Ratios and Rates

October 30, 2013

Mrs. Ford

A restaurant bill will be paid equally between 4

friends. The bill totaled $25.20. How much should each friend pay?

Warm-up

$25.20 / 4 = $6.30

Lesson Essential Question: What is a ratio and how is it used in the real

world?

Areas of Interaction: Approaches To Learning Health and Social Education

Ratios

Ohio State Band

Things to look for: Use of Integers, angles, ratio, proportions,

reflection, rotation, and scale

Opening

What do you know

about ratios and rates?

Travel Abroad

Recipes

Cellphone Rates

Mileage

A ratio is a comparison of two or more quantities

(numbers) and can be written in several different forms. For example, if there were 4 boys and 5 girls in our class today then we could write these two quantities as a ratio, 4/5.”

We could also write this ratio as 4 to 5 or 4:5. These all mean the same thing. We are comparing two quantities, 4 to 5.

Ratios

4/5, 4 to 5, 4:5

This is an example of a part-to-part ratio. What is the actual ratio of boys to girls in our classroom today?

Three Ways to Write A Ratio

Would this change if I asked for the ratio of girls to

boys?

Yes, the numbers would be reversed 5/4

We could use this information to write a part-to-

whole ratio, otherwise known as a fraction. If we put the two parts together, girls and boys, we

would say the total is students. So the ratio of boys to students would be 4/9, since

there are 4 boys and 4+5=9 students altogether.

If there were 4 boys and 5 girls in our class today then we could write these two quantities as a ratio, 4/5

The third kind of ratio we will talk about in this unit is called a rate, which is a comparison of two different things (different units).

One example of a rate is a speed limit, which compares miles to hours, or miles per hour. Can anyone think of another example of a rate?”

(Examples: miles per gallon, dollars per hour, feet per mile)

Rates

So the three kinds of ratios are:

• Part-to-part, • Part-to-whole • Rate

Rates cannot be written as part-to-part ratios or part-to-whole ratios since they are comparing two different units.”

Rates

Ratio, Part-to-part ratio, Part-to-whole ratio, Rate

Vocabulary

Green Textbook Page 317-318 – Do the activity, review

Example 1, Example 2, and Example 3 Page 319, problems 2-36 even only

Classwork

November 6, 2013

Math Mrs. Ford

In Mr. Romero’s auto

shop class, the ratio of boys to girls is 5:2. If there are 35 students in the class, how many

are boys?

Warm Up

In Mr. Romero’s auto shop class, the ratio of boys to girls is 5:2. If there are 35 students in the class, how many are boys?

Warm Up

Boys

Girls

Number of students divided by the number of units7 units = 3535/7 = 5 1 unit = 5

5 units of 55 x 5 = 25 In Mr. Romero’s class, there are 25 boys.

For example: price of wheat is $2 for 3 Kgs,

then the rate would be $2 for 3 Kgs and the unit of rate would be $/Kg.

Similarly if a car goes 100 miles in 1.5 hour, then the rate is 100 miles per 1.5 hour and unit is miles/hr.

Note that ratios are usually don’t have units.

A rate is a form of ratio in which the two terms are in different units.

Rate has a denominator of 1.

For example, if a car goes 60 miles in 1 hour, then the unit rate is 60 miles per hour.

Other examples are: $5 per kg, 5 steps per second and $80 per barrel.

Unit rate is a rate in which the rate is expressed as a quantity of 1.

An example is price of corn

is $2 per ounce and price of petrol is $5 per gallon. Remember that the price is always the numerator and the unit is the denominator.

Unit price is the rate when it is expressed in unit currency like dollar or cent.

Rate can be converted to unit rate simply by

dividing the first term by second term. Consider an example:

If a car travels 45 miles in 30 min, what is the rate at which the car is travelling?

If we express the rate in miles/hr, the rate would simply be 45 miles/0.5 hr which is 90 miles per hr. If we want to express in miles/minute the rate would be 45/30 = 1.5 miles per minute. 45 ÷ 30 = 1.5

Converting rate to unit rate/price

If John bought 2.5 Kgs of rice for $7.5, then

what is the unit price of rice?

Solution: Here the denominator should be 2.5 Kg and numerator is the price $7.5. (7.5/2.5)

The unit price of rice would thus be 7.5 ÷ 2.5 = $3 /Kg.

Converting rate to unit rate/price

It takes 30 minutes for a tap to fill one bucket. How much time would it take to fill 6 buckets? The problem can be done using the concept of unit

rate. The unit rate to fill the buckets would be 1 bucket/0.5 hour which is 2 buckets per hr.

Thus to fill 6 buckets, it would take 6/2 = 3 hours.

Rates and unit rates are used to solve many real world problems.

Example: 240 miles in 4 hours.

= 240 miles/4 hours = 60 miles / 1 hour

Example: Suppose you drove 96 miles to San Francisco in 3 hours. What would be the unit rate?

= 96 miles ÷ 3 hours = 32 mph

Example: Suppose you work at a coffee shop and make $9.50 an hour and work 8 hours. How much would you make? $9.50 x 8 hours = $76.00

Suppose you stayed late and worked 10 hours?

$9.50 x 10 hours = $95.00

Example: An ice cream cone may be 35 calories per ounce. If the ice cream cone is 7 ounces, how many calories are in the ice cream cone.

35 calories/oz. x 7 ounces = 245 calories

Suppose a different cone was 45 calories/ounce. How many calories would be in the whole cone?

45 calories/oz. x 7 ounces = 315 calories

What’s the better buy?A) 12 ounce can of soda for $.84B) 16 ounce bottle for $1.20

$0.84 ÷ 12 = $0.07/oz. $1.20 ÷ 16 = $0.075/oz.

What's the better deal? 16 oz. bottle or 12 oz. can

What’s the better buy?A) 4 oz. Snicker Bar for $0.80B) 6 oz. Three Musketeers Bar for $0.90

0.80 / 4 = .20/oz Snicker 0.90 / 6 = .15/oz Three Musketeers

Unit rates can be used to find the better buy

Blue Textbook

With your partner Investigation 1.1 – Ads That Sell

Investigation 1.2 – Targeting an Audience

Classwork

November 7, 2013

Math Mrs. Ford

A proportion is also a way of comparing. But a

proportion is a way of comparing two ratios. If the ratios are equal, then we can say that they are “in proportion” or “form a proportion.”

Put in your notebook:

A proportion shows that two ratios are equal.Example: 1/6 = 2/12

Proportions

Two ways to tell if the ratios form a

proportion

1. Cross multiply. If the cross products are equal, then the two ratios do form a proportion.

2. Reduce both ratios to their simplest forms. If they are equal in their simplest form, then they form a proportion.

Proportions

3 = 9 7 21

7 x 9 = 63

For this activity, we are going to do an apple juice

taste test that involves ratios

Activity