The fraction of the amount Liang has left is [tex]\frac{2}{21}[/tex]
To derive L (amount of money Liang will have left), add X (amount spent on a pen) and Y (amount spent on books) together, then the derived value be subtracted from M (fraction of total amount Liang has got) i.e.: M – (X + Y)
Therefore, L = M – (X + Y)
Deriving (X + Y)
= X + Y
= [tex]\frac{1}{3}[/tex] + [tex]\frac{4}{7}[/tex]
= (1 x 7) + (3 x 4) / 21
= (7) + (12) / 21
= 7 + 12 / 21
= [tex]\frac{19}{21}[/tex]
X + Y = [tex]\frac{19}{21}[/tex]
Since the lowest common denominator of the fraction of X and Y = 21, then the fraction of M = [tex]\frac{21}{21}[/tex]
Thus, M = [tex]\frac{21}{21}[/tex]
Recall, L = M – (X + Y)
Thus,
L = [tex]\frac{21}{21}[/tex] – [tex]\frac{19}{21}[/tex]
L = (1 x 21) – (1 x 19) / 21
L = (21) – (19) /21
L = 21 – 19 /21
L = [tex]\frac{2}{21}[/tex]
Hence, the amount Liang will have left is [tex]\frac{2}{21}[/tex]
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