Ratios & Rates & Solving Proportions
Explain two ways to tell if two ratios are equivalent
(Chp Review p. 318 #2)
Cross products -if they are the same, they are equivalent fractions and form a proportion
convert to decimals if they are the same, they are equivalent fractions and form a proportion
Use cross products to solve for z
6/2.7 = 40/z
z=18
How are congruent figures different from similar figures?
Congruent figures-- everything is the same: same size, shape, same angles
Similar = same shape, same angles, but not same size. Corresponding sides have the same ratio.
P(event) =
P(event) = # of favorable outcomes
_______________________________
# of possible outcomes
Explain what a tree diagram can help you count.
A tree diagram uses branches to list possible choices. Example: possible outfits if you have 3 jeans and 2 t-shirts
Forrest and Sofia played four ping-pong games in 60 minutes. Find the unit rate: 60 minutes/4 games
60 /4 =15/1 minutes per game
Unit rates have 1 as the denominator. Easier to compare things with a denominator of 1
Chp 6 Review pg 319 #20 simplify first
17/c =34/46
17/c =34/46
c =23
Chp 6 Review pg 321 # 28
If scale is 1 inch: 3 yards then
1/3=14/y
y=42 yards
What's the difference between an outcome and a favorable outcome?
An outcome is ANY possible result
Favorable outcome is the outcome that corresponds to the event you've specified or are looking for. (Say rolling an even number)
What is the formula for the counting principle so you DON'T have to make a tree diagram?
m * n If one event can occur m ways and for each of these ways a second event can occur in n ways, then the number of ways the two events can occur together is m * n
Chp 6 REview #12 - Cereal Problem
Note: 16 oz /1 pound
Lowest price per ounce is the 18 oz box
Chp 6 review pg 319 #22 Field Trip problem
Round up! can't have a portion of a bus so just because b = 4.68 doesn't mean you get 4.68 buses. Remember to check to see if your answer makes sense in context
2/64=b/150 b= 5
chp 6 review pg 321 # 30
66 yards
A bag holds 8 slips of paper numbered 1-8. If you randomly choose a slip of paper, what is the probability that the number on the slip of paper is GREATER than 5?
Chp 6 Standardized Test pg. 323 # 6
3/8
P(greater than 5) = a 6, a 7, an 8 / 8 possible options
3/8
Use the counting principle, m*n , to determine the number of possible outfits if you have 8 shirts, 4 pants, 4 pairs of socks, & 2 belts using one of each type of item.
m*n = 8*4*4*2=256 possible outfits
Chp 6 Review pg 319 #17 Lions problem
5/6 = s/24
s=20 hrs
Chp 6 Review pg 320 #24
ratio of lengths is 2/3
chp 6 standardized test pg. 323 # 5
woman's height /shadow = tree height/shadow
64 /24 = t/67.5
Bag contains 8 blue marbles, 6 red marbles, 15 green marbles, 16 orange marbles. If you choose a marble at random, what is the probability the marble is red?
Chp 6 Test pg. 322 # 22
P(red) = red/total marbles = 6/45 = 2/15
You flip 3 coins. a) a tree diagram to show all the possible outcomes. b) Use the counting principle to show the possible outcomes.
Bonus: how many outcomes are all tails? and what is the probability of all tails?
8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT 2*2*2
Bonus: only one outcome is TTT. P(all tails)=1/8
see page 315 #6 part 1 and 2
18/24 = x/4
x = 3
chp 6 review pg. 20 #26
Line DE is 22 cm
chp 6 chp test pg 322 # 18
scale 1 inch:10 feet
x/8=1/10
x = 0.8
Bag contains 8 blue marbles, 6 red marbles, 15 green marbles, 16 orange marbles. If you choose a marble at random, what are the ODDS IN FAVOR OF GREEN?
Odds in favor of choosing green = favorable outcomes/unfavorable outcomes
15 green marbles (favorable)/ 30 other colors
15 to 30 or 1 to 2
10 digits * 26 letters 10 * 26 = 260 animals
10 digits * 10 digits * 26 letters = 10*10*26=2600 animals