The fractions below are in ascending order. Each fraction in its simplest form.

Question

c is an integer.
Work out the value of c.
7/12, c/4, 5/6, 7/8

Answer 1

To compare fractions, we need to have a common denominator. The smallest common multiple of 4, 6, and 8 is 24. So we make each fraction have a denominator of 24:

7/12 = 14/24
c/4 = 6c/24
5/6 = 20/24
7/8 = 21/24

So the fractions in order are:
14/24, 6c/24, 20/24, 21/24

Simplifying each fraction, we get:
7/12, c/4, 5/6, 7/8

Since the order is already in ascending order, we just need to find where c/4 fits in between 7/12 and 5/6. To do this, we can convert all fractions to have a denominator of 12:

7/12 = 7/12
5/6 = 10/12
c/4 = 3c/12

So we need to find where 3c/12 fits in between 7/12 and 10/12. Simplifying all fractions by dividing by 3/12 (which is the same as multiplying by 4), we get:

7/9, c/3, 5/6

Since the fractions are in ascending order, we know that c/3 must fit in between 7/9 and 5/6. To find where, we can compare the numerators:

7/9 = 28/36
c/3 = (4/3)c/12
5/6 = 20/36

So we need to find where (4/3)c/12 fits in between 28/36 and 20/36. Simplifying all fractions by multiplying by 3/4, we get:

21/28, c/9, 15/28

Again, we know that c/9 must fit in between 21/28 and 15/28. To find where, we can compare the numerators:

21/28 = 15/20.83...
c/9 = (1/9)c
15/28 = 0.5357...

Since c/9 must be greater than 15/20.83... and less than 0.5357..., we can write:

15/20.83... < c/9 < 0.5357...

Multiplying everything by 9, we get:

c > 11.97...
c < 4.821...

Since c is an integer, the only integer that satisfies both inequalities is c = 12. Therefore, the fractions in ascending order are:

7/12, 3, 5/6, 7/8

And c = 12.