Unit 3 – Ratios and Proportional Reasoning –
Class Notes
Date
Writing Ratios and Equivalent Ratios
Learning Target: I can describe relationships using ratio language.
Key Terms

Ratio: A comparison of two quantities by division that can be written in
three ways.
o Example:
29/12
29 to 12
29:12
 Equivalent Ratio: Ratios that have the same comparison.
o Example:
3 to 6
1 to 2
9 to 18
 Equivalent: Having the same value.
Examples
Part A: Writing Ratios
Ratios can be written to compare a part to a part, a part to a whole, or the whole to the part.
Use the table to write each ratio.
1. tulips to daffodils
2. lilies to total number of bulbs
3. total bulbs to crocuses
9/17 (Part to Part)
5 to 51 (Part to Whole)
51:20 (Whole to Part)
Part B: Equivalent Ratios
Equivalent ratios can be made by either multiplying or dividing both parts by the same number.
Try This
Use the table to write each ratio.
4. Write three equivalent ratios to compare the
number of diamonds to the number sof spades in the
pattern.
1. cats to rabbits
2. dogs to total pets
3. total pets to cats
For more help, go to www.khanacademy.org
Page 1
Date
Solving Proportions
Learning Target: I can solve proportions to calculate equivalent ratios.
Key Terms

Proportion: An equation that states that two ratios are equivalent.
Examples
Part A: Solving Proportions
Part B: Word Problems
When completing ratio word problems, use the WKU (Words, Known and Unknown) chart to help you
set up the proportion.
Gerald scored 15 points for his basketball team every 25 minutes he played this season. If he
played 200 minutes in the season, how many points did he score?
Words
Known
Unknown
Try This
Find the missing value in each proportion.
1)
2)
3)
4) Ursula is entering a bicycle race for charity. Her mother pledges $0.75 for every 0.5 mile she bikes. If
Ursula bikes 17.5 miles, how much will her mother donate?
For more help, go to www.khanacademy.org
Page 2
Date
Tables and Graphing
Learning Target: I can use equivalent ratios to find missing values and plot the ordered pairs on the
coordinate grid.
Example:
x
y
(x, y,)
2
3
(2, 3)
12
6
10
6
Try This:
x
y
(x, y,)
35
16
21
24
(21, 24)
7
32
x
y
(x, y,)
1.5
2.5
(1.5, 2.5)
7.5
6
3
12.5
For more help, go to www.khanacademy.org
Page 3
Date
Unit Rate
Learning Target: I can use unit rate to solve real-world problems.
Key Terms


Rate: A ratio that compares two quantities measured in different units.
o Example: $4.98 for 2 pounds
Unit Rate: A rate in which the second quantity in the comparison is one unit.
o Example: 55 miles per hour or 55 mi/hr
Example
To calculate a unit rate, set up a proportion. One ratio will indicate the given information, the other will
show the per one unit. HINT: “Per” usually means to divide.
84 miles in 6 hours
To determine the better buy. Find each unit rate. The smallest unit rate is the better buy.
A 3-pack of paper towels for $2.79 or a 6 pack for $5.46?
Try This
Find each unit rate.
1) 192 students in 4 buses
2) 3600 calories for 6 servings of pie
3) 8 ducks for $23.60
4) 351 chairs in 27 rows
Find the better deal.
5) A 12.5 oz $3.99 bag of Doritos or a 3 oz bag for $1.00
6) 5 gallon bucket of paint for $97.45 or a 1 gallon bucket of paint for $21.95
7) 48 oz big gulp for $1.59 or a 32 oz for $0.89
For more help, go to www.khanacademy.org
Page 4
Date
Percent of a Number
Learning Target: I can find the percent of a number.
Important information:
Example:
Find the percent of each number.
1) 6% of 38
2) 1.5% of 800
3) Mr. Green has a garden. Of the 40 seeds he plants, 35% were vegetable seeds. How many vegetable
plants did he plant?
Try This:
1) Find 36% of 50
2) Find 17% of 95
3) Find 5% of 90
4) Find 20% of 150
5) Crystal has a collection of 72 pennies. If 25% of them are Canadian, how many Canadian pennies
does she have?
For more help, go to www.khanacademy.org
Page 5
Date
Percent of a Number (continued)
Learning Target: I can find the percent of a number.
Important information:
Remember to set up a proportion first by using:
Example:
1) How much is 19% of 45?
2) 6.48 is 18% of what number?
3) What percent of 20 is 8?
Try This
1) 50 is what percent of 16?
2) 88% of 70 is how much?
3) 2% of what number is 1.92?
4) How much is 0.2% of 470?
5) 288 is 144% of what number?
6) What percent of 480 is 198?
For more help, go to www.khanacademy.org
Page 6
Date
Percent Word Problems (Discounts, Tips, Sales Tax)
Learning Target: I can solve real-world problems involving percent.
Important Information:
Examples:
1) A music store sign reads “10% off the regular price.” If Nichole wants to buy a CD whose regular
price is $14.99, how much will she pay for her CD after the discount?
Step 1: Find the amount of the discount.
Think, “What is 10% of 14.99?” Set up a proportion and solve.
Step 2: Subtract the discount from the regular price.
2) Leslie’s lunch bill is $13.95. She wants to leave a tip that is 15% of the bill. How much should she
leave?
Step 1: Find the amount of the tip.
Think, “What is 15% of 13.95?” Set up a proportion and solve.
For more help, go to www.khanacademy.org
Page 7
3) Marc is buying a scooter for $79.65. The sales tax rate is 6%. How much will the total cost of the
scooter be?
Step 1: Find the amount of the sales tax.
Think, “What is 6% of 79.65?” Set up a proportion.
Step 2: Add the tax to the regular price.
Try This:
1) Norine wants to buy a beaded necklace that is on sale for 10% off the regular price. If the regular
price is $8.49, how much will the necklace cost after the discount?
2) Alice and Wagner ordered a pizza to be delivered. The total bill was $12.15. They want to give the
delivery person a tip that is 20% of the bill. How much should the tip be?
3) A bicycle sells for $139.75. The sales tax is 8%. How much will the total cost of the bicycle be?
For more help, go to www.khanacademy.org
Page 8
Date
Conversions
Learning Target: I can use ratios to convert measurement units.
Steps
1. Read the problem to determine the two units of measurements you are dealing with. Write
these as a ratio.
2. Using the following chart, write in the numbers to show how these two units relate to each
other. This will be the left hand side of your proportion.
3. Re-read the problem filling in what you know on the right hand side of the proportion. The unit
you are trying to find should be represented with a variable.
4. Use cross-products to solve your proportion. Be sure to label your final answer.
Examples:
For more help, go to www.khanacademy.org
Page 9
Try This:
1) Linda cut off 1.5 feet of her hair to donate to an organization that makes wigs for children with
cancer. How many inches of hair did she cut off?
2) An adult male of average size normally has about 6 quarts of blood in his body. Approximately how
many cups of blood does the average adult male have in his body?
3) The steel used to make the Statue of Liberty weights about 125 tons. How many pounds of steel
were used to make the Statue of Liberty?
4) ? c = 72 fl oz
5) 20 min = ? sec
6) 14,000 lbs = ? tons
7) 98 days = ? weeks
For more help, go to www.khanacademy.org
Page 10
For more help, go to www.khanacademy.org
Page 11