The fraction 7/8 is larger than the fraction 3/4. There are two different ways you can work out the relative sizes of two fractions - the mathematical way and the intuitive way, or common sense way. Let’s look at the "proper” or mathematical way first.
All fractions have two parts; the number on top which is called the numerator and the part underneath which is called the denominator.
The first step when comparing two fractions is to find a common denominator - that means a denominator that both fractions can be reformulated into. In the case given we need to find a number that is divisible by both four and eight without anything left over, or no remainder.
It’s pretty obvious that both denominators will go into eight, so we’ll use that as the common denominator. Next, we’ll see how many times each denominator will go into the common denominator, and then we’ll multiply the numerator by that number.
For example, eight goes into eight once. One times seven is seven, so we have the same fraction we started with - 7/8. The second fraction’s denominator is four and this goes into eight two times, so we multiply 3 x 2 = 6. So the second fractio , 3/4, can also be written as 6/8.
In words, we have once fraction of seven eighths, and we have a second fraction of six eighths. Put like this, it’s pretty obvious that seven eighths is the bigger of the two fractions.
There is also an intuitive or commonsense way of looking at the same problem. That is to ask yourself, is the denominator a big number or a small number? The bigger the denominator, then the more parts the object in question (whether it’s an apple or your weekly pay packet) is being chopped up into. As there are more parts, they must be small - so there would have to be a lot of them for the fraction to be a big one. Obviously, 1/100 must be a much smaller fraction than 3/4 because there are so many hundredths and so few quarters.
All fractions have two parts; the number on top which is called the numerator and the part underneath which is called the denominator.
The first step when comparing two fractions is to find a common denominator - that means a denominator that both fractions can be reformulated into. In the case given we need to find a number that is divisible by both four and eight without anything left over, or no remainder.
It’s pretty obvious that both denominators will go into eight, so we’ll use that as the common denominator. Next, we’ll see how many times each denominator will go into the common denominator, and then we’ll multiply the numerator by that number.
For example, eight goes into eight once. One times seven is seven, so we have the same fraction we started with - 7/8. The second fraction’s denominator is four and this goes into eight two times, so we multiply 3 x 2 = 6. So the second fractio , 3/4, can also be written as 6/8.
In words, we have once fraction of seven eighths, and we have a second fraction of six eighths. Put like this, it’s pretty obvious that seven eighths is the bigger of the two fractions.
There is also an intuitive or commonsense way of looking at the same problem. That is to ask yourself, is the denominator a big number or a small number? The bigger the denominator, then the more parts the object in question (whether it’s an apple or your weekly pay packet) is being chopped up into. As there are more parts, they must be small - so there would have to be a lot of them for the fraction to be a big one. Obviously, 1/100 must be a much smaller fraction than 3/4 because there are so many hundredths and so few quarters.
