Question

Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
2 kg: 80 kg and 25 g: 625 g.

Answer 1

Hint: To solve this question we need to first know about what does proportion mean here, when it is said that a : b and c : d form a proportion then it means that values of both the ratios are equal and as ratio of two similar quantities will be a unitless quantity so units of a, b, c, and d does not matter here. And middle terms of the proportion will be c and d and extreme terms will be a and d. Now using the above information we will solve this question.

Complete step-by-step answer:
Two ratios are said to be in proportion if their numerical value is equal i.e. if they are equal in ratio or the fractional form then they are in proportion.
We are given the ratios
2 kg: 80 kg and 25 g: 625g,
Now if we consider the first ratio i.e. 2 kg: 80 kg,
Representing it in the fractional form we get,
2 kg: 80 kg = $\dfrac{2\,kg}{80\,kg}$
Now dividing both the numerator and denominator by 2, we get
2 kg: 80 kg = $\dfrac{1}{40}$
Now moving to the second ratio i.e. 25 g: 625g,
Representing it in the fractional form we get,
25 g: 625g = $\dfrac{25\,g}{625\,g}$
Dividing both numerator and denominator by 25, we get
25 g: 625g = $\dfrac{1}{25}$
Now we will compare both the ratios, and get
$\dfrac{1}{40}\ne \dfrac{1}{25}$
So both the ratios are not equal 2 kg: 80 kg $\ne $ 25 g: 625g. so the ratios are not in proportion.

Note: To solve this problem you should convert the given ratios to the fractional form first otherwise if you try to solve directly you may make mistakes. And also remember that a ratio of two similar quantities will give us a unitless quantity so we need not to worry about units while taking a ratio of similar quantities.