In the stock market, changes in value used to be indicated by fractions, which represented portions of $1. If a stock had a value of $11.50, write and evaluate an addition expression to find how much the stock is worth after an increase of 1 /4. How do you know that is the correct expression?

Malik earns an average of 4 1/ 2 points on his daily quizzes. Near the end of the quarter, his average decreases by 3/ 4 point. Write and evaluate a subtraction expression to find his current quiz grade average.
In the stock market, changes in value used to be indicated by fractions, which represented portions of $1. If a stock had a value of $11.50, write and evaluate an addition expression to find how much the stock is worth after an increase of 1 /4. How do you know that is the correct expression?
Malik earns an average of 4 1/ 2 points on his daily quizzes. Near the end of the quarter, his average decreases by 3/ 4 point. Write and evaluate a subtraction expression to find his current quiz grade average.

1 answer

Let's tackle both problems step by step.

Stock Value Increase

  1. Starting Value: The stock is worth $11.50.
  2. Increase: The increase is \( \frac{1}{4} \).
    • To convert \( \frac{1}{4} \) into a dollar value, you can convert it to a decimal, which is \( 0.25 \) dollars.
  3. Expression: The addition expression to find the new stock price is: \[ 11.50 + 0.25 \]
  4. Evaluation: \[ 11.50 + 0.25 = 11.75 \]
  5. Conclusion: Therefore, the stock is worth $11.75 after the increase. This expression is correct because it accurately reflects the original stock value plus the specified increase.

Malik's Quiz Grade Average

  1. Starting Average: Malik's average is \( 4 \frac{1}{2} \), which can be converted to an improper fraction or decimal:
    • As a decimal: \( 4.5 \) (since \( 4 \frac{1}{2} = 4 + 0.5 = 4.5 \))
    • As an improper fraction: \( \frac{9}{2} \) (since \( 4 \times 2 + 1 = 9 \)).
  2. Decrease: His average decreases by \( \frac{3}{4} \).
  3. Expression: The subtraction expression to find his new average is: \[ 4.5 - 0.75 \] or, using improper fractions: \[ \frac{9}{2} - \frac{3}{4} \]
  4. Evaluation (Decimal): \[ 4.5 - 0.75 = 3.75 \] Or using improper fractions: \[ \frac{9}{2} - \frac{3}{4} = \frac{9 \times 2}{2 \times 2} - \frac{3 \times 1}{4 \times 1} = \frac{18}{4} - \frac{3}{4} = \frac{15}{4} = 3.75 \]
  5. Conclusion: Therefore, Malik's current quiz grade average is 3.75 points after the decrease. This expression is correct because it represents the initial average minus the decrease he experienced.

In summary, after evaluating both expressions, we find that:

  • The stock is worth $11.75 after the increase.
  • Malik's current average quiz grade is 3.75 points after the decrease.