Lesson 31 Using rates ratios and proportions Ratio

Lesson 31 Using rates, ratios and proportions

Ratio, rate & proportion • A ratio is a comparison of 2 quantities using division- 2 boys to 3 girls, 2 to 3, 2: 3 • A rate is a ratio that compares quantities measured in different units- 5 feet per 30 seconds • A unit rate is a rate whose denominator is 155 miles per hour • A proportion is an equation that shows 2 ratios are equal- 3 = 9 • 5 15

Which is the better buy? • 5 cans of tuna for $4. 95 or 6 cans for $5. 75 • Find unit price 4. 95 =. 99 • 5 1 can • 5. 75 =. 96 better buy • 6 1 can

Which is better buy? • 10 bananas for $1. 35 or 8 bananas for $1. 20 • Find the unit price of each

Converting rates • A bus driver drives at 30 miles per hour. What is the rate of the bus in miles per minute? • Use a unit ratio as a conversion factor • 30 miles x 1 hour = 30 miles = 1 mile • 1 hour 60 minutes 60 min 2 min • Or 1/2 mile/minute

Converting rates • A car travels at 60 miles per hour. How many miles per minute is this? • An engineer opens a valve that drains 60 gallons of water per minute from a tank. How many quarts were drained per second?

Cross product property • If a = c and b is not 0 and d is not 0 • b d • Then ad = bc • In a = c • b d • Then ad and bc are the cross product

Solving proportions using cross products • X = 2 • 15 3 3 x = 15(2) 3 x = 30 x = 10 • X-1 = 1 • 12 6 • 6(x-1) = 12(1) • X = 3 • 24 4 4 x = 24(3) 6 x-6=12 6 x=18 x=3 4 x = 72 x=18

Solving proportion problems • The ratio of boys to girls in math class is 3: 2. The class has 25 students in all. How many boys and girls are there? • Write a ratio number of boys = 3 • total in group 5 • Solve a proportion 3 = b • 5 25 • Cross multiply 5 b = 3(25) • 5 b = 75 • b = 15 • So there are 10 girls and 15 boys

problems • The ratio of pencils to erasers is 1: 2. there are 24 pencils and erasers in all. How many pencils and erasers are there? • A scale on a map is equal to the ratio 1 cm: 30 km. If a distance on the map is 4. 5 cm, what is the actual distance?

Lesson 36 • Writing and solving proportions

proportions • Proportions are frequently used in math to solve problems. • Solving problems in reading and drawing maps, architecture and construction requires knowledge of proportions and similar figures

similar • If 2 geometric objects or figures are similar, they have the same shape but not necessarily the same size. • When 2 figures are similar, they have sides and angles that correspond. • Corresponding angles in similar figures are congruent, or have the same measure

• • • < W is congruent to < Z <U is congruent to < X <V is congruent to < Y Sides correspond WV = WU = UV ZY ZX XY • The ratio of the sides is called the scale factor • Look at similar figures example 1 , p. 224

Scale drawing • A scale drawing is a drawing that reduces or enlarges the dimensions of an object by a constant factor. • look at example 3 p. 225

Ratios of perimeter, area, and volume of similar figures • If 2 similar figures have a scale factor of a/b, • then the ratio of their perimeters is a/b • the ratio of their areas is a 2/b 2 • The ratio of their volumes is a 3/b 3 Look at example 4 , p. 226