Question

Give two equivalent ratios of 6:8

Answer 1

Hint:A Ratio is a relationship between two numbers (usually involving some kind of measurement). Equivalent ratios are fractions used to convert between units by representing equal measures. The question given is about equivalent ratios. In other ways equivalent ratios are two ratios that express the same relationship between numbers. So, we need to multiply with the same non-zero number on both sides.

Complete step-by-step answer:
Given Ratio $ 6:8 $
The given ratio can be written as $ \dfrac{6}{8} $ or $ 6:8 $ or $ 6{\text{ to 8}} $
Let’s multiply the given ratio with 2 , that is the left hand side of the ratio with 2 and the right hand side of the ratio with 2, only then they are called as equivalent ratios
Therefore,
 $ \Rightarrow $ $ 6 \times 2:8 \times 2 = 12:16 $
And, again let’s multiply the given ratio with 3, that is the left hand side of the ratio with 3 and the right hand side of the ratio with 3,
 $ \Rightarrow 6 \times 3:8 \times 3 = 18:24 $
Thus,
 $ 12:16 $ and $ 18:24 $ are equivalent ratios of $ 6:8 $
Further we can add some more equivalent ratios like by dividing the given ratio which is common for both the numerator and denominator. Here the given ratio is $ 6:8 $
Therefore, it has a common divisor and that is 2
So, we divide the left hand side of the ratio by 2 and the right hand side of the ratio with 2
 $ \Rightarrow $ $ 6 \div 2:8 \div 2 = 3:4 $
Therefore $ 3:4 $ is also an equivalent ratio for $ 6:8 $

Note:We can find the equivalent ratios even by dividing both the numerator and denominator of a given ratio by the same number. They are used to compare two quantities. If we want more equivalent ratios, we can multiply on the both sides of the given ratio with different numbers except 1 and 0.