Question

How do you know if the pair $\dfrac{4}{3}$ and $\dfrac{{16}}{{12}}$ form a proportion?

Answer 1

In this question, two ratios are given. And we have to show that these two ratios are in proportion. If two ratios are equal then we can say that they are in proportion. First, we will convert the ratios into their standard form. Then we will compare two ratios. If both ratios are the same then they are in proportion.

Complete step-by-step answer:
In this question, two ratios are given.
The first ratio is $\dfrac{4}{3}$.
And the second ratio is $\dfrac{{16}}{{12}}$.
The first ratio is in the standard form but the second ratio is not in the standard form.
Therefore, let us convert the second ratio in its standard form.
The numerator of the second ratio is 16.
Now, the factors of 16 are 4 and 4.
The denominator of the second ratio is 12.
And the factors of 12 are 4 and 3.
Therefore, we can write $\dfrac{{16}}{{12}}$as below.
$\Rightarrow \dfrac{{16}}{{12}} = \dfrac{{4 \times 4}}{{4 \times 3}}$
Let us cut out 4 as it is the common factor of the fraction.
That is equal to,
$\Rightarrow \dfrac{{16}}{{12}} = \dfrac{4}{3}$
Hence, the standard form of the second ratio$\dfrac{{16}}{{12}}$ is $\dfrac{4}{3}$.
Now, both ratios are equal.

Hence, we can say that the pair $\dfrac{4}{3}$ and $\dfrac{{16}}{{12}}$ form a proportion.

Note:
We can use an alternate method to check if the ratios are in proportion or not.
For that, we first assume that the given ratios are equal.
$\Rightarrow \dfrac{4}{3} = \dfrac{{16}}{{12}}$
Then, apply the cross multiplication method.
$\Rightarrow 4 \times 12 = 16 \times 3$
Let us multiply both sides.
$\Rightarrow 48 = 48$
Here, we get the left-hand side and the right-hand side are equal.
Hence, we can say that the given ratios $\dfrac{4}{3}$ and $\dfrac{{16}}{{12}}$ form a proportion.