To solve the problems involving absolute values, we need to follow these steps:
1.
Understand the Absolute Value: The absolute value of a number is its distance from zero on the number line, so it is always non-negative. For any number \( x \), \( |x| \) is:
- \( x \) if \( x \geq 0 \)
- \( -x \) if \( x < 0 \)
2.
Simplify Each Expression Step-by-Step:
- Calculate the absolute values first.
- Perform the arithmetic operations (addition, subtraction) as indicated.
Let's solve each problem:
---
Problem 1: \( |-7| + |-11| \)
1. Calculate the absolute values:
- \( |-7| = 7 \)
- \( |-11| = 11 \)
2. Add the results:
\[
7 + 11 = 18
\]
3. Choose the correct answer:
\[
\boxed{c}
\]
---
Problem 2: \( |-8| + |-14| - 9 \)
1. Calculate the absolute values:
- \( |-8| = 8 \)
- \( |-14| = 14 \)
2. Add the absolute values:
\[
8 + 14 = 22
\]
3. Subtract 9:
\[
22 - 9 = 13
\]
4. Choose the correct answer:
\[
\boxed{b}
\]
---
Problem 3: \( |31| - |-51| + 82 \)
1. Calculate the absolute values:
- \( |31| = 31 \)
- \( |-51| = 51 \)
2. Subtract the absolute values:
\[
31 - 51 = -20
\]
3. Add 82:
\[
-20 + 82 = 62
\]
4. Choose the correct answer:
\[
\boxed{d}
\]
---
Problem 4: \( 18 + |-21| - 49 \)
1. Calculate the absolute value:
- \( |-21| = 21 \)
2. Add 18 and 21:
\[
18 + 21 = 39
\]
3. Subtract 49:
\[
39 - 49 = -10
\]
4. Choose the correct answer:
\[
\boxed{a}
\]
---
Problem 5: \( |34| + |15| - 21 \)
1. Calculate the absolute values:
- \( |34| = 34 \)
- \( |15| = 15 \)
2. Add the absolute values:
\[
34 + 15 = 49
\]
3. Subtract 21:
\[
49 - 21 = 28
\]
4. Choose the correct answer:
\[
\boxed{d}
\]
---
Problem 6: \( |24| - |-91| + 52 \)
1. Calculate the absolute values:
- \( |24| = 24 \)
- \( |-91| = 91 \)
2. Subtract the absolute values:
\[
24 - 91 = -67
\]
3. Add 52:
\[
-67 + 52 = -15
\]
4. Choose the correct answer:
\[
\boxed{a}
\]
---
Final Answers:
\[
\boxed{c, b, d, a, d, a}
\]
Parent Tip: Review the logic above to help your child master the concept of absolute value worksheet 7th grade.
