Rational Numbers
Solve:
1/2 - 4/5
ANSWER: -3/10
David started at Point A. He walked 100 ft East and stopped for a second. He then walked 100 ft West. How far away is he from point A now?
ANSWER: 0 ft from Point A.
100 ft East = +100
100 ft West = -100
ANSWER: 100 + -100 = 0
Solve: 50 + (-4) - 20
ANSWER: 26
Step 1 (KSF): 50 + (-4) + (-20)
Step 2: 46 + (-20)
Step 3: 26
F and G are on opposite sides of the number line and have the same absolute value. What is the sum of F + G?
ex. F = -6 and G = 6
F + G
-6 + 6 = 0
Rewrite the following expression as addition:
15 - 31 - (14 + 0.8)
15 - 31 - (14 + 0.8)
ANSWER: 15 + (-31) + -(14 + 0.8)
ANSWER: 15 + (-31) + (-14) + (-0.8)
Which of the following are equivalent to -4/9? Chose ALL that apply.
a) 4/-9
b) -4/-9
c) -(4/9)
d) - 4/9
e) 4/9
ANSWER: A, C, D
A diver dropped down -2.4 meters per minute over 10 minutes. What was the diver's total change in elevation?
ANSWER: -24 meters
Step 1: -2.4 x 10
Solve: -20 ÷ 4 * -5
ANSWER: 25
-20 ÷ 4 * -5
Step 1: -5 * -5
Step 2: 25
The temperature in Alaska decreased by 84 degrees over 7 months. What was the change in temperature per month.
ANSWER: -12 degrees per month
-84 ÷ 7 = -12
M is positive. N is on the opposite side of the number line and has a larger absolute value than M. What do you know about the sum of M+N?
a) It's positive
b) It's negative
c) It's zero
ANSWER: b) It's negative
ex.
M = +5 N = -8
M + N =
5 + -8 =
-3
Plot -1.6 (-1 3/5 or -8/5) on a number line
ANSWER: On board
The temperature in New Jersey decreased by 1.5 degrees each hour over 5 hours. What was the total change?
ANSWER: -7.5 degrees
-1.5 x 5 = -7.5
Simplify:
-4/5 + 2/5 ÷ -3/4
ANSWER: -20/15 = -4/3 = -1 1/3
-4/5 + 2/5 ÷ -3/4
DIVISION
-4/5 + 2/5 x -4/3
-4/5 + -8/15
ADDITION
-12/15 + -8/15 = -20/15
What is 55 more than -9?
ANSWER: 46
-9 + 55 = 46
Solve: 1/3(4/5 - 3/4)
ANSWER: 1/60
1/3(4/5 + -3/4)
1/3(16/20 + -15/20)
1/3(1/20)
1/60
Simplify:
-1/2 + 4/5 - 3/4
ANSWER: -9/20
KSF:
-1/2 + 4/5 + (-3/4)
COMMON DENOMINATOR:
-10/20 + 16/20 + (-15/20)
ADD:
6/20 + (-15/20) = -9/20
John had a bank account balance of $-32 on Friday. On Sunday, his balance was $20. Which statement is true about his balance?
a) It decreased by $12
b) It increased by $12
c) It decreased by $52
d) It increased by $52
ANSWER: d) It increased by $52
Start = -32 End = 20
Change = End - Start
Change = 20 - (-32)
Change = 20 + 32 = 52
Use a number line to solve:
1.5 + -3.2
How can we always use a number line to find a sum? Label start, change, and end.
ANSWER: -1.7
We can start at 1.5 and move to the left by 3.2 units since our change is negative 3.2. When we move 3.2 units to the left on our number line from 1.5, we end up at -1.7 which is our final answer.
ANSWER: $42.97
31.55 + 11.42 = 42.97
Find the area of a rectangle with dimensions of a length of 12 ft and a width of 8 ft.
Find the area of a different rectangle that has an area that is 1/4 as big.
ANSWER: 96 ft squared and 24 ft squared
RECTANGLE 1: A = L x W = 12 x 8 = 96
RECTANGLE 2: 1/4 x 96 = 24
Write 2 fractions that are equivalent to -30/7
ANSWER:
-(30/7)
30/-7
Sanai descends 2.7 feet every minute while scuba diving. After how many minutes is she 16.2 ft below sea level?
ANSWER: 6 minutes
-2.7 x 1 = -2.7
-2.7 x 2 = -5.4
-2.7 x 3 = -8.1
-2.7 x 4 = -10.8
-2.7 x 5 = -13.5
-2.7 x 6 = -16.2
What is the sum of -1.8 + 1.8? EXPLAIN how you know using the terms absolute value and additive inverse in your explanation.
-1.8 + 1.8 = 0
I know this because they are additive inverses. This means they have opposite signs (1 positive, 1 negative) and the same absolute value (1.8). When added together, additive inverses always sum to 0.
Solve:
1/2(3/4 - 2/5) + 1/5 ÷ 2/3
ANSWER: 19/40
1: PARENTHESES
1/2(15/20 - 8/20) + 1/5 ÷ 2/3
1/2(7/20) + 1/5 ÷ 2/3
2: MULTIPLY
7/40 + 1/5 ÷ 2/3
3: DIVIDE
7/40 + 1/5 x 3/2
7/40 + 3/10
4: ADD
7/40 + 12/40 = 19/40