For this case, they ask us to find the time that Angela practices on the piano during the weekend.
Friday:
[tex]2 \frac {1} {2} = 2 + \frac {1} {2} = \frac {2 * 2 + 1 * 1} {2 * 1} = \frac {5} {2}[/tex]
Saturday:
[tex]2 \frac {1} {3} = 2 + \frac {1} {3} = \frac {3 * 2 + 1 * 1} {3 * 1} = \frac {7} {3}[/tex]
Sunday:
[tex]3 \frac {2} {3} = 3 + \frac {2} {3} = \frac {3 * 3 + 2 * 1} {3 * 1} = \frac {11} {3}[/tex]
Adding we have:
[tex]\frac {5} {2} + \frac {7} {3} + \frac {11} {3} =\\\frac {5} {2} + \frac {18} {3} =\\2.5 + 6 =\\8.5[/tex]
So, Angela practiced 8.5 hours during the weekend. This is equivalent to [tex]8 \frac {1} {2}[/tex]
Answer:
8.5 hours
[tex]8 \frac {1} {2}[/tex] hours
Angela practiced piano during the weekend (Saturday and Sunday) for 6 hours.
To determine the total amount spent on both days of the weekend =
Amount Angela spent on Saturday + Amount Angela spent on Sunday =
= [tex]2\frac{1}{3}[/tex] (otherwise expressed as [tex]\frac{7}{3}[/tex]) + [tex]3\frac{2}{3}[/tex](otherwise expressed as [tex]\frac{11}{3}[/tex])
Significantly, we look for the lowest common denominator (LCD) of both denominators (3 and 3). Since both values are same, we therefore make use of 3.
LCD = 3
= [tex]\frac{7}{3}[/tex] + [tex]\frac{11}{3}[/tex]
= (1 x 7) + (1 x 11) / 3
= (7) + (11) / 3
= 7 + 11 / 3
= [tex]\frac{18}{3}[/tex]
= 6 hours
Friday is not included because weekend starts on Saturday and ends on Sunday.
Hence, on Saturday, she practiced for [tex]2\frac{1}{3}[/tex] hours; On Sunday she practiced for [tex]3\frac{2}{3}[/tex] hours. The addition of the hours spent on both days is 6 hours.
The above mathematical expression denotes a number problem, and it deals with fraction. In order to derive a solution, it is important an order of operations i.e BODMAS is applied.
The denominators of the both fractions are the same (3), thereby it was used to factor out the numerators (7) and (11), and subsequently arriving at the final answer which is 6 hours.
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