1. Do now w/b
Can you solve this riddle? There are no passengers on the bus at the beginning of its journey. Three people get on. Then two more people get on with one getting off. Four more people get on with two getting off. Five more get on with no one getting off at that stop. Six people get on with nine getting off. How many people were on the bus after the nine people got off? Answer: There were nine people, not eight, because the bus driver was still on the bus.

2. 1.6 Addition and subtraction of Real Numbers
By: Renee Cowger

3. Add real numbers using a number line
Remember the flipped number line? You can use it to evaluate 3+(-4) When you have a positive and a Negative sign together, negative always wins-so you can remove the double sign Start at 3 and go DOWN 4 You are now at -1 2 1 4 3 -5 5 -4 -2 -3 -1

4. Some examples
– 4 + 2
Think ~ you are four ft. under water, and you are going up 2 ft. You can also think ~ if you have 2 different signs, subtract the smaller absolute value from the larger.
Where are you?
You are still 2 ft. under water, or at -2
(-2)
Get rid of the double sign (negative always wins)
-3 – 2
You are 3 ft. under water and going DOWN 2 more
You are -5 ft. under water

5. You try it w/b
-7 + 3
-2 + (-5)
10 + (-10)
Answers -4 -7

6. Below zero temperatures
Below zero temperatures are expressed as negative numbers. If it were 3 degrees below zero, it would be expressed as -3, then if the temperature dropped 4 more degrees, it could be expressed as (- 4) What is the temperature? -7 degrees brrrr!

7. The same concept can be applied to fractions and decimals
Examples
2. 𝟕 𝟏𝟔 + −𝟐 𝟑
A common denominator will have to be found which would be… 48
𝟐𝟏 𝟒𝟖 + −𝟑𝟐 𝟒𝟖 = −𝟏𝟏 𝟒𝟖 remember-negative always wins

8. You try it w/b −𝟑 𝟒 + 𝟐 𝟗 −𝟑 𝟓 + 𝟒 𝟕 -17.56 + (-19.23) Answers −𝟏𝟗 𝟑𝟔
−𝟑 𝟓 + 𝟒 𝟕
(-19.23)
Answers
−𝟏𝟗 𝟑𝟔
−𝟏 𝟑𝟓
-36.79

9. Profit or loss?
A scrapbook company had a loss of $3000 for the first 4 months of the year and a profit of $37,400 for the last 8 months of the year-find the net profit or loss Think ~ they make a profit of $37,440, but they had to make up for the $3000 loss so… $37,400-$3000= $34,400

10. Formative assessment (on small paper)
If we add a positive number and a negative number, will the answer be positive, negative, or can it be either?
If we add two negative numbers, will the sum be a positive number or a negative number?
Explain how to add two numbers with like signs.
Explain how to add two numbers with unlike signs.

11. End 1.6

12. 1.7 subtraction of Real Numbers

13. Subtract numbers
Remember in a problems like 9 – (+4) ~ negative always wins so Re-write as 9 – 4 = 5 What is the answer? 8 – (+3) = 5

14. Other examples
Evaluate 1. 5 – 3 = – 9 = = -2 Not too hard right?

15. Here’s where things get squirrely
4 – (-2) = huh? Any ideas?-never fear! Super squirrel says, “When you have two negatives…” Your right! Change them to positives So = 6 Ever wondered WHY? What a problem like that is really saying is hey IF I did 4 + (-2) I would get 2 right? So they are saying UNDO this action it 4 – (-2). We’re saying go the other (opposite) direction on the number line.

16. More squirrely examples
15 + (-4) 11
– 3
-19
3. -9 – (-3) -6

17. This applies to fractions too
𝟑 𝟓 − 𝟕 𝟖 =
- 𝟐𝟒 𝟒𝟎 − 𝟑𝟓 𝟒𝟎 =
−𝟐𝟒−𝟑𝟓 𝟒𝟎 = −𝟓𝟗 𝟒𝟎

18. Had enough?
007 squirrel says-you ain’t seen nothin yet! Here is where algebra is going with this. You will see problems like: -5 – (-9) + (-12) + (-3) = What you can do is get rid of all Double signs first-remember either Negative always wins, or two negatives make a positive so = now just follow PEMDAS left to right 4 – 12 – 3 -8 – 3 -11

19. Formative assessment w/b
9 –
-7 – 15 – 6
– 8
-7 – (-3) + (-13) + (-2)
Answers
-28
-12
-19

20. End 1.7