . So, we can write the number $ \dfrac{2}{7} $ as $ \dfrac{8}{{28}} $ by multiplying $ 4 $ to numerator and denominator both. Similarly, we can write the number $ \dfrac{3}{4} $ as $ \dfrac{{21}}{{28}} $ by multiplying $ 7 $ to numerator and denominator both. So, now we have to write four rational numbers between $ \dfrac{8}{{28}} $ and $ \dfrac{{21}}{{28}} $ . We know that the whole numbers $ 9,10,11,12 $ are lying between $ 8 $ and $ 21 $ . Hence, the rational numbers $ \dfrac{9}{{28}},\dfrac{{10}}{{28}},\dfrac{{11}}{{28}},\dfrac{{12}}{{28}} $ are lying between $ \dfrac{8}{{28}} $ and $ \dfrac{{21}}{{28}} $ . That is, four rational numbers are $ \dfrac{9}{{28}},\dfrac{{10}}{{28}},\dfrac{{11}}{{28}},\dfrac{{12}}{{28}} $ between $ \dfrac{2}{7} $ and $ \dfrac{3}{4} $ .

Note: A number is called a rational number if it can be written in the form $ \dfrac{p}{q} $ where $ p $ and $ q $ are integers and $ q \ne 0 $ . Remember that a rational number between two numbers $ x $ and $ y $ is obtained by $ \dfrac{{x + y}}{2} $ . One can use this information to find rational numbers between the given numbers. In fact there are infinitely many rational numbers between $ \dfrac{2}{7} $ and $ \dfrac{3}{4} $ but we write only four rational numbers as mentioned in the problem. In general, there are infinitely many rational numbers between two given rational numbers.