Question

Arrange the ratios $7:20,13:25,17:30,11:15$ in decreasing order.

Answer 1

Hint: Use the basic definition of ratio to convert all the ratios in $7:20,13:25,17:30,11:15$ , to fractional form and then take the LCM of all the denominators and make the denominators for all the ratios same and accordingly change the numerators as well. Then just arrange the fractions such that the numerators are in decreasing order to get the answer.

Complete step by step solution:
Let us first know what a ratio is.
A ratio, in basic words, is a quantity used to define a comparison between two quantities. A bit toward the advanced side, it is the quantity which defines how many times of one quantity is that of others.
 At our level, apart from the definition, we will treat it as a simple fraction that defines a relation between two given quantities.
Now, starting with the question.
Let us first write all the ratios $7:20,13:25,17:30,11:15$ in fractional form. On doing so, the fractions we get are: $\dfrac{7}{20},\dfrac{13}{25},\dfrac{17}{30},\dfrac{11}{15}$ .
Now let us try to find the LCM of the denominators of the fractions. The denominators are: 20, 25, 30, 15. We know we can write 20, 25, 30 and 15 as:
$\begin{align}
  & 20=2\times 2\times 5 \\
 & 25=5\times 5 \\
 & 30=2\times 3\times 5 \\
 & 15=3\times 5 \\
\end{align}$
So, the LCM of these numbers are: $LCM=2\times 2\times 5\times 5\times 3=300$ . SO, now we will multiply the denominator and numerator of the fractions by the same number to make their denominators equal to 300.
$\dfrac{7\times 15}{20\times 15},\dfrac{13\times 12}{25\times 12},\dfrac{17\times 10}{30\times 10},\dfrac{11\times 20}{15\times 20}$
Therefore, the fractions we get are: $\dfrac{105}{300},\dfrac{156}{300},\dfrac{170}{300},\dfrac{220}{300}$ .
Now as the denominators are the same, we have to only arrange the numerators in decreasing order. We know 220>170>156>105.
Therefore, the decreasing order of fractions is:
$\dfrac{220}{300}>\dfrac{170}{300}>\dfrac{156}{300}>\dfrac{105}{300}$
If we again convert them back to their simplest form, we get
$\dfrac{11}{15}>\dfrac{17}{30}>\dfrac{13}{25}>\dfrac{7}{20}$
Now, if we represent this in ratio form, we get
$11:15>17:30>13:25>7:20$

Note: You could have also solved the above question by converting all the ratios to decimals, but that could be more time consuming and if the difference in the number is very less, i.e., of the order ${{10}^{-5}}$ or less then decimal form might not be much of use.