As per the problem
Jing spent [tex] \frac{1}{3} [/tex] of her money on a pack of pens.
[tex] \frac{1}{2} [/tex] of her money on a pack of markers.
and [tex] \frac{1}{8} [/tex] of her money on a pack of pencils.
Total fraction of money spent cab be given as below
Fraction of Money Spent =[tex] \frac{1}{3} +\frac{1}{2}+\frac{1}{8} [/tex]
Take the LCD of denominator, we get LCD of (3,2,8)=24
Fraction of Money Spent =[tex] \frac{8+12+3}{24} =\frac{23}{24} \\
[/tex]
[tex] \\
\text{Hence fraction of Money Spent }=\frac{23}{24} \\
\\
\text{Fraction of Money left}=1-\frac{23}{24} \\
\\
\text{Simplify, we get}\\
\\
\text{Fraction of Money left}=\frac{24-23}{24} \\
\\
\text{Fraction of Money left}=\frac{1}{24} [/tex]
The fraction of the amount of money that Jing had left is [tex]\frac{1}{24}[/tex]
One way to determine the total fraction of the amount of money she spent = the fraction of the money left - the fraction of the amount she spent on pack of pens + fraction of the amount spent on marker + fraction of the money she spent on pencils
Firstly, without the fraction of the money left, we have:
= [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{8}[/tex]
= [tex]\frac{8}{24}[/tex] + [tex]\frac{12}{24}[/tex] + [tex]\frac{3}{24}[/tex], it also the same as
= (8+12+3) / 24 (24 is the lowest common denominator)
= [tex]\frac{23}{24}[/tex]
Since the fraction of the money left = 1
Therefore we have:
= 1 – [tex]\frac{23}{24}[/tex]
= (24 x 1) – (23 x 1) / 24 (24 is the smallest number that can divide the denominators)
Therefore we have:
= 24 – 23 / 24
= [tex]\frac{1}{24}[/tex].
Therefore the fraction of the amount that Jing has left is [tex]\frac{1}{24}[/tex].
Notably, we solve this question using the BODMAS rule.
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