Question

what is the least natural number which when subtracted from both the numerator and denominator of fraction 7/8 gives a ratio less than 17:22​

Answer 1

To find:

The least natural number which when subtracted from both the numerator and denominator of fraction $\dfrac{7}{8}$ gives a ratio less than 17 : 22

Step-by-step explanation:

• Let us consider that the least natural number be x.

• Then by the given condition,

• $\quad \dfrac{7-x}{8-x}<\dfrac{17}{22}$

• ⇒ 22 (7 - x) < 17 (8 - x)

• ⇒ 154 - 22x < 136 - 17x

• ⇒ - 22x + 17x < 136 - 154

• ⇒ - 5x < - 18

• ⇒ 5x > 18

• ⇒ x > 3.6

• So our required natural number is greater than 3.6 and thus x = 4, 5, 6, ... ...

Final Answer:

The required least natural number is 4.