Question

The product of two numbers is $ 14 $ . If one of the numbers is $ \dfrac{{ - 8}}{7} $ , find the other.

Answer 1

Hint:Here we are given that the product of two numbers is $ 14 $ and one of the numbers is given as $ \dfrac{{ - 8}}{7} $ . We need to find the other number. To find the other number, we just need to bring the number $ \dfrac{{ - 8}}{7} $ to the other side of the equation. Also, we can verify the obtained number.

Complete step by step answer:
We are given that the product of two numbers is $ 14 $ . That means, when we multiply the two numbers, we will get the answer $ 14 $ .
Next, it is given that one of the numbers is $ \dfrac{{ - 8}}{7} $ . That means, we are given one of the two numbers as $ \dfrac{{ - 8}}{7} $
We need to find the other number.
To find: the other number
Let us consider $ x $ and $ y $ to denote the two numbers. That means when we multiply $ x $ and $ y $ , we will get the answer $ 14 $ . In mathematically, we denote $ x \times y = 14 $
Let $ y $ be one of the two numbers. Then $ y = \dfrac{{ - 8}}{7} $ and we have $ x \times \dfrac{{ - 8}}{7} = 14 $
Let $ x $ be the other number that we need to find.
 $ x \times \dfrac{{ - 8}}{7} = 14 $
Now, we shall take the term $ \dfrac{{ - 8}}{7} $ to the other side of the equation. To take the term to the other side, we need to take reciprocal. Reciprocal refers just to flip the term (Example: $ \dfrac{3}{2} \to \dfrac{2}{3} $ ).
Here we need to take reciprocal for the number $ \dfrac{{ - 8}}{7} $ when we take it into the other side of the equation.
Thus, we have $ \dfrac{{ - 8}}{7} \to \dfrac{7}{{ - 8}} $
Hence, we get $ x = 14 \times \dfrac{7}{{ - 8}} $
 $ \Rightarrow x = 7 \times \dfrac{{ - 7}}{4} $
 $ \Rightarrow x = \dfrac{{ - 49}}{4} $
Hence, we got the other number $ \dfrac{{ - 49}}{4} $ .

Note:Now, we shall verify whether the obtained answer is correct or not. Since we have assumed that $ x $ and $ y $ are the two numbers. That means when we multiply $ x $ and $ y $ , we will get the answer $ 14 $ . Mathematically, we denote $ x \times y = 14 $ . We have $ y = \dfrac{{ - 8}}{7} $ and $ x = \dfrac{{ - 49}}{4} $ .
Now, we need to substitute the values in the equation $ x \times y = 14 $ .
 $ \Rightarrow \dfrac{{ - 49}}{4} \times \dfrac{{ - 8}}{7} = 14 $
 $ \Rightarrow 7 \times 2 = 14 $
 $ \Rightarrow 14 = 14 $
Here we got the same number on both sides and hence we verified.