Answer :
- Calculate the total increase: $2 \times 14 \frac{2}{3} = \frac{88}{3}$.
- Calculate the total decrease: $10 + 8 \frac{1}{3} + 12 \frac{2}{3} = 31$.
- Calculate the net change: $\frac{88}{3} - 31 = \frac{-5}{3}$.
- Express the net change as a mixed number: $\boxed{{-1 \frac{2}{3}}}$.
### Explanation
1. Calculate the total increase
First, we need to calculate the total increase in the stock value. The stock increases $14
\frac{2}{3}$ points twice. So, the total increase is $2 \times 14 \frac{2}{3}$.
2. Convert mixed number to improper fraction
$14 \frac{2}{3}$ can be written as an improper fraction: $14 \frac{2}{3} = \frac{14 \times 3 + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3}$. So, the total increase is $2 \times \frac{44}{3} = \frac{88}{3}$.
3. Calculate the total decrease
Now, we need to calculate the total decrease in the stock value. The stock decreases by 10 points, $8 \frac{1}{3}$ points, and $12 \frac{2}{3}$ points. So, the total decrease is $10 + 8 \frac{1}{3} + 12 \frac{2}{3}$.
4. Convert mixed numbers to improper fractions and sum
$8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}$ and $12 \frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3}$. So, the total decrease is $10 + \frac{25}{3} + \frac{38}{3} = 10 + \frac{25 + 38}{3} = 10 + \frac{63}{3} = 10 + 21 = 31$.
5. Calculate the net change
Now, we need to calculate the net change by subtracting the total decrease from the total increase. The total increase is $\frac{88}{3}$ and the total decrease is 31. So, the net change is $\frac{88}{3} - 31$.
6. Convert to common denominator and subtract
To subtract 31 from $\frac{88}{3}$, we need to convert 31 to a fraction with a denominator of 3: $31 = \frac{31 \times 3}{3} = \frac{93}{3}$. So, the net change is $\frac{88}{3} - \frac{93}{3} = \frac{88 - 93}{3} = \frac{-5}{3}$.
7. Convert improper fraction to mixed number
Finally, we need to express the net change as a mixed number. $\frac{-5}{3} = -1 \frac{2}{3}$.
8. State the final answer
Therefore, the value of the stock changed by $-1 \frac{2}{3}$ points that week.
### Examples
Understanding stock fluctuations can be useful in personal finance. For example, if you own stock in a company, knowing how to calculate the net change in its value over a week can help you make informed decisions about when to buy or sell. This involves tracking increases and decreases in value and calculating the overall change, similar to the problem we just solved. By understanding these changes, you can better manage your investment portfolio and make strategic financial decisions.
- Calculate the total decrease: $10 + 8 \frac{1}{3} + 12 \frac{2}{3} = 31$.
- Calculate the net change: $\frac{88}{3} - 31 = \frac{-5}{3}$.
- Express the net change as a mixed number: $\boxed{{-1 \frac{2}{3}}}$.
### Explanation
1. Calculate the total increase
First, we need to calculate the total increase in the stock value. The stock increases $14
\frac{2}{3}$ points twice. So, the total increase is $2 \times 14 \frac{2}{3}$.
2. Convert mixed number to improper fraction
$14 \frac{2}{3}$ can be written as an improper fraction: $14 \frac{2}{3} = \frac{14 \times 3 + 2}{3} = \frac{42 + 2}{3} = \frac{44}{3}$. So, the total increase is $2 \times \frac{44}{3} = \frac{88}{3}$.
3. Calculate the total decrease
Now, we need to calculate the total decrease in the stock value. The stock decreases by 10 points, $8 \frac{1}{3}$ points, and $12 \frac{2}{3}$ points. So, the total decrease is $10 + 8 \frac{1}{3} + 12 \frac{2}{3}$.
4. Convert mixed numbers to improper fractions and sum
$8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}$ and $12 \frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3}$. So, the total decrease is $10 + \frac{25}{3} + \frac{38}{3} = 10 + \frac{25 + 38}{3} = 10 + \frac{63}{3} = 10 + 21 = 31$.
5. Calculate the net change
Now, we need to calculate the net change by subtracting the total decrease from the total increase. The total increase is $\frac{88}{3}$ and the total decrease is 31. So, the net change is $\frac{88}{3} - 31$.
6. Convert to common denominator and subtract
To subtract 31 from $\frac{88}{3}$, we need to convert 31 to a fraction with a denominator of 3: $31 = \frac{31 \times 3}{3} = \frac{93}{3}$. So, the net change is $\frac{88}{3} - \frac{93}{3} = \frac{88 - 93}{3} = \frac{-5}{3}$.
7. Convert improper fraction to mixed number
Finally, we need to express the net change as a mixed number. $\frac{-5}{3} = -1 \frac{2}{3}$.
8. State the final answer
Therefore, the value of the stock changed by $-1 \frac{2}{3}$ points that week.
### Examples
Understanding stock fluctuations can be useful in personal finance. For example, if you own stock in a company, knowing how to calculate the net change in its value over a week can help you make informed decisions about when to buy or sell. This involves tracking increases and decreases in value and calculating the overall change, similar to the problem we just solved. By understanding these changes, you can better manage your investment portfolio and make strategic financial decisions.
