Addition
Subtraction
Multiplication
Division
So Random
100
When will the sum of a positive integer and a negative integer be positive?
When the absolute value of the positive integer is greater than the absolute value of the negative integer.
100
What is the algorithm to find out distance or change between two rational numbers a and b?
|a - b|
100
What is the relationship between multiplication and division?
They are inverse operations!
100
What do "P" and "Q" represent in a division problem?
P = dividend
Q = divisor
100
What are our two main rules for adding and subtracting negatives?
add negative = subtract positive
subtract negative = add positive
200
On the number line a and b are the same distance from 0. What will their sum be? Why?
If they are the same distance from 0 then they have the same absolute value but a is negative and b is positive so they are opposites. The sum of additive inverses is 0.
200
Assume x > 0 and y < 0. For each statement, determine whether it is sometimes, never, or always true.
y - x < 0
Always true. Y is negative and x is positive so a negative - positive is the same as the sum of two negatives so the answer is always negative.
200
When will the product of some factors be negative?
When multiplying an odd number of negatives
200
How do we convert fractions to decimals and when will the decimal repeat or terminate?
We convert fractions to decimals by dividing the numerator by the denominator. The decimal will repeat when we have a prime number as the denominator and it will terminate otherwise.
200
What is a strategy that we can use when solving multiple choice questions with expressions as options?
Solve each individual expression and then see which one matches the problem.
300
John had to solve the equation
5 2/5 + 7 - 0.25 +12 - 19.7
as
7 + 12 + (- 0.25 ) + (- 19.7) + 5 2/5
What properties and rules allowed him to do that?
The cummutative property of addition
The addition rule that says when adding negatives we are subtracting positive
300
Joan lives 5 miles east of the school, Jessica lives 7 miles to the west of the school. Joan leaves her house to go to Jessica's house, how many miles did she walk?
Include the algorithm.
12 miles
|5 - (-7)| = |12| = 12
300
How do we represent multiplication of a positive and negative number on a number line?
When multiplying a positive and a negative on a number line on a number line, the positive number represents the amount of vectors we have and then negative number represents the magnitude and direction of the vectors.
300
3. Determine whether each fraction below is equivalent to a terminating decimal or a repeating decimal. Then, convert each to a decimal.
a.
−12/9
b.
4 8/32
A is repeating since in it's simplest form it is
-4/3
and the denominator is a prime number so the decimal repeats.
B is terminating since in it's simplest form it is
4 1/4
and the denominator is not a prime number so decimal terminates.
300
What are rules for going left on a number line?
1. Adding negative
2. subtracting positive
3. multiplying an odd number of negatives
4. dividing an odd number of negatives
400
Iris starts her hike at
21/7
feet below sea level. She ascends
17/6
feet from her starting point. What is her current elevation?
-21/7 + 17/6 = -1/6
She is currently 1/6 feet below sea level.
400
At midnight the temperature was 12 degrees, by 6:00 AM the temperature decreased to -5 degrees. Write an expression that shows the temperature change.
| 12 - (-5)|
or
|-5 - 12|
400
Tamika is rock climbing. Each minute, she travels 2 feet in a downwards direction. If she starts at an elevation of 312 feet and continues her downward climb for 16 minutes, what rational number represents her elevation at the end of her climb? Write an expression that represents this problem.
312 + (-16 * 2)
Her elevation at the end of the climb is 280 ft.
400
Three brothers each have their own savings. They borrow $72 from their parents for concert tickets. Each brother must pay back an equal part of this loan. What rational number represents each brother’s individual debt?
-72/3 = -24
400
How can we solve multistep problems?
We can group all the negatives together and all the positives together and then solve to find our final answer.
500
Jose is competing in a wrestling match. He currently weighs 212 lbs and he needs to lose exactly 12 pounds this week in order to compete on Friday night. The table below shows how his weight changed each morning.
Monday = +7
Tuesday = -18
Wednesday = -3
Thursday = -4
Friday = +11
What was his overall weight change? Can he compete Friday night?
His overall weight change was -7 lbs so now he weights 205 lbs and he cannot compete on Friday.
500
Sally was told to practice playing violin for
12/13
of an hour per day. Sally has already played
2/5
of an hour today. How many hours does Sally still need to practice today?
34/65 of an hour
500
Teddy and Janet each pay back $183.50 on their loans each month. Since they both work in a public school, half of their loans have now been ‘forgiven.’ In other words, each of them only has to pay half as much. Given their loan forgiveness status, what integer represents how much they pay back, combined, after three months? Write an expression representing this problem.
(183.5/2)*3
They have to pay back $275.25 each after three months.
500
One track coach wants her athletes to race
5 1/4
miles around a track to measure how fast each person can run. If the track is
1 3/7
miles around, then how many laps around the track will the athletes have to run to complete the race?
Write the final answer as a decimal
137/40
= 3.675
500
What can help us solve this problem in the correct order?
Solve:
(−3)−(−4 3/4)+(−6.2 ÷ 4)
GEMDAS
-0.80