Question

George says that, to subtract fractions with different denominators, you always have to multiply the denominators to find the common unit; for example:

3/8 - 1/6 = 18/48 - 8/48

Show George how he could have chosen a denominator smaller than 48, and solve the problem.

Answer 1

`(5)/(24)`

Explanation:

We have been given an equation solved by George. We are asked to solve the problem by choosing a denominator smaller than 48.

`(3)/(8)-(1)/(6)`

To subtract to fraction with different denominators, we need to make a common denominator.

The common denominator would be the least common multiple of both denominators.

In our given problem, we can see that the numbers in denominators are 8 and 6.

Let us find LCM of 8 and 6:

Multiples of 8: 8, 16, 24, 32, 40,...

Multiples of 6: 6, 12, 18, 24, 30,...

We can see that LCM of 8 and 6 is 24.

Let us solve our given problem by making a common denominator:

`(3*3)/(8*3)-(1*4)/(6*4)`

`(9)/(24)-(4)/(24)`

Combine numerators:

`(9-4)/(24)`

`(5)/(24)`

Therefore, the answer for our given problem would be
`(5)/(24)`.