Question

-76 + 46
5 + (-57)
-5 - (-102)
18 - (-8)
12 - 120
-5 - (12)
-5 + (-2)
18 - (-7)
10 - 120
-4 - (10)
-6 + (-4)

Explanation:

To solve these arithmetic problems, we'll use the rules of adding and subtracting integers. Remember that subtracting a negative number is the same as adding its positive counterpart, and adding a negative number is the same as subtracting its positive counterpart. Let's solve each problem one by one:

First Row:

1. \( -76 + 46 \)

• Explanation: Add the two numbers. Since the signs are different, subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.
• Calculation: \( |-76| = 76 \), \( |46| = 46 \), \( 76 - 46 = 30 \). The sign is negative because \( -76 \) has a larger absolute value. So, \( -76 + 46 = -30 \).

1. \( 5 + (-57) \)

• Explanation: Adding a negative number is like subtracting the positive.
• Calculation: \( 5 - 57 = -52 \).

1. \( -5 - (-102) \)

• Explanation: Subtracting a negative is like adding the positive.
• Calculation: \( -5 + 102 = 97 \).

Second Row:

1. \( 18 - (-8) \)

• Explanation: Subtracting a negative is like adding the positive.
• Calculation: \( 18 + 8 = 26 \).

1. \( 12 - 120 \)

• Explanation: Subtract the two numbers. Since \( 120 > 12 \), the result will be negative.
• Calculation: \( 12 - 120 = -108 \).

1. \( -5 - (12) \)

• Explanation: Subtracting a positive is just subtracting.
• Calculation: \( -5 - 12 = -17 \).

1. \( -5 + (-2) \)

• Explanation: Adding two negative numbers, add their absolute values and keep the negative sign.
• Calculation: \( |-5| + |-2| = 5 + 2 = 7 \), so \( -5 + (-2) = -7 \).

Third Row:

1. \( 18 - (-7) \)

• Explanation: Subtracting a negative is like adding the positive.
• Calculation: \( 18 + 7 = 25 \).

1. \( 10 - 120 \)

• Explanation: Subtract the two numbers. Since \( 120 > 10 \), the result will be negative.
• Calculation: \( 10 - 120 = -110 \).

1. \( -4 - (10) \)

• Explanation: Subtracting a positive is just subtracting.
• Calculation: \( -4 - 10 = -14 \).

1. \( -6 + (-4) \)

• Explanation: Adding two negative numbers, add their absolute values and keep the negative sign.
• Calculation: \( |-6| + |-4| = 6 + 4 = 10 \), so \( -6 + (-4) = -10 \).

Final Answers:

• First Row: \( -30 \), \( -52 \), \( 97 \)
• Second Row: \( 26 \), \( -108 \), \( -17 \), \( -7 \)
• Third Row: \( 25 \), \( -110 \), \( -14 \), \( -10 \)

If you need any specific problem re - checked or have more questions, feel free to ask!

Answer:

To solve these arithmetic problems, we'll use the rules of adding and subtracting integers. Remember that subtracting a negative number is the same as adding its positive counterpart, and adding a negative number is the same as subtracting its positive counterpart. Let's solve each problem one by one:

First Row:

1. \( -76 + 46 \)

• Explanation: Add the two numbers. Since the signs are different, subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.
• Calculation: \( |-76| = 76 \), \( |46| = 46 \), \( 76 - 46 = 30 \). The sign is negative because \( -76 \) has a larger absolute value. So, \( -76 + 46 = -30 \).

1. \( 5 + (-57) \)

• Explanation: Adding a negative number is like subtracting the positive.
• Calculation: \( 5 - 57 = -52 \).

1. \( -5 - (-102) \)

• Explanation: Subtracting a negative is like adding the positive.
• Calculation: \( -5 + 102 = 97 \).

Second Row:

1. \( 18 - (-8) \)

• Explanation: Subtracting a negative is like adding the positive.
• Calculation: \( 18 + 8 = 26 \).

1. \( 12 - 120 \)

• Explanation: Subtract the two numbers. Since \( 120 > 12 \), the result will be negative.
• Calculation: \( 12 - 120 = -108 \).

1. \( -5 - (12) \)

• Explanation: Subtracting a positive is just subtracting.
• Calculation: \( -5 - 12 = -17 \).

1. \( -5 + (-2) \)

• Explanation: Adding two negative numbers, add their absolute values and keep the negative sign.
• Calculation: \( |-5| + |-2| = 5 + 2 = 7 \), so \( -5 + (-2) = -7 \).

Third Row:

1. \( 18 - (-7) \)

• Explanation: Subtracting a negative is like adding the positive.
• Calculation: \( 18 + 7 = 25 \).

1. \( 10 - 120 \)

• Explanation: Subtract the two numbers. Since \( 120 > 10 \), the result will be negative.
• Calculation: \( 10 - 120 = -110 \).

1. \( -4 - (10) \)

• Explanation: Subtracting a positive is just subtracting.
• Calculation: \( -4 - 10 = -14 \).

1. \( -6 + (-4) \)

• Explanation: Adding two negative numbers, add their absolute values and keep the negative sign.
• Calculation: \( |-6| + |-4| = 6 + 4 = 10 \), so \( -6 + (-4) = -10 \).

Final Answers:

• First Row: \( -30 \), \( -52 \), \( 97 \)
• Second Row: \( 26 \), \( -108 \), \( -17 \), \( -7 \)
• Third Row: \( 25 \), \( -110 \), \( -14 \), \( -10 \)

If you need any specific problem re - checked or have more questions, feel free to ask!