Problem 30 - Elementary and Intermediate Algebra

Question

Substitute to find the value of each expression. Olympic Softball. A softball player's batting average is \(h / a,\) where \(h\) is the number of hits and \(a\) is the number of "at bats." In the 2008 Summer Olympics, Jessica Mendoza had 8 hits in 22 at bats. What was her batting average? Round to the nearest thousandth.

Step-by-Step Solution

Answer

Batting average = 0.364

Step 1 - Identify Given Values

The problem provides the number of hits, which is 8, and the number of at bats, which is 22. These values will be used in the formula for batting average.

Step 2 - Write the Formula

Write down the formula for batting average: \[\text{Batting Average} = \frac{h}{a}\] where \(h\) is the number of hits and \(a\) is the number of at bats.

Step 3 - Substitute the Values

Substitute the given values into the formula: \[h = 8\] \[a = 22\] \[\text{Batting Average} = \frac{8}{22}\]

Step 4 - Perform the Division

Calculate the division to find the batting average: \[\text{Batting Average} = \frac{8}{22} \approx 0.363636\]

Step 5 - Round to the Nearest Thousandth

Round the computed value to the nearest thousandth: \[0.363636 \approx 0.364\]

Key Concepts

Batting Average

A batting average is a way to measure a player's performance in hitting during games. It gives an idea of how often a player gets a hit. The formula for batting average is \(\text{Batting Average} = \frac{h}{a}\) where \(h\) is the number of hits and \(a\) is the number of at bats.
For example, let's say a player had 8 hits and went up to bat 22 times (at bats). We substitute these values into the formula to find the batting average:
\[\text{Batting Average} = \frac{8}{22} \]

Division

Division is a mathematical operation where you split a number into equal parts. In the context of our batting average calculation, we're dividing the number of hits by the number of at bats. Using our example, we divide 8 by 22:
\[\frac{8}{22} \]
When you divide 8 by 22, you end up with a decimal number. It's important to perform the division correctly to get an accurate batting average.

Rounding Numbers

After performing division, you might get a long decimal number. Rounding helps simplify this number while keeping it accurate to a certain degree. Rounding to the nearest thousandth means we keep three decimal places.
In our example, the result of the division was approximately \(0.363636\).
To round to the nearest thousandth, look at the fourth decimal place. If it's 5 or more, round up. If it's less than 5, round down. \(\text{So, 0.3636 rounds to 0.364}\).

Fractions in Algebra

Fractions are a way to represent parts of a whole. In algebra, they often appear in formulas like our batting average formula. The fraction \( \frac{8}{22} \) is an algebraic expression where 8 is the numerator (top part) and 22 is the denominator (bottom part).
Fractions can be simplified or divided to find their decimal form. This simplifies calculations and comparisons.
Always be attentive when dealing with fractions in mathematical expressions and ensure proper division and simplification.