Ratios

Fall 2014

Ratios

• A to B, A:B, A/B

• We describe ratio relationships with words, such as to, for each, for every.

• No zeros! Or Negatives.• Order Matters! A:B ≠ B:A unless A and B are

equal• Similar to fractions but not a fraction. Ratios are

a comparison of two quantities• No units needed

Modeling

• Table• Tape diagram• Double line diagram

Equivalent Ratios

• If you can multiply BOTH quantities in a ratio by the same number, then they are equivalent

• 2:3 = 12 : 18 because 2 x 6 : 3 x6• Or 2/3 = 12/18

• In a bag of mixed walnuts and cashews, the ratio of the number of walnuts to the number of cashews is 5:6. Determine the amount of walnuts that are in the bag if there are 54 cashews. Use a tape diagram to support your work. Justify your answer by showing that the new ratio you created of the number of walnuts to the number of cashews is equivalent to 5:6.

RATIOS vs FRACTIONS

• Fractions are part/whole

• Ratios can be part to part; part to whole, whole to part, etc

Multiple Ratios from 2 quantities

In our class there are 6 girls and 7 boys. Write the following ratios:1. girls to boys2. boys to girls3. girls to total4. Total to girls5. Boys to total6. Total to boys

1.6:72.7:63.6:134.13:65.7:136.13:7

In the month of August, a total of 192 registrations were purchased for passenger cars and pickup trucks at the local Department of Motor Vehicles (DMV). The DMV reported that in the month of August, for every 5 passenger cars registered, there were 7 pickup trucks registered. 1. How many of each type of vehicle were

registered in the county in the month of August? 2. Make a table and a diagram to support your

answer.

Differences and Total

• There is more information in a ratio than just the two quantities.

• Add third line to your table. Label it total and enter the totals in your table. What do you notice?

cars 5 10 15 50

trucks 7 14 21 70

total 12 24 36 120

Solve the following. Use a table or a diagram to support your answer:

1. The ratio of the number of people who own a smartphone to the number of people who own a flip phone is 4:3. If 500 more people own a smartphone than a flip phone, how many people own each type of phone?

2. Sammy and David were selling water bottles to raise money for new football uniforms. Sammy sold 5 water bottles for every 3 water bottles David sold. Together they sold 160 water bottles. How many did each boy sell

3. At a country concert, the ratio of the number of boys to the number of girls is 2:7. If there are 250 more girls than boys, how many boys are at the concert?

Comparing Ratios

• Using tables• Comparing the ratio directly • Unit rates

Let’s compare two methods of mixing grey paint. One method has a 2/5 ration of black to white paint. The second method has a 3/7 ratio of black to white paint. Complete the tables.

black white

3 7

35

black white

2 5

35

Which ratio produces a darker grey? Explain your evidence.

Let’s compare two methods of mixing grey paint. One method has a 2/5 ration of black to white paint. The second method has a 3/7 ratio of black to white paint.

black white

3 7

15 35

6 14

black white

2 5

14 35

6 15

There are several ways to explain. When the white is equal at 35 the first mixture has 14 parts black which is less than 15parts in the second mixture, so the second mixture will be darker. Or if the black is emade equal at 6 parts you should see that the first mixture has more white making it lighter.

Value of the ratio

Comparing ratios. Which ratio is larger?One way to compare ratios is to use tables as we just did

Another way is to compare ratios like fractions. Which is larger 2/5 or 3/7? Use common

denominators14/35 or 15/35?

Unit rates

• A third way to compare ratios is to use unit rates• A ratio of two quantities, with different units, such

as 5 miles per 2 hours, a rate.• A unit rate is simply a rate with 1 as the

denominator, (per 1 unit)• UNITS and ORDER matter!• “per” indicates the divisor. Miles per gallon means

Miles ÷ gallon; km per hour means km ÷ hour• Unit price is a unit rate $ per unit. Dollars ÷ units

Teagan went to Gamer Realm to buy new video games. Gamer Realm was having a sale: $65 for 4 video games. He bought 3 games for himself and one game for his friend, Diego, but Teagan does not know how much Diego owes him for the one game. What is the unit price of the video games? What is the divisor? What is the dividend? What are the units?$65 ÷ 4 = $16.25 dollars per game

You may use a calculator but be sure to estimate your answer first

A publishing company is looking for new employees to type novels to be published. The publishing company wants to find someone who can type at least 45 words per minute. Dominique discovered she can type at a constant rate of 704 words in 16 minutes. Does Dominique type at a fast enough rate to qualify for the job? Explain why or why not.

Dave can clean pools at a constant rate of 3/5 pools per hour.

1. Write the ratio in a different format.2. How many pools can Dave clean in 10

hours?3. How long does it take Dave to clean 15

pools?4. How many pools does Dave clean in 1

hour?

3 to 5 , 3:5

6 pools in 10 hours

25 hours to clean 15 pools

3/5 or 0.6 pools in 1 hour

Graphing ratios

A ratio of two quantities, such as in 2 hours to travel 5 km hours, can be written as another quantity called a rate.Make a table of equivalent ratiosThese become a table of ordered pairshours distance2 5

x y2 5

Graphing the ratio

• Choosing intervals for the graph• Since the x values are increasing by 2, we

could choose 2 for the interval of the x axis• Since the y values are increasing by 3, we can

use 3 for the y interval

Dist

ance

in K

m

Time in Minutes

Label the axis, Label the intervals, and plot the points from the table

Watch out for:

• Title• Axes• Interval• Labels • Scale

TAILS

Graphing Example• A TV station broadcast a specific website so viewers could

find information on adopting pets. The website, two hours after the broadcast, had 24 views. An additional hour later, the website had 36 views. Assuming a constant rate of hits:

• Write the ratio of hours to views ________• Make a table of equivalent ratios

• From the table, create ordered pairs• Make a graph of the relationship of views to time.

Remember TAILS.

Hours Views

Review• Be able to write a ratio in all formats and use

ratio language• Be able to find equivalent ratios• Be able to use tables and diagrams to support

your reasoning• Be able to extract all the information in a ratio

including using the total and difference• Be able to compare ratios using tables, values

of ratios and unit rates• Be able to graph ratios