7.RP
Ratios and Proportions
Ratios and Proportions
A person hikes 3/4 mile in 1/3 hour. What is the unit rate in miles per hour?
(3/4) ÷ (1/3) = 9/4 miles per hour or 2.25 miles per hour.
A submarine is 300 ft below sea level. It rises 300 ft. Where is it now?
Answer: 0 ft; sea level
Write an equivalent expression of 3(x - 2) using distribution (sometimes called expansion).
Answer: 3x-6
A spinner was spun 200 times. It landed on green 60 times, yellow 100 times, and red 40 times. What is the experimental probability of red?
You may answer as a decimal or as a percent.
Answer: 0.2 or 20%
Two similar triangles have side lengths 3, 4, 5 and 6, 8, 10. What is the scale factor?
SF=2
What is the shape of the cross-section when slicing a pyramid perpendicular to the base through the face of the pyramid?
Answer: Trapezoid.
A table shows the cost of sandwiches:
1 = $2.50
2 = $5.00
3 = $7.25
Is the relationship proportional? Why or why not?
No; the increase in X and the increase in y do not remain constant.
Evaluate: 7 + (-2 + -5)
Answer: 0
7 + (-2 + -5) --> 7+(-7)=0
7+ (-2+ -5) --> (7 + -2) + -5 --> 5+ -5=0
A 15% discount can be written as p - 0.15p. Rewrite this expression and explain what it means.
Answer: 0.85p or 85% of p.
p - 0.15p --> 1p - 0.15p = 0.85p
100% of P - 15% of p = 85% of p.
The MAD for Team A is 2, and for Team B it’s 5. Which team is more consistent and how do you know?
Team A; MAD is closer to 0.
A scale drawing has a rectangle 4 cm by 6 cm. If the scale is 1 cm = 2 ft, what is the actual area of the rectangle represented by the scale drawing?
Answer: 8 ft × 12 ft = 96 ft²
A circle has a diameter of 10 cm. What is the circumference (use π ≈ 3.14)?
Answer: 31.4 cm
C = πd = 3.14x10=31.4 cm
An item increases from $50 to $65. What is the percent change?
Answer: 30% increase.
(15 ÷ 50) × 100 = 30%
or 15/50=3/10=0.30=30%
If temperature drops 2 degrees every hour for 6 hours, what is the total change?
Answer: -12 degrees
Solve: 4(x - 2) = 20
Answer: x = 7
4(x-2) = 20 --> 4x-8=20 --> 4x=28 --> x=7
--Or--
4(x-2) = 20 --> x-2=5 --> x=7
One class has an IQR of 8; another has an IQR of 4. Which class shows greater variability in the middle 50% of the data? How do you know?
Answer: The first class (IQR = 8); higher IQR means higher variability.
A triangle has sides of 3cm, 4cm, and third unknown side. What could the length of the third side be?
Answers: 2, 3, 4, 5, or 6.
Third side must be greater than the difference of the two sides, but less than the sum of the two sides. Third Side: 1<x<7
If two angles are vertical and one is 2x + 10, the other is 40. Solve for x.
Answer: x = 15
A student estimates a test score to be 80, but it was actually 72. What is the percent error?
Answer: 11.11%
|80 - 72| ÷ 72 × 100 = 11.11%
A recipe calls for 3/4 cup of oil. You spill 1/3 cup. How much do you have left?
Answer: 5/12 cup
3/4 - 1/3 = 9/12 - 4/12 = 5/12
You earn $12/hour and want at least $96. Write and solve an inequality.
12x ≥ 96 → x ≥ 8 hours
You flip a coin and roll a regular die. What is the probability of getting heads and an even number?
Answer: 1/4, 0.25, or 25%
2x6 = 12 possible outcomes
H2, H4, and H6 meet the criteria of heads and even number.
3/12 = 1/4 = 0.25 = 25%
What shape results from slicing a right rectangular prism parallel to its base?
Answer: Rectangle.
A triangular prism has a base area of 24 cm² and height of 10 cm. What is its volume?
Answer: 240 cm³
A bank offers 4% simple interest on $500 for 3 years. How much interest is earned?
Answer: $60
Interest = Principal x Rate (as a decimal) x Time (in years)
$500 x 4% x 3 years ---> 500 × 0.04 × 3 = $60
Convert
-4/6
to a decimal. Round to the nearest thousandths place.
Answer: -0.667
Solve: (-3(x+5))/4=3
x=-9
In a standard deck of cards, what is the probability, as a simplified fraction, that you would draw a red card or an ace?
Answer: 7/13
52 Cards: 26 red, 26 black.
4 Aces in a Deck: 2 red, 2 black.
26/52+4/52-2/52=28/52=14/26=7/13
Find the area of a circle with radius 7 inches (π ≈ 3.14)
Answer: A = πr² = 3.14 × 49 = 153.86 in²
Find the surface area of a cube with side length 5 cm.
Answer: 6 × 25 = 150 cm²