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Adding Positive and Negative Integers. WARM-UP. Order from least to greatest 7, -3, 0, -1, 3. 2) Insert. a) -15 -16 b) 1 2. 3) Find the sum: 748 + 93 =. Review. A variable is a letter that stands for a number.
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AddingPositiveand Negative Integers Confidential
WARM-UP • Order from least to greatest 7, -3, 0, -1, 3 2) Insert a) -15 -16 b) 1 2 3) Find the sum: 748 + 93 = Confidential
Review A variable is a letter that stands for a number We use variables when we don’t know the number A variable can be any letter Confidential
Review We can also write VARIABLE EXPRESSIONS such as s + 9 8 n 16 x h A VARIABLE EXPRESSION contains a variable and an operation such as addition, subtraction, multiplication, division. Confidential
Word phrases can be translated into VARIABLE EXPRESSIONS Word Phrase Variable Expression 2 more than n 2 + n k times 8 k x 8 Confidential
Absolute Value The absolute value of a number is its distance from zero on the number line The absolute value of 4 is written as 4 The absolute value is always positive! Confidential
Opposites Confidential
When we add an integer and its opposite, the sum is zero EXAMPLES: (-5) + 5 = 0 98 + (-98) = 0 Opposites are also called ADDITIVE INVERSES. Confidential
Today we are going to learn how to add integers. We will explore 3 different METHODS METHOD 1 - ZERO PAIRS + + - - - + - The red chips are NEGATIVE. The grey chips are POSITIVE Confidential
Zero Pair - + + = 0 1 red chip 1 grey chip We call 1 red chip and 1 grey chip a ZERO PAIR Confidential
Lets take an Example If we want to add 3 + 2 + + + We begin with 3 grey chips + + And we add 2 more grey chips 3 + 2 = 5 FOR A TOTAL OF 5 GREY CHIPS Confidential
If we want to add -2 + (-4) Remember red chips are negative We begin with 2 red chips - - And we add 4 more red chips - - - - -2 + (-4) = -6 FOR A TOTAL OF 6 RED CHIPS. Do you have any questions so far???? Confidential
Adding integers with different signs BUT if we want to add integers with different signs, we must use ZERO PAIRS - + These 2 chips form a ZERO PAIR. These 2 chips equal zero. Confidential
Lets see with an Example Let's add (-5) + 3 - - - We begin with 5 red chips - - And we add 3 grey chips + + + Confidential
Adding (-5) + 3 - - We begin with 5 red chips - - - And we add 3 grey chips + + + We circle the Zero Pairs and remove them! (Remember a ZERO PAIR equals zero.) Confidential
Result We begin with 5 red chips - - And we add 3 grey chips We are now left with 2 red chips OR -2 Therefore, (-5) + 3 = -2 Confidential
You try a few. Use your red and black pens to make your chips. (-3) + 1 = 4 + (-5) = Confidential
10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 METHOD 2 - Number Line We can use a number line to find the sum of 2 integers. WE ALWAYS START AT ZERO! Confidential
10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Lets add 3 + 4 by number line 2. 1. 1. Start at zero and move to the right (in a positive direction) 3 spaces. 2. Next, move further to the right 4 spaces. 3 + 4 = 7 3. Your answer is 7. Confidential
10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Now, let's add (-2) + (-8) 1. Start at zero and move to the left (in a negative direction) 2 spaces. 2. Next, move further to the left 8 spaces. 3. Your answer is -10. (-2) + (-8) = -10 Confidential
10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Let's see what happens when we add a positive AND a negative number. (-6) + 8 = • Start at zero and move to the left (in a negative direction) • 6 spaces. 2. Next, move to the RIGHT 8 spaces. 3. Your answer is 2. as (-6) + 8 = 2 DO YOU HAVE ANY QUESTIONS?? Confidential
10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 You try a couple..... Start at zero and draw your arrows! 4 + (-7) = (-2) + (-5) = Confidential
Method 3 - Rules for adding integers Adding the The sum of 2 positive numbers is POSITIVE. Same sign The sum of 2 negative numbers is NEGATIVE. Example: 4 + 7 = 11 (-3) + (-6) = (-9) 11 + 8 = (-9) + (-1) = Confidential
Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Example: (-2) + 9 = Absolute Values Step 1.) 2 9 Step Subtract 2.) 9 - 2 Sign of the larger number Step 3.) +7 Confidential
Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Try (-11) + 5 = Step 1.) Absolute Values 11 , 5 Subtract Step 2.) 11 – 5 = 6 Sign of the larger number - 6 Step 3.) Confidential
1.) The temperature in Minneapolis was 7 degrees F at noon. By 8 pm, the temperature had dropped 15 degrees F. What was the temperature at 8 pm? Confidential
2.) You have $60 in your bank account. You withdraw (or take out) $45 to buy new tires for your bike. You then deposit (or add in) your babysitting money of $18.What is the new balance in your bank account? Confidential
10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 10 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 Let's see how well we understood the lesson today. Use a number line to find each sum. 1.) (-7) + 12 = 2.) 4 + (-10) = Confidential
Find each sum. Remember your Addition Rules! 3.) (-7) + (-11) = 4.) 12 + (-5) = 5.) 22 + 7 = 6.) (-9) + 5 = 7.) 3 + (-10) = 8.) (-8) + 20 = 9.) 1 + (-30) = 10.) (-15) + (-5) = 11.) Opposites are also called A_________ I__________. Confidential
Let's Review... There are 3 METHODS we can use to Add Integers. METHOD 1 We can add integers using ZERO PAIRS. Confidential
To add (-5) + 3 = Then we are left with 2 red chips. Therefore, (-5) + 3 = -2 Confidential
METHOD 2 We can also use a number line to find the sum of 2 integers. . Confidential
METHOD 3 Rules Adding the Same Sign – The sum of 2 positive numbers is POSITIVE. The sum of 2 negative numbers is NEGATIVE. Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Confidential
You had a great lesson today! Be sure to practice what you learned! Confidential