Question

stock market at the beginning of the day the stock market goes up $50\frac{3}{4}$ points and stays at this level for most of the day. at the end of the day the stock market goes down $80\frac{1}{2}$ points from the high at the beginning of the day. what is the total change in the stock market from the beginning of the day to the end of the day?
the total change in the stock market is \\(\square\\) points.
(type an integer, proper fraction, or mixed number.)

Explanation:

Step1: Identify the changes

The stock market goes up by \( 50\frac{3}{4} \) points and then down by \( 80\frac{1}{2} \) points. To find the total change, we need to subtract the downward change from the upward change (or add the upward and the negative of the downward change).

Step2: Convert mixed numbers to improper fractions

\( 50\frac{3}{4}=\frac{50\times4 + 3}{4}=\frac{200+3}{4}=\frac{203}{4} \)
\( 80\frac{1}{2}=\frac{80\times2+1}{2}=\frac{160 + 1}{2}=\frac{161}{2} \)

Step3: Make the denominators the same

To subtract, we need a common denominator. The common denominator of 4 and 2 is 4. So, \( \frac{161}{2}=\frac{161\times2}{2\times2}=\frac{322}{4} \)

Step4: Calculate the total change

Total change \(=\frac{203}{4}-\frac{322}{4}=\frac{203 - 322}{4}=\frac{- 119}{4}=-29\frac{3}{4}\) (or we can think of it as \(50\frac{3}{4}-80\frac{1}{2}\), converting to decimals: \(50.75-80.5=-29.75=-29\frac{3}{4}\))

Answer:

\(-29\frac{3}{4}\)