1. Understanding Ratio, Proportion, and Percent
Chapter Thirteen

2. RATIOS & PROPORTIONS
A ratio is a comparison of two numbers by division.
To write ratios, use the word to, a colon, or a fraction bar.
EXAMPLE #1: John read 3 books in 4 days. Write the ratio of books to days.
Words: 3 to 4
Colon: 3:4
Fraction: 3/4

3. RATIOS & PROPORTIONS
A proportion is a statement that two ratios are equal.
EXAMPLE #2: Is a proportion?
Find the cross products.
30 = 30 TRUE
If TRUE, the statement is a proportion.

4. RATIOS & PROPORTIONS 20 = 21 FALSE EXAMPLE #3: Is a proportion?
Find the cross products.
20 = FALSE
If FALSE, the statement is NOT a proportion.

5. RATIOS & PROPORTIONS EXAMPLE #4: Solve the proportion:
Find the cross products.
Divide both sides by 10. 10

6. RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.

7. Equal ratios
Beginning activities should include number patterns and repeated addition
In a basketball game, Amy made 3 of 5 free throws and Diane made 4 of 7 attempts. Which performance was better? 3 5 7 21 35 x =
Answer:
AMY 4 7 5 20 35 x =

8. Cross Products Travel On
A car travels 212 km in 4 hours. At this rate of speed, how far would it travel in 7 hours?
212 km
4 hrs.
x km
7 hrs. =
4x = 1484
X = 371 km

9. Cross Products Travel On 8 people 6 onions 12 people x onions =
A recipe for soup for 8 people calls for 6 onions. How many onions should be used to make enough soup for 12 people?
8 people
6 onions
12 people
x onions =
8x = 72
X = 9 onions

10. SCALE DRAWINGS
A scale drawing is a drawing of an object with dimensions proportional to those of the actual object. To find lengths from scale drawings, set up and solve proportions.
Mary is 5 ft 6 inches tall.
She casts a 2 foot shadow.
The tree casts a 7 foot shadow.
How tall is the tree?

11. Mary is 5 ft 6 inches tall.
She casts a 2 foot shadow.
The tree casts a 7 foot shadow.
How tall is the tree?
Mary’s height
Tree’s height
Mary’s shadow
Tree’s shadow = x
5.5 2 7

12. Mary is 5 ft 6 inches tall.
She casts a 2 foot shadow.
The tree casts a 7 foot shadow.
How tall is the tree?
5.5 x 2 7 =
Mary’s height
Tree’s height
Mary’s shadow
Tree’s shadow = x
5.5 2 7

13. 5.5 x 2 7 = x
7 ( 5.5 ) = 2 x
= 2 x
x = 7
The height of the tree is feet

14. SCALE DRAWINGS USING PROPORTIONS
EXAMPLE#1: ¼ in = 5 ft is a scale for a rock band’s concert stage.
A. The scale length of the drum stand is 1 in. What is the actual length of the drum stand?
Cross multiply.
Divide by .25

15. SCALE DRAWINGS USING PROPORTIONS
EXAMPLE#2: ¼ in = 5 ft is a scale for a rock band’s concert stage.
B. The actual length of the stage is 60 ft. What is the scale length of the stage?
Cross multiply.
Divide by 5
5 5

16. Percent Meaning and notation Number sense
Term percent means “parts per hundred”
Part-to-whole ratio that has 100 as its second term
Can be thought of as fractions with denominators of 100
Number sense
Introductory activities should help children to develop visual images and a quantitative feel for numbers expressed as percents
Concrete Level – Base-ten blocks
Pictorial Level – Squares on a 10-by-10 grid

17. Percent (cont’d) Fraction and decimal equivalents
Decimals as percents involves finding an equivalent decimal in hundredths.
Fractions as percents can be determined by finding an equivalent fraction with a denominator of 100.
Another method – first write the fraction in decimal form and then multiply the number by 100.
Percents as fractions with a denominator of 100 can be done by using the definition of percent.

18. Finding a Percent of a Number
Everyday situations include:
Sales tax
Discounts
Commission
Interest
Early examples should include percents that have simple fraction or decimal equivalents
10% of % of 80
50% of 14 1% of 324
25% of % of 52

19. Percents
Most real-life computations will be carried out on a calculator which means instruction should focus on
Estimating answers
Justifying the reasonableness of the results
What’s the estimate of the following problems?
52% of 65
17% of 543
61% of 46
9.5% of 628

20. Other Procedures for Solving Percent Problems
The proportion method
Of the sixth-grade children in a school, 21 usually walk to school. This represents 30% of the sixth grade children. How many sixth graders are there? 21 x 30
100 =
30x = 2100
x = 70

21. Other Procedures for Solving Percent Problems (cont’d)
The equation method
50% of _____ = 32
.5x = x = 64
6 is 10% of ______
6 = .10x = x
78 is 120% of some number. What do you know about the number?
78 = 1.20x = x

22. Solving Equations Containing Percents Most percent problems are word problems and deal with data. Percents are used to describe relationships or compare a part to a whole.
Sloths may seen lazy, but their extremely slow movement helps make them almost invisible to predators. Sloths sleep an average of hours per day. What percent of the day do they sleep?
Solution

23. What percent of 24 is 16.5. n · 24 = 16.5 n = 0.6875 n = 68.75%
Proportional method
Part Part
Whole Whole
Equation Method
What percent of 24 is n · 24 = n = n = %