Question

From the following pairs of numbers, find the reduced form of ratio of the first number to the second number.
(i)$72,60$
(ii)$38,57$
(iii)$52,78$

Answer 1

Hint: We have to find the reduced form of the ratio of the first number to second number. We can write the ratio as-
Ratio=$\dfrac{{{\text{First number}}}}{{{\text{second number}}}}$ . We will first find the factors of the numbers and then from those factors we will choose the highest common factor. Then divide the numerator and denominator by the highest common factor and you’ll get the reduced form of the ratio.

Complete step-by-step answer:
(i)Given numbers are$72,60$.
We have to find the ratio of the first number to the second number.
So we can write the ratio of the numbers in the form-
Ratio=$\dfrac{{{\text{First number}}}}{{{\text{second number}}}}$
On putting values we get-
$ \Rightarrow $ Ratio=$\dfrac{{72}}{{60}}$
Here we know that $72 = 12 \times 6$ and $60 = 12 \times 5$ so the highest common factor of the numerator and denominator is$12$.
So on dividing the highest common factor we get-
Answer-Ratio= $\dfrac{6}{5}$
(ii)Given numbers are-$38,57$
We have to find the ratio of the first number to the second number.
So we can write the ratio of the numbers in the form-
Ratio=$\dfrac{{{\text{First number}}}}{{{\text{second number}}}}$
On putting values we get-
$ \Rightarrow $ Ratio=$\dfrac{{38}}{{57}}$
Here we know that $38 = 19 \times 2$ and $57 = 19 \times 3$ so the highest common factor of the numerator and denominator is$19$.
So on dividing the highest common factor we get-
Answer-Ratio= $\dfrac{2}{3}$
(iii) Given numbers are$52,78$.
We have to find the ratio of the first number to the second number.
So we can write the ratio of the numbers in the form-
Ratio=$\dfrac{{{\text{First number}}}}{{{\text{second number}}}}$
On putting values we get-
$ \Rightarrow $ Ratio=$\dfrac{{52}}{{78}}$
Here we know that $52 = 13 \times 4$ and $78 = 13 \times 6$ so the highest common factor of the numerator and denominator is$13$.
So on dividing the highest common factor we get-
$ \Rightarrow $ Ratio=$\dfrac{4}{6}$
We can see that it can be further reduced by dividing both the numerator and denominator by$2$
So on dividing by $2$, we get-
Ratio= $\dfrac{2}{3}$

Note: We can also solve this question by simply dividing the numerator and denominator by prime numbers by which both of them will be divisible. We continue dividing till the numbers of numerator and denominator do not have any common factors and hence cannot be reduced further.