Ratios & Unit Rate
A class has 12 boys and 8 girls. What is the ratio of boys to girls?
12 to 8 or 3 to 2.
Simplify:
3x + 5x + 4 + 7
8x + 11
Solve:
x + 5 = 12
X = 7
Find the mean:
4, 6, 8, 10, 12, 20
mean = 10
Find area: rectangle (l=6, w=4)
Area = 24
Plot point: (2, 3). Which quadrant?
Quadrant I
A car travels 180 miles in 3 hours. What is the unit rate?
60 miles/hour.
Are these equivalent? 4(x + 2) and 4x + 2
No, 4(x + 2) should equal 4x + 8.
Solve:
3x = 18
X = 6
Find the median:
3, 7, 9, 10, 11, 13, 15, 17, 19, 21
Median = 12
Find area: triangle (base=10, height=6)
Area = 30
Plot: (-4, 5). Which quadrant?
Quadrant II
Which is the better buy:
Simplify:
5(2x + 3)
10x + 15
Solve:
x − 4 > 6
X > 10
Find the range:
5, 8, 12, 15, 18, 23, 32, 40
Range = 35
Find volume: 3 × 4 × 5 prism
Volume = 60
Find distance between (1,2) and (1,7)
The distance is 5 units
Solve: 4/x = 12/9
X = 3
Write an expression:
“7 more than twice a number”
2x + 7 or 7+ 2x
Graph:
x ≤ 3
A closed circle at 3, graph is shaded to the left.
Which is more affected by outliers: mean or median?
The Mean
Find surface area of a cube with side length 3
Surface Area = 54
Draw a triangle with points (0,0), (2,0), (2,3). What type is it?
Right triangle
A hydroponic system uses 18 gallons of water for 9 plants. How many gallons are needed for 25 plants at the same rate?
50 gallons
Simplify:
3x + 4 + 2x − 6 + x
6x - 2
A number decreased by 7 equals 15. Find the number.
X = 22.
Data Set A: 5, 5, 5, 20
Data Set B: 7, 8, 9, 10
Which has greater variability? Explain.
Data Set A
A prism has fractional edges: 1/2, 1/3, 1/4. Find volume.
Volume = 1/24
Find missing point to form rectangle:
(1,1), (1,4), (5,4), (?)
The missing point is (5, 1)
A student says: “If 6 apples cost $3, then 12 apples cost $9.”
Explain the mistake.
12 apples should cost $6.
Explain why:
2(3x + 4) = 6x + 8
Because using the distributive property 2 times 3x = 6x and 2 times 4 = 8.
Solve and explain:
2x + 4 = 16
X = 6
Why is median better than mean for income data?
Median not affected by extreme values
A box is 10 × 5 × 2. If doubled in height, how does volume change?
Doubles
A point moves from (2,3) to (6,9). Describe the change.
+4 in x, +6 in y