Problem: Solve the division problems involving integers.
The worksheet asks us to find the quotients for the following integer divisions:
1. \( 20 \div (-5) \)
2. \( -15 \div (-3) \)
3. \( -42 \div (-7) \)
4. \( 52 \div (-2) \)
5. \( -81 \div (-9) \)
6. \( 12 \div (-6) \)
Solution:
#### Rule for Dividing Integers:
- When dividing two integers with the
same sign (both positive or both negative), the result is
positive.
- When dividing two integers with
different signs (one positive and one negative), the result is
negative.
Let's solve each problem step by step:
---
1. \( 20 \div (-5) \)
- Here, we are dividing a positive integer by a negative integer.
- According to the rule, the result will be
negative.
- Perform the division: \( 20 \div 5 = 4 \).
- Since the signs are different, the result is \( -4 \).
Answer: \( -4 \)
---
2. \( -15 \div (-3) \)
- Here, we are dividing a negative integer by another negative integer.
- According to the rule, the result will be
positive.
- Perform the division: \( 15 \div 3 = 5 \).
- Since the signs are the same, the result is \( 5 \).
Answer: \( 5 \)
---
3. \( -42 \div (-7) \)
- Here, we are dividing a negative integer by another negative integer.
- According to the rule, the result will be
positive.
- Perform the division: \( 42 \div 7 = 6 \).
- Since the signs are the same, the result is \( 6 \).
Answer: \( 6 \)
---
4. \( 52 \div (-2) \)
- Here, we are dividing a positive integer by a negative integer.
- According to the rule, the result will be
negative.
- Perform the division: \( 52 \div 2 = 26 \).
- Since the signs are different, the result is \( -26 \).
Answer: \( -26 \)
---
5. \( -81 \div (-9) \)
- Here, we are dividing a negative integer by another negative integer.
- According to the rule, the result will be
positive.
- Perform the division: \( 81 \div 9 = 9 \).
- Since the signs are the same, the result is \( 9 \).
Answer: \( 9 \)
---
6. \( 12 \div (-6) \)
- Here, we are dividing a positive integer by a negative integer.
- According to the rule, the result will be
negative.
- Perform the division: \( 12 \div 6 = 2 \).
- Since the signs are different, the result is \( -2 \).
Answer: \( -2 \)
---
Final Answers:
1. \( 20 \div (-5) = \boxed{-4} \)
2. \( -15 \div (-3) = \boxed{5} \)
3. \( -42 \div (-7) = \boxed{6} \)
4. \( 52 \div (-2) = \boxed{-26} \)
5. \( -81 \div (-9) = \boxed{9} \)
6. \( 12 \div (-6) = \boxed{-2} \)
Boxed Final Answer:
\[
\boxed{-4, 5, 6, -26, 9, -2}
\]
Parent Tip: Review the logic above to help your child master the concept of free pre algebra worksheet with answer key.
