Question

Alec and Magnus are building a fence. After 5 minutes, Alec has completed 3/4 of the fence and Magnus has completed 1/5 of the fence. How much more of the fence has Alec completed than Magnus?

Answer 1

In order to know how much more of the fence Alec has completed than Magnus we need to subtract the part each completed. This is done below:

`\text{dif = }(3)/(4)-(1)/(5)`

Since the denominator of the fractions are different we need to apply the LCM techinique, which consistis of finding the least common multiplier of both. To do that we need to break them in factors as shown below:

`\begin{gathered} 4=4\cdot1 \\ 5=5\cdot1 \end{gathered}`

We now take all the factors that appear and multiply them.

`\text{LCM = 4}\cdot5=20`

We can now change the denominator of the fractions by dividing the LCM by the previous denominators and multiplying the results by the numerators.

`\begin{gathered} \text{dif =}(5\cdot3-4\cdot1)/(20) \\ \text{dif = }(15-4)/(20) \\ \text{dif = }(11)/(20) \end{gathered}`

Alec completed 11/20 of the fence more than Magnus.