Question

Compare the ratio and find the larger ratio $5:6$ and $6:7$ ?

Answer 1

Hint:We can write ratio \[a:b\] in fraction as $\dfrac{a}{b}$ . We can compare any two fractions. We must cross-multiplied both fractions, and the values found in the cross-multiplication must be compared. We can also compare two fractions by making their denominator same and then compare their numerator.

Complete step by step answer:
We have given two ratios $5:6$ and $6:7$. We will first convert them in fraction. We can write them in fraction as $\dfrac{5}{6}$ and $\dfrac{6}{7}$. We will now do cross-multiplication of the two fraction that is product of numerator of first fraction with denominator of second fraction, product of denominator of first fraction with numerator of second fraction.We will multiply 5 with 7 and 6 with 6.
$ \Rightarrow 5 \times 7 = 35$
$ \Rightarrow 6 \times 6 = 36$

By cross-multiplication, we obtain two numbers: 35 and 36, respectively. Let us now compare the values obtained by cross-multiplication. It is obvious that 36 is higher than 35.
$ \Rightarrow 35 < 36$
$ \Rightarrow 5 \times 7 < 6 \times 6$
So, the fraction
$ \Rightarrow \dfrac{5}{6} < \dfrac{6}{7}$
$ \therefore 5:6 < 6:7$

Hence, the ratio $5:6$ is smaller than $6:7$.

Note:We can also solve these types of questions by simplifying the fraction in decimal form then compare both the values. This method is very useful when there is a larger fraction.The method is also called Vedic mathematics.