Rational Numbers & Proportional Reasoning
Which category of numbers includes positive and negative values, but does not include decimals or fractions
Integers
Cameron made 46 doughnuts using 6 cups of sugar. What is the constant of proportionality that relates the number of doughnuts made, y, to the number of cups of sugar used, x?
7.5 doughnuts per cup
Kaelan is setting up for a party and set out 10 cups of regular soda and 20 cups of diet soda. What is the probability that a guest randomly selects a cup of diet soda?
2/3, 66%, .66
The angles of triangle ABC are as follows:
A: 68*
B: (3x)*
C: (2x-18)*
What is the value of x?
Patrick drives his car at a constant rate of 35 miles per hour. Write a table to represent the relationship between y, the number of miles and x the number of hours?
0 hours 0 miles
1hours 35 miles
2 hours 70 miles
3 hours 105 miles
A chef uses 31.5 ounces of sauce for 7 plates of Alfredo. At this rate how many ounces would they need for 1 plate of Alfredo?
4.5 ounces
Draw a number line to represent the solution to the following inequality,
250x+500>3750
x>13
A spinner has 5 sections labelled 1, 2, 3, 4 and 5. If the spinner is spun 25 times what is a reasonable prediction for the number of times the spinner will land on an odd number?
3/5 = 15/25
15 times on an odd number
A circular swimming pool has a radius of 3.5 meters. If you wanted to build a fence around the edge of the pool, what would the length of the fence be?
21.98 meters
A company pays 3255 dollars per month with a 950 dollar signing bonus. Write an equation the can be used to y, the amount of money you will make, if x represents the number of months.
y=3255x+950
A student increased their typing speed from 80 words per minute to 100 word per minute. By what percentage did they INCREASE their speed?
What equation best represents the relationship between x and y on a graph that passes through the points, (-2,0) and (0,-3)?
y=-3/2x - 3
A bag of candy contains the following flavors. 5 strawberry, 8 grape, 10 cotton candy and 12 butterscotch. Which of the following statements is true?
A. The candy is twice as likely to be butterscotch as grape.
B. The candy is 2 times more likely to be butterscotch than cotton candy
C. The candy is twice as likely to be cotton candy as strawberry.
C. The candy is twice as likely to be cotton candy as strawberry.
A dog toy in the shape of square pyramid is 18 cm tall. The square base has a side length of 8 cm. What is the volume of the toy in cubic centimeters.
384 centimeters cubed
Draw a graph to represent the equation y=-2x+2
Hint: Think about the slope and y-intercept
x
If John buys 3 chips, 2 sodas and a hotdog and pays using a $20 bill. How much change will he receive based on the prices below.
Hotdog: $2.45
Soda: $1.20
Chips: $2.15
$9.10
The number of minutes that Pam drives each day is represented by P.
The number of minutes Jim drives each day is 3.5 times the number Pam drives.The total number of minutes Jim and Pam drive each day is 76.5
What is P, the number of minutes Pam drives each day?3.5p+p=76.5
P=17 minutes
There are two bags of candy. The first has 3 chocolates and 5 lollipops. The second bag has 4 chocolates and 2 lollipops. What is the probability that someone randomly selects a chocolate from both bags?
3/8*4/6=6/24=1/4
1/4 or 25% or 0.25
A semi-circle has a diameter of 12 feet. What is the area of the semi-circle?
56.52
There are 22 students on Andres' swim team. They want to raise $4500 to travel to California to attend the national championship. They have already raised 2373.70. If each student raises the same amount, how much more money must each student raise?
$96.65
An architecture student is designing a building. Her model uses a scale of 1 inch represents 12 meters. The actual height of the building is going to be 168 meters tall. How many inches tall must the model be?
14 inches tall
James needs to make enough money to pay his monthly rent of 1695. This month, he's already made 850. He makes $25 per hour at work. Write an inequality to find the number of hours he still needs to have enough money to pay for rent.
25h+850>1695
You're playing a card game and your friend is holding an Ace, King, Queen, Jack and 10. What is the probability that you select the Ace, keep it, and then select the King?
1/5*1/4 = 1/20
1/20 of 5% or 0.05
A triangular prism has a height of 12 meters. The dimensions of the base are 13 meters by 22 meters. What is the volume of the prism?
1716 meters cubed
Solve the following inequality.
-1.3x + 1.4 > 4.13
x < -2.1