Determine if the following is in proportion: 33, 121, 9, 96

Hint: We are going to find the ratio of 33, 121 and 9, 96; then we will reduce both of them into simpler form so that we can compare both ratios, in the same proportion means the ratio must be the same of the two different pairs of numbers. So, if the ratio comes out to be the same then it is in proportion.

Complete step-by-step solution -
First we will understand the meaning of proportion,
In the same proportion means the ration must be the same of the two different pairs of numbers.
Definition of Proportion is a mathematical concept, which states the equality of two ratios or fractions. It refers to some categories over the total. When two sets of numbers increase or decrease in the same ratio, they are said to be directly proportional to each other.
Let’s first find the ratio of 33 and 121,
$\dfrac{33}{121}=\dfrac{3}{11}$
Now let’s find the ratio of the other two number,
$\dfrac{9}{96}=\dfrac{3}{32}$
Now we are going to compare the two ratio,
Since,
$\dfrac{3}{11}\ne \dfrac{3}{32}$
Hence, these two ratios are not similar therefore, these are not in proportion.

Note: As we have stated the difference between ratio and proportion which is a very important concept that one should understand before solving this question. Students might get confused in these two words and then it will increase the chance of mistakes.