why is 1/6 greater than 1/8 but less than 1/3? EXPLAIN
consider a pizza
if cut into 3 equal slices, they are bigger than if it were cut into 6 slices.
Similarly , slices of 1/8 are smaller than 1/6
The denominator indicates how many parts are created out of the whole, so the bigger the denominator, the smaller the fraction.
Imagine three identical pizzas.
One is cut into 6 equal sized pieces.
One is cut into 8 equal sized pieces.
One is cut into 3 equal sized pieces.
Which pizza has the largest size piece? Which has the smallest?
If necessary, draw these on a piece of paper.
it is pretty simple
Bigger the denominator, the smaller the fraction
6 is less than 8 so 1/6 is greater than 1/8. And 3 is smaller than 8 so 1/3 is greater than 1/8
Why is one sixth greater than one eighth but less than one third???
Well, imagine you have a pie that you want to share among friends. Now, if you cut that pie into only 6 pieces, each person gets a bigger slice compared to when you cut it into 8 pieces. So 1/6 is more generous than 1/8 because you have a larger portion of the pie.
But then, if you cut that same pie into just 3 pieces, each person gets an even larger piece! So, while 1/6 is bigger than 1/8, it's still smaller than 1/3 because you have an even smaller portion of the pie to share. It's like going from "having more pie than your friend" to "having even less pie than your friend".
So, in short, 1/6 is greater than 1/8 because it gives you a larger portion, but it's still less than 1/3 because it gives you a smaller portion. Just think of it as the joy of eating pie, but with fractions!
To determine why 1/6 is greater than 1/8 but less than 1/3, we need to compare the three fractions and consider their denominators. The denominator represents the number of equal parts the whole is divided into, while the numerator represents the number of those parts we are considering.
Let's compare the fractions step by step:
1. 1/6 and 1/8:
- To compare fractions with different denominators, we need to find a common denominator.
- In this case, the least common multiple (LCM) of 6 and 8 is 24.
- So, we rewrite the fractions with the common denominator of 24: 4/24 and 3/24.
- Now, it's clear that 4/24 (or 1/6) is greater than 3/24 (or 1/8) because 4 is greater than 3.
2. 1/6 and 1/3:
- Again, we need to find a common denominator to make a fair comparison.
- The LCM of 6 and 3 is simply 6 because 6 is divisible by both 6 and 3.
- We rewrite the fractions with the common denominator of 6: 1/6 and 2/6.
- Now, it's evident that 2/6 (or 1/3) is greater than 1/6 because 2 is greater than 1.
Therefore, 1/6 is greater than 1/8, but it is less than 1/3 when comparing the fractions. By finding a common denominator and comparing the resulting numerators, we were able to determine the relationships between the fractions.