7.RP
Ratios and Proportions
Ratios and Proportions
The unit rate if a car travels 180 miles in 3 hours.
What is 60 miles per hour?
Evaluate: -5 + 8
3
Simplify: 5x - 3 + 2x + 6
7x + 3
A map uses a scale of 1 inch = 5 miles. If two cities are 3.2 inches apart on the map, how far are they in real life?
Answer: 16 miles
A company surveys 200 customers out of 2,000. Is this a sample or a population?
Sample.
A student has $20. She spends $7.25, then earns $5.50, then spends $3. What is her final balance?
Answer: $20 - $7.25 + $5.50 - $3 = $15.25
The unit rate of sugar to oil of a recipe that uses 2/3 cup of sugar for every 1/4 cup of oil.
What is 8/3 or 2 2/3
cups of sugar per 1 cup of oil?
Evaluate: -3 - (-7)
4
Rewrite 6x + 9 using factoring
3(2x + 3)
Triangle A has side lengths of 3, 4, 5 and Triangle B has side lengths of 1.5, 2, 2.5. Are these similar figures? And if so, what is the scale factor from A to B?
The scale factor is 0.5 (B is smaller than A).
A cereal company only surveys customers at their own stores. Is the sample representative or biased?
Biased; only asks regular customers at their own stores, not all customers who buy their product.
A coat originally cost $60 but is marked down by 25%. 8% tax is then added at checkout. What is the final price?
Answer: $60 - $15 = $45; tax = $3.60 → $48.60
Two stores sell the same backpack. Store A sells it for $40 and Store B sells it for the same price with a 20% discount at checkout. This is the price you would pay at Store B.
What is $32?
Original price is $40; 20% of 40 = $8; $40 - $8 = $32.
Evaluate: (-4)(3.5)
-14
A rectangle’s perimeter is 54 cm. The width is 6 cm. What is the length of the rectangle?
length = 21cm
2(l+w)=p so:
2(6+l)=54 --> 6+l=27
--->
l=21
Can a triangle be made with sides 3 cm, 4 cm, and 8 cm? Why or why not?
No, because it does not follow the Triangle Inequality Theorem: the value of any one side must be less than the sum of the two other sides (a+b>c or c<a+b).
4+8>3, 8+3>4, but 3+4<8.
A spinner lands on blue 40 out of 100 times. What is the estimated probability as a fraction, a decimal, and as a percent?
40/100 , 0.4 or 0.40, 40%.
A circle has a radius of 5 cm. What is the circumference. Use
pi=3.14
C = 2x(3.14)x5cm = 10cm(3.14) = 31.4 cm
The equation of a line in the form
y=kx
on a graph that shows a line traveling through the origin and the point (4, 10).
What is y=2.5x ?
k=((y2-y1)/(x2-x1)) so,
k=((10-0)/(4-0))=(10/4)=2.5
A submarine is at -250 meters and descends 45 meters more. Where is the depth now?
-295 meters.
You earn $12/hour and want at least $96. Write and solve an inequality.
12x ≥ 96 → x ≥ 8 hours
This is a a quadrilateral that has four equal-length sides and no right angles.
What is a rhombus?
A die has faces 1 through 6. What is the probability of rolling an even number?
3/6 or 1/2 , 0.50, or 50%
Two angles form a straight line. One is 70°, the other is unknown. Find the unknown angle.
Answer: 110°
Sarah wants to buy a laptop that costs $950. If the sales tax is 7.5%, this is how much will she pay in total.
What is $1,021.25?
Since she will be paying the full price 100% AND 7.5% tax, we can multiply the original price ($950) times 107% as a decimal (1.075) to get our answer.
$950xx1.075=$1,021.25
Convert 5/8 to a decimal using long division. Is this number rational? How do you know?
5/8=0.625
This number is rational because:
- It can be represented as a fraction of two non-zero integers 5/8
- It terminates (it ends).
Draw a number line and graph the solution to the following inequality:
-x+5<11
x>-6, so: open circle on -6, pointing to the right.
This is the shape of the cross-section when slicing a pyramid perpendicular to the base through the apex.
What is a triangle?
What is the sample space for flipping a coin and rolling a 6-sided die?
12 outcomes (H1-H6, T1-T6)
Find the area of a composite figure made from a 6 cm by 4 cm rectangle and a triangle with base 4 cm and height 3 cm.
Answer: 24 + 6 = 30 cm²