Question

Are the ratio 1:2 and 2:3 equivalent?

Answer 1

Hint: First, we will convert the given ratios in the form of fractions. Then, we will compare them by converting them into like fractions. We can do so by trying to make the denominator of both fractions the same. Like fractions equal and if the given ratios make like fractions then they are equivalent.

Complete step-by-step answer:
To check if two ratios are equivalent we need to compare them. To do this, we need to write the ratios in the form of fractions and then compare them by converting them to like fractions. i.e. to convert both these ratios in such a way that the fractions will be the same. If these like fractions are equal, then we can say that the ratios are equivalent.
We can find the equivalent ratios by multiplying or dividing the numerator and denominator by the same number. We have been given the ratio 1:2 and 2:3. Now, converting it into fractions we get $${\displaystyle \frac{1}{2}}$$ and $${\displaystyle \frac{2}{3}}$$.
The denominators are 2 and 3. So, to make it equal, we will use the LCM of 2 and 3, i.e 6. So, we will multiply numerator and denominator such that the denominator of both these fractions is 6.
Let us multiply by 3 in the numerator and denominator of $${\displaystyle \frac{1}{2}}$$.
$${\displaystyle \frac{1\times 3}{2\times 3}}={\displaystyle \frac{3}{6}}$$
Now multiply by 2 in the numerator and denominator of $${\displaystyle \frac{2}{3}}$$.
$${\displaystyle \frac{2\times 2}{3\times 2}}={\displaystyle \frac{4}{6}}$$
From the above we can say that $${\displaystyle \frac{3}{6}}<{\displaystyle \frac{4}{6}}$$ which means that, $${\displaystyle \frac{1}{2}}<{\displaystyle \frac{2}{3}}$$.
Hence we can say that the ratios 1:2 and 2:3 are not equivalent.

Note: If the ratios given where 1:2 and 1:3, where we can see that the numerator would be the same. Even then the ratios will not be equivalent. Multiplying the numerator and denominator by 3 for $${\displaystyle \frac{1}{2}}$$ and 2 for $${\displaystyle \frac{1}{3}}$$, we get as $${\displaystyle \frac{3}{6}}$$ and $${\displaystyle \frac{2}{6}}$$ which are not equal. So by seeing the same number in the fraction, do not jump into conclusion that they will be equivalent.