Adding and Subtracting Integers
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- Integers other than zero are either negative or positive.
Identifying the Integers
When working with numbers, it is helpful to remember that the “+” or “-“ directly in front of a number is attached to the number and acts as its sign. Mathematical expressions are combinations of positive and/or negative terms.
- What are the two integers being combined in the expression -10 + 8? ______.
Sometimes expressions will begin with numbers that have no sign in front of it, such as the “3” in the expression 3 – 5. When there is no sign, the number is automatically a ______.
Other expressions may contain a double sign, such as “(-7)” in the expression -12 – (-7) or “+21” in the expression 6 + (-21). When there is a double sign, use the rules of multiplying positives (+) and negatives (-) to decide which sign to use. In the expression -12 – (-7), the integers being combined are really -12 and 7.
- Attaching a single sign to each number, what integers are combined in the expression 20 – (-11)?
______
- Attaching a single sign to each number, what integers are combined in the expression -7 +(-5)?
When an expression involves subtraction, think of subtraction as “adding the opposite.” In the expression
-14 – (-3), subtracting -3 is the same as adding 3. The expression can be rewritten as -14 + 3.
- Rewrite the expression 9 – 6 as addition and identify the integers being combined. ______
- Rewrite the expression -13 – (-4) as additional and identify the integers being combined. ______
Adding and Subtracting Integers
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Combining Integers with the Same Sign
When you combine two numbers with the same sign, you get more of the type, positive or negative, you have. Just as mixing apples with apples makes more apples, combining positives with positives makes more positives, and combining negatives with negatives makes more negatives.
- What operation is suggested when you see the word “combining”? ______
- What would be the result of combining 3 apples and 4 apples? ______
- What would be the result of combining 5 cups of sugar and 13 cups of sugar? ______
- What would be the result of combining 8 and 3? ______
- What would be the result of combining -14 and -11? ______
Mathematicians use the word simplify to indicate combining terms.
- Simplify the expression 20 + 11. ______
- Simplify the expression -14 – 21. ______
- Simplify the expression -10 – 19. ______
- Simplify the expression -30 + (-12).______
- Simplify the expression 3 + 21.__- ______
Combining Integers with Different Signs
With integers, having more positive numbers than negative numbers will yield a positive answer; having more negative numbers than positive numbers will result in a negative answer.
To combine numbers with different signs, follow the two steps below:
Step 1: Determine the sign of your final answer by identifying the sign of the larger number.
Step 2: Subtract the smaller number from the larger number, and apply the sign you found in Step 1.
Follow these steps to simplify the expression 2 – 13.
- Which number is larger: 2 or 13? ______
- What is the sign of the larger number? ______
- Subtract the smaller number from the larger number. ______
- Write the simplified expression, applying the sign you found above. ______
Adding and Subtracting Integers
Name: Date:Class:
Answer the following questions, using your knowledge about adding and subtracting integers. Be sure to show your work.
- What is the simplified value of negative 12 combined with negative 20?
- What is the simplified value of positive 30 combined with negative 50?
- Simplify:
- -31 + (-2)
- -20 + 25
- 22 – (-33)
- Liv is hanging a picture on the wall. She started by hanging it 71 inches above the ground, but then decided it was too low, so she raised it 6 more inches. How high is the picture now?
- In chemistry class you run an experiment when you combine chemicals that have opposite effects. Each drop of acid solution will subtract 1 from the pH value, which each drop of base solution will add 1 to the pH value. What will the overall effect on the pH be if you combine 3 drops of acid solution and 5 drops of base solution?
- If each lemon is positive and each cup of sugar is negative, what amount of lemons or sugar alone would produce the same taste as combining 7 lemons and 5 cups of sugar?