In Jacob’s class, six out of every 14 students play tennis. In Noah’s class, nine out of every 27 play tennis. Is the ratio of students who play tennis in Jacob’s class the same as the ratio who play tennis in Noah’s class?
For the first step, let’s write out the ratios of students who play tennis in Jacob’s class and in Noah’s class. In Jacob’s class, six out of 14 students play tennis. In Noah’s class, nine out of 27 play tennis. We can write these ratios as fractions. For Jacob, six out of 14, six over 14. And for Noah, nine over 27. We need to know, is six out of 14 the same as nine out of 27? Are these equivalent fractions? Are they equal ratios?
To compare these two ratios, we wanna reduce their fractions. On the left-hand side, both six and 14 are even numbers which means we can divide the numerator and the denominator by two. Six divided by two is three. 14 divided by two is seven. We’ve reduced six fourteenths to three-sevenths. Now, we want to check and see if nine over 27 can be reduced. Both nine and 27 are divisible by nine. Nine divided by nine is one. 27 divided by nine is three. The ratio nine twenty-sevenths can be reduced to one-third.
However, it’s still not clear whether these two ratios are equal. We’re still not totally sure if three-sevenths is equal to one-third or not. Just like when we compare fractions, when we compare ratios, we want to find a common denominator. We could use the denominator of 21. We know that seven times three equals 21. Seven times three equals 21. And if we multiplied the denominator by three, we need to multiply the numerator by three. Three times three equals nine.
The ratio three-sevenths is equivalent to nine twenty-firsts. We’ll follow the same procedure to convert one-third into a fraction out of 21. Three times seven equals 21. We multiplied the denominator by seven, so we need to multiply the numerator by seven. One times seven equals seven. And we’ve rewritten one-third as seven twenty-firsts.
Here’s what we can say. In Jacob’s class, we have a ratio of nine twenty-firsts. And we need to compare that to Noah’s class, which has a ratio of seven out of 21. Our question is asking, is the ratio the same in Jacob and Noah’s Class’? Nine over 21 is not the same as seven over 21. So, we would say no, the ratio of students who play tennis in Jacob’s class is not the same as the ratio of students who play tennis in Noah’s class.