What is the answer of 2 + (-2)? Explain your reasoning using the number line.
0 because on the number line if you add a negative, you move the sum to the left.
100
What is the absolute value of the difference between -5 and 4? Show your work on a number line.
These two values are opposites on the number line. We must add them together to find the absolute value, or distance between them. ANSWER: 9
100
Pete has 13 more baseball hats than his friend. If Pete has 54 hats how many hits does his friend have?
x + 13 = 54
x = 41
100
Simplify: 5a – (3a – 7)
5a-3a+7
2a + 7
100
Use the distributive property to simplify the expression below. 6(x -3)
6x-18
200
Jane owes her friend $10 and her brother $5. How much money does Jane currently have? Use a number line to solve the problem.
-$15. She is in debt, thus we continue to move into the negatives on the number line.
200
The temperature yesterday was 17 degrees. The temperature today is -30 degrees. What is the absolute value of the change in temperature?
17 + 30 = 47
Absolute value is the distance between two points on the number line.
200
Is 2/3 a rational number? Explain your reasoning.
Yes, because it can be written as a fraction and its decimal is a repeating digit (0.66).
200
For the expression below indicate which the like terms are.
3n + 8 – 2n – 1
Like terms:
3n and -2n
8 and -1
200
If we use 40 x 90 to estimate the value of 39 x 88, will our estimate be greater than to less than the actual value? Explain your answer for full credit.
Greater because 40>39 and 90>88 so it will be an OVERestimate of the actual value.
300
Explain how a number line is used to solve addition and subtraction math problems.
Move to the left or right on the number line depending on the operation (addition or subtraction).
300
When you divide a negative number by a negative number, what is the sign in the final answer? Explain why.
Positive, because in multiplication and division, two negative signs cancel out and equal a positive sign in the product.
300
Simplify the expression: 6 x 9 x -10 / 3
PEMDAS
Multiplication before division: 6*9*-10 = -540
-540/3 = -180
300
Write the expression below using fractions.
.25 x + 1/2x - 3
1/4 x + 1/2 x -3/1
3/4 x - 3/1
300
Solve the equation for x. 5x = x +12
5x - x = 12
4x = 12
x = 3
400
Solve and show using a number line: -20 - 5
-25
400
Which of the following fractions is equivalent to 1/4? Explain your answer giving reasons for each option.
a) -1/4 b) 2/8 c) 1/-4
b, because all the other fractions are negative. Also 1/4 = 2/8.
400
Indicate whether the following numbers are rational or irrational. Explain your reasoning.
5/3 5/4
Both are rational.
5/3 = 1 2/3 = 1.66 rational number because repeating decimal
5/4 = 1 1/4 = 1.25 rational number because decimal ends
400
Jane got a 20/25 on her test, Richard got a 90% and Kate got a 1. What was the order of students based on their grade in percentages from highest to lowest?
Highest to lowest:
Kate 100%
Richard 90%
Jane 20/25 = 0.8 = 80%
400
Solve: 4d + 14 + d = 74.
5d = 60
d = 12
500
Write a real world problem (with solution) about adding and/or subtracting integers.
You toss 6 pieces of fish food into your goldfish's bowl. The goldfish eats 4. How many pieces of food are left in the fishbowl? 6-4=2
500
Identify the following property examples:
a) 5a(3bc) = (5a3)bc
b) 2(11 + h) = 22 + 2h
c) a + b + c = c + a + b
a) associative
b) distributive
c) commutative
500
During four days in January the temperature was near zero almost every day. On the four days the temperature was -4/7 , -8/7 , 1/7 and 3/ 7. What was the average temperature during the 4 days? Show your work.
Average of the four temperatures: -8/28
500
Put in order from least to greatest:
8/9, 89%, .88
Least to greatest:
.88 = 88%
8/9 = 0.8888888 = 88.9%
89%