Warm – up #61. Find the inverse of

3x – 15 = –5y

Homework LogThurs

12/3

Lesson 4 – 7

Learning Objective: To simplify ratios, solve proportions, and convert units of measures

Hw: #408 Pg. 261 #1 – 18

12/3/15 Lesson 4 – 7 Ratios, Proportions, & Converting Day 1

Advanced Math/Trig

Learning Objective

To simplify ratios

To convert units of measures

To solve problems using proportions

Measurement Conversions

1 foot = 12 inches

1 yard = 3 feet

1 mile = 5280 feet

1 meter = 100 cm

1 km = 1000 m

1 pound = 16 ounces

1 ton = 2000 lbs

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 16 ounces

1 min = 60 secs

1 hour = 60 min

RatiosRatio of a to b

a:b or Quotient

***If 2 measures are the same type, need to same units!

1. 1 yard to 18 inches (both measure length)

= Or =

RatiosExpress each of the following ratios as a quotient

2. $20 to 5 tickets

3. 50 miles to minutes

=

= 4 dollars/ticket

= 50 miles

= 50 miles

50𝑚𝑖𝑙𝑒𝑠23𝑚𝑖𝑛𝑠

= 75 miles/min

Ratios4. Express 60 miles per hour in terms of feet per second.

1 mile = 5280 feet

1 hour = 60 min

1 min = 60 sec

= 88 ft/sec

Ratios5. Express 60 miles per hour in terms of yards per minute.

1 mile = 5280 feet

1 yard = 3 feet

1 hour = 60 min

= 1760 yd/min

ProportionsProportions – equality of two ratios

a is to b as c is to d

a:b = c:d

Or

Ratios6. If a car travels at a uniform rate of speed and travels 400 km in 8 hours, how far does it travel in 6 hours?

Word ratio

8x = 400(6) 8x = 2400= 300 km

Ratios7. If milk must be mixed with water at a ratio of 3:2, how many pints of milk must be used with 6 gallons of water?

Word ratio

2x = 48(3)2x = 144= 72 pints of milk

6 gal

= 48 pints of water

Ratios8. If two people divide $48 in a ratio of 3 to 5, how much money will each receive?

Word ratio

5x = 3(48 – x) 5x = 144 – 3x

8x = 144

Person 1 = x

Person 2 = 48 – x

$18 person 1 $30 person 2

Ratios9. If a mixture contains 30% water, how many ounces of water are in 16 ounces of the mixture?

Word ratio

100x = 30(16)

100x = 480 4.8 oz of water

Ticket Out the Door

If a mixture contains 40% alcohol, how many ounces of alcohol are in 6 ounces of the mixture?

Homework

#408 Pg. 261 #1 – 18