Question

the table.
questions k
day
change in copy paper on hand (lb)
monday
-40\frac{1}{4}
tuesday
-60.5
wednesday
120\frac{3}{4}
thursday
-55\frac{1}{3}
friday
-60.\overline{6}
how many pounds of copy paper does the store have on hand at the end of friday? express your answer as a mixed number in simplest form.
__ lb

Explanation:

Step1: Convert decimals and mixed - numbers to improper fractions

• $-40\frac{1}{4}=-\frac{40\times4 + 1}{4}=-\frac{161}{4}$
• $-60.5=-\frac{605}{10}=-\frac{121}{2}$
• $120\frac{3}{4}=\frac{120\times4+3}{4}=\frac{483}{4}$
• $-55\frac{1}{3}=-\frac{55\times3 + 1}{3}=-\frac{166}{3}$
• $-60.\overline{6}=-\frac{182}{3}$

Step2: Find a common denominator

The common denominator of 4, 2 and 3 is 12.

• $-\frac{161}{4}=-\frac{161\times3}{4\times3}=-\frac{483}{12}$
• $-\frac{121}{2}=-\frac{121\times6}{2\times6}=-\frac{726}{12}$
• $\frac{483}{4}=\frac{483\times3}{4\times3}=\frac{1449}{12}$
• $-\frac{166}{3}=-\frac{166\times4}{3\times4}=-\frac{664}{12}$
• $-\frac{182}{3}=-\frac{182\times4}{3\times4}=-\frac{728}{12}$

Step3: Add the fractions

\[

$$\begin{align*} &-\frac{483}{12}-\frac{726}{12}+\frac{1449}{12}-\frac{664}{12}-\frac{728}{12}\\ =&\frac{-483-726 + 1449-664-728}{12}\\ =&\frac{-483-726-664-728 + 1449}{12}\\ =&\frac{-(483 + 726+664+728)+1449}{12}\\ =&\frac{-(2601)+1449}{12}\\ =&\frac{-1152}{12}\\ =& - 96 \end{align*}$$

\]

Answer:

$-96$