Question

From the following pairs of numbers, find the reduced form of the ratio of the first number to the second number.
A.72,60
B.38,57
C.52,78

Answer 1

Hint: We will first consider the numbers given and as we have to find the reduced form of each pair so, we will divide the numerator to the denominator and divide until it does not get reduced further and that will only give us the correct answer for each pair. For all the three pairs we have to use the same method to find the reduced form.
Complete step-by-step answer:
A.We will first consider the first pair that is 72, 60.
Now, we have to find the reduced form of the ratio of the first number to the second number. Thus, we can write it as,
\[ \Rightarrow \dfrac{{72}}{{60}}\]
Now, we will divide the numerator with denominator and as we can see 2 is common in both the numbers, so, we will get,
\[ \Rightarrow \dfrac{{2 \times 36}}{{2 \times 30}} = \dfrac{{36}}{{30}}\]
We can see that the obtained ratio can further be reduced as 2 is common in both the numbers.
Thus, we get,
\[ \Rightarrow \dfrac{{2 \times 18}}{{2 \times 15}} = \dfrac{{18}}{{15}}\]
Now, we will further reduce it as 3 is common in both the numbers.
\[ \Rightarrow \dfrac{{3 \times 6}}{{3 \times 5}} = \dfrac{6}{5}\]
Hence, as we can see that the ratio can not get further reduced so, this is the reduced form only.
Thus, for the pair, 72,60, the reduced form is \[\dfrac{6}{5}\].
B.We will consider the second pair that is 38,57.
Now, we have to find the reduced form of the ratio of the first number to the second number. Thus, we can write it as,
\[ \Rightarrow \dfrac{{38}}{{57}}\]
Now, we will divide the numerator with denominator and as we can see 19 is common in both the numbers, so, we will get,
\[ \Rightarrow \dfrac{{19 \times 2}}{{19 \times 3}} = \dfrac{2}{3}\]
Hence, as we can see that the ratio cannot get further reduced so, this is the reduced form only.
Thus, for the pair, 38,57, the reduced form is \[\dfrac{2}{3}\].
C.We will consider the second pair that is 52,78.
Now, we have to find the reduced form of the ratio of the first number to the second number. Thus, we can write it as,
\[ \Rightarrow \dfrac{{52}}{{78}}\]
Now, we will divide the numerator with denominator and as we can see 26 is common in both the numbers, so, we will get,
\[ \Rightarrow \dfrac{{26 \times 2}}{{26 \times 3}} = \dfrac{2}{3}\]
Hence, as we can see that the ratio cannot get further reduced so, this is the reduced form only.
Thus, for the pair, 52,78, the reduced form is \[\dfrac{2}{3}\].
Note: Whenever we have to find the reduced form, we need to divide the numerator and denominator and divide till when it does not get reduced further and this is the only method that to take commonly from the numbers and factor it out. The reduced form is the simplest form that does not have a common factor in it.