Integers Study Guide Name:________________________
Date:____________
Class:________ Integers
The set of whole numbers and their opposites.
…,●-3, -2, -1, 0, 1, 2, 3, ...
Absolute Value
The distance a number is from zero on the number line.
Absolute
● value is always positive
Represent
● absolute value => |3|
Two numbers
● with the same absolute value are opposites. Ex: 5 & -5, |5|=5, |-5|=5
Find each absolute value
1.
2.
| − 16| =
3.
|45| =
| − 14| = 4.
| − 179| =
ddition Rules:
If the numbers have
● the same sign: Add the absolute values and keep the same sign.
If the numbers have
● different signs: Subtract the absolute values and keep the sign of the number with the
bigger absolute value.
expression
Example: Add: ­9 + 13
Same sign? Subtract the absolute values.
Choose the sign.
No
13 ­ 9 = 4 |13| > |­9| , so answer is positive. Example: Add: ­7 + ­4
Same sign? Add the absolute values.
Choose the sign.
negative Same Sign? (yes/no)
Yes
7 + 4 = 11 Both numbers are negative, so the answer is Add or Subtract Absolute values
Sum
no
16 - 9 = 7
-7
− 23 + (− 14)
45 + (− 63)
− 179 + (− 86)
− 35 + 35
67 + 109
− 16 + 9
Integers Study Guide Name:________________________
Date:____________
Class:________ Essential Question: How do you know if the sum of a positive plus a negative will be positive? an addition problem. (Add
● the opposite)
●
Example: Subtract: ­9 ­ 13
Rewrite as addition, (add ­13).
Same sign? Add the absolute values.
Choose the sign.
­9 + (­13) Yes
9 + 13 = 22 Same sign, so keep that sign. Example: Subtract: ­7 ­ (­4) Rewrite as addition, (add 4)
Same sign? Subtract the absolute values.
Choose the sign.
Same Sign?
Add or Subtract Absolute
values
­7 + 4
No
7 ­ 4 = 3 |­7| > |4|, so the answer is negative. Sum
− 16 + (− 9)
Yes
16 + 9 = 25
-25
− 23 − (− 14)
45 − (− 63)
− 179 − (− 86)
− 35 − 35
67 − 109
− 16 − 9
Essential Question: Will a negative minus a negative always be negative? Explain. Integers Study Guide Name:________________________
Date:____________
Class:________ ●
●
●
Example: Divide: ­39 ÷ 13
Divide absolute values
.
Same sign? Different signs, so the quotient is negative.
Example: Multiply: ­7 ∙ (­4) Multiply absolute values.
Same sign? Same sign, so the product is positive.
39 ÷ 13 = 3 No
­39 ÷ 13 = ­3 7 ∙ 4 = 28
Yes
­7 ∙ (­4) = 28 duct or Quotient
(16)( 9) = 144
No
-144
(− 28) ÷ (− 14)
4(− 6)
− 145 ÷ 9
(− 15)(− 15)
324
−18
− 16 • 9
Essential Question: How can you tell if a product of five integers will be positive or negative?
If the black chip represents positive one and the white chip represents negative one, what addition problem is modeled on the board? What is the value of the chips on the board? If the black chip represents positive one and the white chip represents negative one, what addition problem is modeled on the board below? What is the value of the chips on the board? Integers Study Guide Name:________________________
Date:____________
Class:________ ​6 + (­4) = 2 6 + (­10) = ­4 If the black chip represents positive one and the white chip represents negative one, what subtraction problem is modeled on the board below? What is the value of the chips on the board? ­7 ­ (­3) = ­4 Write an addition expression to model the Panthers drive against the Patriots. What was the net result of the yards gained or lost on the drive? What was their average yardage gained or lost per play? ●
Lost 4 yds ●
Gained 23 yards ●
Gained 6 yard
­4+23+6+(­10)+18+11+(­10)+(­12)+5 ●
Lost 10 yards
27 total yards ●
Gained 18 yards
27 ÷ 9 = 3 yards gained per play ●
Gained 11 yards ●
Lost of 10 yards ●
Lost 12 yards ●
Gained 5 yards
The morning temperature was 61oF. The high temperature for the day was 83oF. Write a subtraction expression using integers to model the change in temperature. What was the change in temperature for the day? 83 ­ 61 = 22 degrees Teddy posted a picture of the Grand Canyon on his social media account. He gained 20 new followers a day for the next 3 days. Write an expression using integers to model this situation. How many new followers did Teddy gain? 20 ∙ 3 = 60 new followers Integers Study Guide Name:________________________
Date:____________
Class:________ Miesha started a new workout plan. She lost 4 lbs per month. Write and expression to determine how long it took her to lose 16 lbs. How long did it take? ­16 ÷ ­4 = 4 weeks