Let's analyze the problem from the image:

Problem Recap:

• At the beginning of the day, the stock market goes up $6 \frac{1}{2}$ points and stays at this level for most of the day.
• At the end of the day, the stock market goes down $12 \frac{3}{4}$ points from the high at the beginning of the day.
• The question is to find the total change in the stock market from the beginning of the day to the end of the day.

Solution:

1. Convert Mixed Numbers to Improper Fractions:

   • $6 \frac{1}{2} = \frac{13}{2}$
   • $12 \frac{3}{4} = \frac{51}{4}$

2. Express Both Fractions with a Common Denominator:

   • The common denominator for $\frac{13}{2}$ and $\frac{51}{4}$ is 4.
   • Convert $\frac{13}{2}$ to $\frac{26}{4}$.

3. Calculate the Total Change:

   • Since the stock first increased by $\frac{26}{4}$ and then decreased by $\frac{51}{4}$, the total change is: $\frac{26}{4} - \frac{51}{4} = \frac{26 - 51}{4} = \frac{-25}{4}$
   • Simplifying, $\frac{-25}{4} = -6.25$.

Answer:

The total change in the stock market from the beginning of the day to the end of the day is -6.25 points.

Would you like further details or have any other questions?

Follow-Up Questions:

1. How do you convert a mixed number to an improper fraction?
2. What is the process for finding a common denominator?
3. How can the stock market’s total change be interpreted?
4. What are some scenarios where the stock market might behave similarly?
5. How do positive and negative changes in the stock market affect investors?

Tip:

When dealing with mixed numbers, always convert them to improper fractions before performing operations like addition or subtraction.