Adv. Math Chapter 6 ReviewAdv. Math Chapter 6 Review

6-1 Ratios6-1 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 ways6-1 Ratios: written in 3 waysA drama club sells 35 student tickets, A drama club sells 35 student tickets,

24 adult tickets, and 11 senior 24 adult tickets, and 11 senior citizen tickets. Write each ratio in citizen tickets. Write each ratio in three ways.three ways.

1.1. Students to adultsStudents to adults35 to 24, 35:24, 35/2435 to 24, 35:24, 35/24

2. Adults to senior citizen2. Adults to senior citizen24 to 11, 24:11, 24/11 24 to 11, 24:11, 24/11

3. Senior citizen to total number of tickets3. Senior citizen to total number of tickets11 to 70, 11:70, 11/7011 to 70, 11:70, 11/70

6-1 Ratios: Writing Equal Ratios6-1 Ratios: Writing Equal Ratios

• Divide or multiply each term by the Divide or multiply each term by the same number.same number.

1.1. 6 to 18 6 to 18

sample: 3 to 9, 12 to 36, 1 to 3, etc.sample: 3 to 9, 12 to 36, 1 to 3, etc.

2.2. 4/14 4/14

sample: 2/7, 8/28, 12/42, etc.sample: 2/7, 8/28, 12/42, etc.

3.3. 8:108:10

sample: 4:5, 16:20, 80:100, etc. sample: 4:5, 16:20, 80:100, etc.

6-1 Ratios in Simplest Form6-1 Ratios in Simplest Form• To find simplest form divide by the GCFTo find simplest form divide by the GCF

1.1. 6/15 6/15

2/52/5

2.2. 40:3040:30

4:34:3

3.3. 42 to 5042 to 50

21 to 2521 to 25

6-1 Ratios: Find the Value6-1 Ratios: Find the Value

Complete to make ratios equal:Complete to make ratios equal:

1.1. 6 to 9, ___ to 3 6 to 9, ___ to 3

22

2.2. 18/3, 54/___18/3, 54/___

99

3.3. ___:96, 4:6___:96, 4:6

6464

6-2 Unit Rates6-2 Unit Rates• A A rate rate is a ratio that compares two is a ratio that compares two

quantities measured in different units. quantities measured in different units. Example: the rate 150 heartbeats/2minutes Example: the rate 150 heartbeats/2minutes

compares heartbeats to minutes compares heartbeats to minutes

• A A unit rateunit rate is the rate for one unit of a is the rate for one unit of a given quantity. given quantity. Denominator is always 1!Denominator is always 1!

• Example: 150 heartbeats/2 minutes - Example: 150 heartbeats/2 minutes - 150150÷2= 75 ÷2= 75

So the unit rate is 75 heartbeats per minuteSo the unit rate is 75 heartbeats per minute

6-2 Unit Rates6-2 Unit RatesFind the unit rate for the following:Find the unit rate for the following:

1.1. 210 heartbeats in 3 minutes 210 heartbeats in 3 minutes

70 heartbeats per minutes70 heartbeats per minutes

2.2. $19.50 for 3 T-shirts$19.50 for 3 T-shirts

$6.50$6.50

3.3. 45 miles in 5 hours45 miles in 5 hours

9 mph9 mph

6-2 Unit Rates6-2 Unit RatesWrite the unit rate as a ratio. Then Write the unit rate as a ratio. Then

find an equal ratio:find an equal ratio:

1.1. The cost is $6.75 for 1 t-shirt. The cost is $6.75 for 1 t-shirt. Find the cost of 8 t-shirts. Find the cost of 8 t-shirts.

$6.75/1t-shirt = $54/8t-shirts$6.75/1t-shirt = $54/8t-shirts

2.2. There are 3 feet in 1 yard. Find There are 3 feet in 1 yard. Find the number of feet in 15 yards. the number of feet in 15 yards.

3ft/1yd = 45ft/15yd3ft/1yd = 45ft/15yd

6-2 Unit Rates6-2 Unit Rates• Tell which unit rate is greater:Tell which unit rate is greater:

1.1. Krysta earns $44.55 in 9 hours. Krysta earns $44.55 in 9 hours. Megan earns $51 in 12 hours. Megan earns $51 in 12 hours.

Answer: $44.55 in 9 hoursAnswer: $44.55 in 9 hours

2.2. Austin reads 60 pages in 2 hours. Austin reads 60 pages in 2 hours. Tony reads 99 pages in 3 hours. Tony reads 99 pages in 3 hours.

Answer: 99 pages in 3 hoursAnswer: 99 pages in 3 hours

Proportions 6-3Proportions 6-3• A A proportion proportion is an equation is an equation

stating that two ratios are equal.stating that two ratios are equal.

• Example:Example: ½ = 4/8 ½ = 4/8

• Example: Example: 27/18 = 9/627/18 = 9/6

Proportions 6-3Proportions 6-3Do the ratios in each pair form a Do the ratios in each pair form a

proportion?proportion?1.1. 4/12 = 6/84/12 = 6/8

NONO2.2. 42/6 = 504/7242/6 = 504/72

YESYES3.3. 10/20 = 30/4010/20 = 30/40

NONO

Proportions 6-3Proportions 6-3• Find the value that completes Find the value that completes

each proportion.each proportion.1.1. 7/35 = 21/___7/35 = 21/___

1051052.2. 12/4 = ___/2812/4 = ___/28

84843.3. ___/190 = 3/114___/190 = 3/114

55

Using Cross Products 6-4Using Cross Products 6-4• You can find the You can find the Cross ProductsCross Products of of

two ratios by multiplying the two ratios by multiplying the denominator of each ratio by the denominator of each ratio by the numerator of the other rationumerator of the other ratio

• The .The .1.1. 7/35 = 21/ n 7/35 = 21/ n

n =n = 1051052.2. 12/4 = r /2812/4 = r /28

r =r = 84843.3. m /190 = 3/114m /190 = 3/114

m = 5m = 5