Explain how you know that 7/12 is greater than 1/3 but less than 2/3?

The easiest way to compare fractions is by having a common denominator for both fractions.

This is because, when the denominator is the same in both fractions, we will simply compare the numerators and the greater fraction will be the one having greater numerator

Part 1:

The first given fraction is

The second given fraction is

We can make the denominator in the second one equal to 12 by multiplying it by 4.

However, to preserve the value of the fraction, we will multiply it by

This will give us:

* =

Now, the two fractions became and

The denominator is the same, so we will compare numerators.

Since 7 is greater than 4, therefore:

is the greater fraction

Part 2:

The first given fraction is

The second given fraction is

We can make the denominator in the second one equal to 12 by multiplying it by 4.

However, to preserve the value of the fraction, we will multiply it by

This will give us:

* =

Now, the two fractions became and

The denominator is the same, so we will compare numerators.

Since 8 is greater than 7, therefore:

is the greater fraction

Hope this helps :)