Transcript Adv. Math Chapter 6 Review

Adv. Math Chapter 6 Review
6-1 Ratios
• Ratio: a comparison of two numbers
by division. Each number in a ratio is
called a term.
Example: 6 cups party mix to 2 cups pretzels
• 3 ways to write a Ratio:
in words- 6 to 2
with a symbol- 6:2
as a fraction- 6/2
6-1 Ratios: written in 3 ways
A drama club sells 35 student tickets,
24 adult tickets, and 11 senior
citizen tickets. Write each ratio in
three ways.
1. Students to adults
35 to 24, 35:24, 35/24
2. Adults to senior citizen
24 to 11, 24:11, 24/11
3. Senior citizen to total number of tickets
11 to 70, 11:70, 11/70
6-1 Ratios: Writing Equal Ratios
•
Divide or multiply each term by the
same number.
1. 6 to 18
sample: 3 to 9, 12 to 36, 1 to 3, etc.
2. 4/14
sample: 2/7, 8/28, 12/42, etc.
3. 8:10
sample: 4:5, 16:20, 80:100, etc.
6-1 Ratios in Simplest Form
•
To find simplest form divide by the GCF
1. 6/15
2/5
2. 40:30
4:3
3. 42 to 50
21 to 25
6-1 Ratios: Find the Value
Complete to make ratios equal:
1. 6 to 9, ___ to 3
2
2. 18/3, 54/___
9
3. ___:96, 4:6
64
6-2 Unit Rates
• A rate is a ratio that compares two
quantities measured in different units.
Example: the rate 150 heartbeats/2minutes
compares heartbeats to minutes
• A unit rate is the rate for one unit of a
given quantity. Denominator is always 1!
• Example: 150 heartbeats/2 minutes 150÷2= 75
So the unit rate is 75 heartbeats per minute
6-2 Unit Rates
Find the unit rate for the following:
1. 210 heartbeats in 3 minutes
70 heartbeats per minutes
2. $19.50 for 3 T-shirts
$6.50
3. 45 miles in 5 hours
9 mph
6-2 Unit Rates
Write the unit rate as a ratio. Then
find an equal ratio:
1. The cost is $6.75 for 1 t-shirt.
Find the cost of 8 t-shirts.
$6.75/1t-shirt = $54/8t-shirts
2. There are 3 feet in 1 yard. Find
the number of feet in 15 yards.
3ft/1yd = 45ft/15yd
6-2 Unit Rates
• Tell which unit rate is greater:
1. Krysta earns $44.55 in 9 hours.
Megan earns $51 in 12 hours.
Answer: $44.55 in 9 hours
2. Austin reads 60 pages in 2 hours.
Tony reads 99 pages in 3 hours.
Answer: 99 pages in 3 hours
Proportions 6-3
• A proportion is an equation
stating that two ratios are equal.
• Example:
½ = 4/8
• Example:
27/18 = 9/6
Proportions 6-3
Do the ratios in each pair form a
proportion?
1. 4/12 = 6/8
NO
2. 42/6 = 504/72
YES
3. 10/20 = 30/40
NO
Proportions 6-3
• Find the value that completes
each proportion.
1. 7/35 = 21/___
105
2. 12/4 = ___/28
84
3. ___/190 = 3/114
5
•
Using Cross Products 6-4
You can find the Cross Products of
two ratios by multiplying the
denominator of each ratio by the
numerator of the other ratio
• The .
1. 7/35 = 21/ n
n = 105
2. 12/4 = r /28
r = 84
3. m /190 = 3/114
m=5