Complete 75 thirds, what, 90 fifths using the symbols for is less than, is equal to, or is more than.
Here we’re given two fractions, seventy-five thirds and ninety-fifths, and a gap in the middle of them. And, that’s a gap we need to fill in using a symbol. Let’s look more closely at the fractions. We have seventy-five thirds and ninety-fifths. The first thing to notice is that these are both improper fractions. In other words, they’re worth more than one. And we know this because both numerators, the top number, are larger than both denominators, the bottom number.
Some people might make the mistake of looking at these two fractions and thinking that 90 is more than 75, so the second fraction must be greater than the first fraction. But it’s not as easy as that to compare these two fractions because the denominators are different. A third is different than a fifth. So the way to find the answer is to think carefully about how to convert these improper fractions into mixed numbers. What each improper fraction worth?
Firstly, we know that three-thirds are the same as one whole. So, we can find out how many wholes there are in seventy-five thirds by dividing 75 by three. You might know what the answer is straight away because it’s a number that we use quite regularly. But if we don’t, we could partition the number 75 into 60 and 15 to help us. 60 divided by three equals 20. And 15 divided by three equals five. So as you may have known already, 75 split into three equals 25. So we can say that seventy-five thirds is the same as 25.
Now, let’s do the same with the second fraction. Here, we have ninety-fifths. We know that five-fifths are the same as one whole. So to find the value of ninety-fifths, we need to find out how many fives there are in 90. What is 90 divided by five? Well, 90 is very close to 100. And, we know that there are 20 fives in 100. 90 is 10 less than 100 or two lots of five less than 100. So instead of 20 fives, 90 is made up of 18 fives. The fraction ninety-fifths is the same as 18 wholes.
We know that 25 is greater than 18. So, we can also say that seventy-five thirds is greater than ninety-fifths. So, which symbol are we going to use? Don’t forget, the wider end of each symbol points towards the larger number. So if we read this symbol from left to right, it means is less than. We know this one stands for is equal to. And with this last symbol, we can see that the number on the left must be larger than the number on the right because the open end of the symbol is pointing towards the left. So, it means is greater than.
So, the symbol we need to use to compare these two improper fractions is this one. We found the answer by converting each improper fraction to see what they were worth. Seventy-five thirds is greater than ninety-fifths.