Question

What are equivalent ratios 7 to 10?

Answer 1

Hint: The term equivalent means almost identical and in terms of fractions, the term “equivalent” means that we need to find some more ratios which when reduced to simplest form gives back the same result. We are given a fraction here and we need to find the equivalent ratios of it. We should keep in mind that if we multiply both the numerator and the denominator then the magnitude of the fraction does not change but the representation becomes a bit different. So, we only need to do that.

Complete step by step solution:
We are required to find the equivalent ratio of the fraction given. First we make the fraction out of the mathematical term which is “7 to 10” which simply means that the fraction should be “7 upon 10”. So, the fraction we are given is $\dfrac{7}{10}$. Now, we are aware of the fact that if we want to change the fraction but we do not want to change the value of it then we simply multiply the numerator and denominator by any integer other than 0. Here, we choose the integer to be 2, so we get:
$\dfrac{7}{10}\times\dfrac{2}{2}=\dfrac{7\times 2}{10\times 2}=\dfrac{14}{20}$
Now, we choose the integer to be 3:
$\dfrac{7}{10}\times\dfrac{3}{3}=\dfrac{7\times 3}{10\times 3}=\dfrac{21}{30}$
In this way we can find infinite ratio equivalents of the ratio $\dfrac{7}{10}$.

Note: You can also use negative integers to multiply in both the numerator and the denominator. Because ultimately when the fraction will be reduced to the simplest form then the same sign will also get cancelled. So, of course negative numbers can be used, but keep in mind that you have to multiply both the numerator and denominator by the same number. Multiplying a numerator with a different number and then a denominator with a different number will change the magnitude of the fraction which will lead to an invalid result. Also, do not multiply both numerator and denominator by 0 because the form $\dfrac{0}{0}$ is not defined.