Absolute Value Word Problems Worksheets - 15 Worksheets Library - Free Printable

Problem Analysis:

The task involves writing absolute value expressions for the differences in various tennis-related statistics. Absolute value is used to represent the magnitude of a difference without considering its direction (positive or negative). The general form of an absolute value expression for the difference between two values \( a \) and \( b \) is:

\[
|a - b|
\]

We will solve each problem step by step.

---

1. Serve Speed

- Teddy's serve speed: 100 miles per hour
- Mateo's serve speed: 120 miles per hour

The absolute value expression for the difference in their serve speeds is:

\[
|100 - 120| = | -20 | = 20
\]

Answer:
\[
\boxed{|100 - 120|}
\]

---

2. Return Accuracy

- Olivia's return accuracy: \( \frac{8}{10} \)
- Mia's return accuracy: \( \frac{12}{15} \)

First, simplify Mia's return accuracy:
\[
\frac{12}{15} = \frac{4}{5}
\]

Now, express both accuracies as decimals for easier comparison:
- Olivia: \( \frac{8}{10} = 0.8 \)
- Mia: \( \frac{4}{5} = 0.8 \)

The absolute value expression for the difference in their return accuracies is:

\[
|0.8 - 0.8| = |0| = 0
\]

Answer:
\[
\boxed{\left| \frac{8}{10} - \frac{12}{15} \right|}
\]

---

3. Double Faults

- Alex committed 6 double faults.
- Ben committed 8 double faults.

The absolute value expression for the difference in their double faults is:

\[
|6 - 8| = |-2| = 2
\]

Answer:
\[
\boxed{|6 - 8|}
\]

---

4. Points Won

- Henry won 18 points.
- Owen won 25 points.

The absolute value expression for the difference in points won is:

\[
|18 - 25| = |-7| = 7
\]

Answer:
\[
\boxed{|18 - 25|}
\]

---

5. Game Differential

- Harper won 2 games.
- Avery won 6 games.

The absolute value expression for the difference in game differentials is:

\[
|2 - 6| = |-4| = 4
\]

Answer:
\[
\boxed{|2 - 6|}
\]

---

6. Sets Won

- Emily won 3 sets.
- Ella won 5 sets.

The absolute value expression for the difference in sets won is:

\[
|3 - 5| = |-2| = 2
\]

Answer:
\[
\boxed{|3 - 5|}
\]

---

7. Ace Count

- Luca served 10 aces.
- Leo served 15 aces.

The absolute value expression for the difference in the number of aces is:

\[
|10 - 15| = |-5| = 5
\]

Answer:
\[
\boxed{|10 - 15|}
\]

---

8. Unforced Errors

- Wyatt made 20 unforced errors.
- Joe made 30 unforced errors.

The absolute value expression for the difference in unforced errors is:

\[
|20 - 30| = |-10| = 10
\]

Answer:
\[
\boxed{|20 - 30|}
\]

---

9. Break Points Saved

- Hans saved 4 out of 10 break points.
- Layla saved 8 out of 12 break points.

First, calculate the save percentages:
- Hans: \( \frac{4}{10} = 0.4 \)
- Layla: \( \frac{8}{12} = \frac{2}{3} \approx 0.6667 \)

The absolute value expression for the difference in break points saved is:

\[
|0.4 - 0.6667| = | -0.2667 | = 0.2667
\]

However, since the problem asks for the raw counts, we use:

\[
|4 - 8| = |-4| = 4
\]

Answer:
\[
\boxed{|4 - 8|}
\]

---

10. Match Duration

- Ivy played for 2 hours.
- Zoe played for 3 hours.

The absolute value expression for the difference in match durations is:

\[
|2 - 3| = |-1| = 1
\]

Answer:
\[
\boxed{|2 - 3|}
\]

---

Final Answers:

1. \(\boxed{|100 - 120|}\)
2. \(\boxed{\left| \frac{8}{10} - \frac{12}{15} \right|}\)
3. \(\boxed{|6 - 8|}\)
4. \(\boxed{|18 - 25|}\)
5. \(\boxed{|2 - 6|}\)
6. \(\boxed{|3 - 5|}\)
7. \(\boxed{|10 - 15|}\)
8. \(\boxed{|20 - 30|}\)
9. \(\boxed{|4 - 8|}\)
10. \(\boxed{|2 - 3|}\)

---

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \ |100 - 120| \\
2. & \ \left| \frac{8}{10} - \frac{12}{15} \right| \\
3. & \ |6 - 8| \\
4. & \ |18 - 25| \\
5. & \ |2 - 6| \\
6. & \ |3 - 5| \\
7. & \ |10 - 15| \\
8. & \ |20 - 30| \\
9. & \ |4 - 8| \\
10. & \ |2 - 3|
\end{aligned}
}
\]