30 pupils out of a class of 50 pupils went on a trip. What fraction of the class went on the trip?
We’re told that 30 pupils go on a trip. And that these 30 pupils are out of a class that has 50 pupils all together. We can think of the line in between two numbers in a fraction as representing out of a possible. So if we write 30 above and 50 below, this represents 30 out of a possible 50. The denominator in a fraction, that’s the bottom number, shows us the number of parts in the whole amount. The whole class contains 50 pupils. So the number of parts in the whole amount is 50. Now, the numerator or the top number in the fraction shows us the number of parts in the whole that have been selected. The number that we’re talking about. And in this problem, we’re talking about 30 out of 50. And that’s why the top number is 30. So we could answer the question by writing thirty fiftieths. This is a fraction. And it’s the fraction of the class that did go on the trip.
But is there a way we can simplify this fraction? Can we write it more simply but at the same time keep the value the same? What number can we divide both 30 and 50 by? Well, there are lots of numbers. Both 30 and 50 are in the two times table. So we could divide by two. They’re also in the five times table and the 10 times table. We want to choose the largest possible number to divide by. This way, we don’t have to keep simplifying. We just do it in one step. So let’s divide by 10. 30 divided by 10 equals three. And five divided by 10 equals five. Can you see the similarities between both fractions? We’ve lost the zeros. Both numbers have become 10 times less. But the value of the fraction is still the same. Thirty fiftieths is the same as three-fifths.
And so if 30 pupils out of a class of 50 pupils went on a trip, we could write the fraction of the class that went on the trip as thirty fiftieths. But we could also simplify this and write it as three-fifths. Three-fifths of the class went on the trip.