Question

Economics On Monday, the starting value of EdCorp stock was \(9 \frac{1}{4}\) During the week, the value changed by the following amounts: Monday Tuesday Wednesday Thursday Friday \\[ +1 \frac{1}{2} \quad-\frac{7}{8} \quad+1 \frac{3}{4} \quad+\frac{5}{8} \quad+1 \frac{1}{4} \\] a. What was the value of EdCorp stock at the end of Friday? b. How much did the stock gain or lose during the week? c. What were the stock's highest and lowest values during the week? On what days did each of these values occur?

Short answer

a. \(12 \frac{7}{8}\) b. \(3 \frac{5}{8}\) gain c. Highest: \(12 \frac{7}{8}\) on Friday, Lowest: \(9 \frac{1}{4}\) on Monday

Step-by-step solution

- Determine Monday's value

Starting value of EdCorp stock on Monday is given as \(9 \frac{1}{4}\). Convert this to an improper fraction: \[9 \frac{1}{4} = 9 + \frac{1}{4} = \frac{36}{4} + \frac{1}{4} = \frac{37}{4}\]

- Add Tuesday's change

Change on Tuesday is \(+1 \frac{1}{2}\). Convert to an improper fraction: \[1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}\]. Adding this to Monday's value: \[\frac{37}{4} + \frac{3}{2} = \frac{37}{4} + \frac{6}{4} = \frac{43}{4} = 10 \frac{3}{4}\]

- Subtract Wednesday's change

Change on Wednesday is \(-\frac{7}{8}\). Starting from Tuesday's value (as an improper fraction): \[10 \frac{3}{4} = \frac{43}{4}\]. Subtract \(\frac{7}{8}\): \[\frac{43}{4} - \frac{7}{8} = \frac{86}{8} - \frac{7}{8} = \frac{79}{8} = 9 \frac{7}{8}\]

- Add Thursday's change

Change on Thursday is \(+1 \frac{3}{4}\). Convert to an improper fraction: \[1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}\]. Adding this to Wednesday's value: \[\frac{79}{8} + \frac{7}{4} = \frac{79}{8} + \frac{14}{8} = \frac{93}{8} = 11 \frac{5}{8}\]

- Add Friday's change

Change on Friday is \(+1 \frac{1}{4}\). Convert to an improper fraction: \[1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4}\]. Adding this to Thursday's value: \[\frac{93}{8} + \frac{5}{4} = \frac{93}{8} + \frac{10}{8} = \frac{103}{8} = 12 \frac{7}{8}\]

- Week's total change

Calculating the net change for the week. Starting value was \(9 \frac{1}{4}\): \[12 \frac{7}{8} - 9 \frac{1}{4} = \frac{103}{8} - \frac{37}{4} = \frac{103}{8} - \frac{74}{8} = \frac{29}{8} = 3 \frac{5}{8}\]. The stock increased by \(3 \frac{5}{8}\) during the week.

- Identify highest and lowest values

The stock values at the end of each day are: Monday \(9 \frac{1}{4}\), Tuesday \(10 \frac{3}{4}\), Wednesday \(9 \frac{7}{8}\), Thursday \(11 \frac{5}{8}\), Friday \(12 \frac{7}{8}\). The highest value was \(12 \frac{7}{8}\) on Friday and the lowest value was \(9 \frac{1}{4}\) on Monday.

Key concepts

fractions

Fractions are a way to represent parts of a whole. They consist of a numerator and a denominator, separated by a slash. The numerator indicates how many parts are taken, and the denominator shows the total number of parts the whole is divided into. For example, in the fraction \(\frac{3}{4}\), 3 is the numerator and 4 is the denominator, meaning three parts out of a total four.

Fractions can be proper or improper. Proper fractions have a numerator smaller than the denominator. Improper fractions have a numerator larger than or equal to the denominator. Example: \(\frac{7}{4}\) is improper.

Converting between mixed numbers and improper fractions is essential in calculations. For instance, an improper fraction like \(\frac{37}{4}\) can be turned into a mixed number \(\text{9 }\frac{1}{4}\) by dividing the numerator by the denominator. Understanding and converting fractions are key in solving many math problems.

stock value calculation

Stock value calculation involves finding the worth of a stock over a specific period. In the exercise, we start with a base value of EdCorp stock and calculate its value across the week. The starting value is \(9 \frac{1}{4}\), which we convert to an improper fraction \(\frac{37}{4}\).

This conversion helps in handling additions and subtractions efficiently during the week’s fluctuations:

• Adding the change on Tuesday \(+\frac{3}{2}\)
• Subtracting the change on Wednesday \(-\frac{7}{8}\)
• Adding the change on Thursday \(1 \frac{3}{4}\)
• Adding the change on Friday \(1 \frac{1}{4}\)

The final stock value at the end of the week is found by adding these daily changes to the initial value. Through correct fractional arithmetic, we determine the stock ended at \(12 \frac{7}{8}\). Calculating stock values helps in financial planning and understanding market trends.

improper fractions

Improper fractions have numerators larger than or equal to the denominators. This characteristic means they represent values greater than or equal to one.

For example, \(\frac{9}{4}\) is an improper fraction, as 9 is greater than 4. Converting improper fractions to mixed numbers can make them easier to understand. For example, \(\frac{9}{4}\) can be expressed as \(\text{2 }\frac{1}{4}\)

This is done by dividing the numerator by the denominator to find the whole number part and then using the remainder as the numerator of the fractional part. Properly managing improper fractions in calculations, like those shown in the exercise, is vital for obtaining accurate results.

real-world math applications

Math word problems, like stock value calculations, show the importance of math in real-world situations. Understanding stock changes helps investors make informed decisions.

For example, knowing how to calculate the net change in stock value over a week lets investors determine profitability. In this problem, we calculated the stock value change by converting mixed numbers to improper fractions, adding or subtracting changes, and finally determining the stock’s highest and lowest values.

• The stock's highest value was on Friday, at \(12 \frac{7}{8}\).
• The lowest was on Monday, at \(9 \frac{1}{4}\).

These calculations apply beyond stocks to areas like budgeting, shopping discounts, and interest rates, proving math's daily utility.