Grade 7 Integers

Step 1: When adding integers with the same sign, add their absolute values.

Step 2: Keep the original sign in the answer.

Step 3: For \( 5 + 3 \): Both are positive. Add absolute values: \( |5| + |3| = 5 + 3 = 8 \). The sign is positive.
5 + 3 = 8

Step 4: For \( -5 + (-3) \): Both are negative. Add absolute values: \( |-5| + |-3| = 5 + 3 = 8 \). The sign is negative.
-5 + (-3) = -8

Answer: \( 5 + 3 = 8 \) and \( -5 + (-3) = -8 \).

Step 1: When adding integers with different signs, find the difference between their absolute values.

Step 2: The result takes the sign of the integer with the larger absolute value.

Step 3: For \( 7 + (-4) \): Absolute values are \( |7| = 7 \) and \( |-4| = 4 \). The difference is \( 7 - 4 = 3 \). The integer with the larger absolute value is 7 (which is positive).
7 + (-4) = 3

Step 4: For \( -6 + 9 \): Absolute values are \( |-6| = 6 \) and \( |9| = 9 \). The difference is \( 9 - 6 = 3 \). The integer with the larger absolute value is 9 (which is positive).
-6 + 9 = 3

Answer: \( 7 + (-4) = 3 \) and \( -6 + 9 = 3 \).

Step 1: Subtracting an integer is the same as adding its opposite.
The opposite of a positive number is negative (e.g., opposite of 3 is -3).
The opposite of a negative number is positive (e.g., opposite of -5 is 5).

Step 2: For \( 5 - 8 \): This is the same as \( 5 + (-8) \). Add integers with different signs (as in Example 2). Difference of absolute values: \( |8| - |5| = 3 \). Sign of the larger absolute value (8 is negative) is negative.
5 - 8 = 5 + (-8) = -3

Step 3: For \( 7 - (-3) \): This is the same as \( 7 + 3 \). Add integers with same signs (as in Example 1). Add absolute values: \( 7 + 3 = 10 \). Sign is positive.
7 - (-3) = 7 + 3 = 10

Step 4: For \( -2 - 4 \): This is the same as \( -2 + (-4) \). Add integers with same signs (as in Example 1). Add absolute values: \( |-2| + |-4| = 2 + 4 = 6 \). Sign is negative.
-2 - 4 = -2 + (-4) = -6

Answer: \( 5 - 8 = -3 \), \( 7 - (-3) = 10 \), and \( -2 - 4 = -6 \).

Step 1: When multiplying integers, multiply their absolute values.

Step 2: Determine the sign of the product based on the signs of the two integers:

• Positive $\times$ Positive = Positive
• Negative $\times$ Negative = Positive
• Positive $\times$ Negative = Negative
• Negative $\times$ Positive = Negative

(Same signs give a positive product; different signs give a negative product).

Step 3: For \( 4 \times 3 \): Absolute values are 4 and 3. Product is \( 4 \times 3 = 12 \). Signs are positive and positive.
4 \times 3 = 12 (Positive)

Step 4: For \( -4 \times 3 \): Absolute values are 4 and 3. Product is \( 4 \times 3 = 12 \). Signs are negative and positive.
-4 \times 3 = -12 (Negative)

Step 5: For \( 4 \times (-3) \): Absolute values are 4 and 3. Product is \( 4 \times 3 = 12 \). Signs are positive and negative.
4 \times (-3) = -12 (Negative)

Step 6: For \( -4 \times (-3) \): Absolute values are 4 and 3. Product is \( 4 \times 3 = 12 \). Signs are negative and negative.
-4 \times (-3) = 12 (Positive)

Answer: \( 4 \times 3 = 12 \), \( -4 \times 3 = -12 \), \( 4 \times (-3) = -12 \), \( -4 \times (-3) = 12 \).

Step 1: When dividing integers, divide their absolute values.

Step 2: Determine the sign of the quotient based on the signs of the two integers, using the same rules as multiplication:

• Positive $\div$ Positive = Positive
• Negative $\div$ Negative = Positive
• Positive $\div$ Negative = Negative
• Negative $\div$ Positive = Negative

(Same signs give a positive quotient; different signs give a negative quotient).

Step 3: For \( 12 \div 3 \): Absolute values are 12 and 3. Quotient is \( 12 \div 3 = 4 \). Signs are positive and positive.
12 \div 3 = 4 (Positive)

Step 4: For \( -12 \div 3 \): Absolute values are 12 and 3. Quotient is \( 12 \div 3 = 4 \). Signs are negative and positive.
-12 \div 3 = -4 (Negative)

Step 5: For \( 12 \div (-3) \): Absolute values are 12 and 3. Quotient is \( 12 \div 3 = 4 \). Signs are positive and negative.
12 \div (-3) = -4 (Negative)

Step 6: For \( -12 \div (-3) \): Absolute values are 12 and 3. Quotient is \( 12 \div 3 = 4 \). Signs are negative and negative.
-12 \div (-3) = 4 (Positive)

Answer: \( 12 \div 3 = 4 \), \( -12 \div 3 = -4 \), \( 12 \div (-3) = -4 \), \( -12 \div (-3) = 4 \).