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
45
Embed
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.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
RATIOS & PROPORTIONS
There are 5 men and 6 women in my class.
1. What is the ratio of women to men using a fraction?
2. What is the ratio of women to students in my class (use a colon)?
3. What is the ratio of men to students in my class (use words)?
RATIOS & PROPORTIONS
There are 5 men and 6 women in my class.
1. What is the ratio of women to men using a fraction? 5
6
2. What is the ratio of women to students in my class (use a colon)? 6:11
3. What is the ratio of men to students in my class (use words)?
5 to 11
RATIOS & PROPORTIONS A proportion is a statement that
two ratios are equal.
EXAMPLE#2: Is a proportion?15
6
5
2
Find the cross products.
65152 30 = 30 TRUEIf TRUE, the
statement is a proportion.
RATIOS & PROPORTIONS
EXAMPLE#3: Is a proportion?
5
3
7
4
Find the cross products.
RATIOS & PROPORTIONS
EXAMPLE#3: Is a proportion?
5
3
7
4
Find the cross products.
3754 20 = 21 FALSEIf FALSE, the
statement is NOT a proportion.
RATIOS & PROPORTIONS
7
3
9
4
RATIOS & PROPORTIONS
7
3
9
4
3974
2728 FALSE – Not a proportion
RATIOS & PROPORTIONS
20
9
9
4
RATIOS & PROPORTIONS
20
9
9
4
99204 8180
FALSE – Not a proportion
RATIOS & PROPORTIONS
Are the following proportions?
27
12
9
4
RATIOS & PROPORTIONS
27
12
9
4
129274 108108
TRUE – this is a proportion
RATIOS & PROPORTIONS
EXAMPLE#4: Solve the proportion:10
4
5
Find the cross products. Multiply both sides of the proportion.
4510 x2010 x
10 10
2x
Divide both sides by 10.
RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.
21
93
9213 x
x963
x79 9
RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.
10
5
4
RATIOS & PROPORTIONS
Find the missing numbers to make the following proportions.
10
5
4
5410 x2010 x
10 10 2x
If 5 ounces of a medicine must be mixed with 8 ounces of water, how many ounces of medicine would be mixed with 36 ounces of water?
If 5 ounces of a medicine must be mixed with 8 ounces of water, how many ounces of medicine would be mixed with 36 ounces of water?
Solution Let m represent how much medicine would be needed.
5
8 3
Medicine needed How much medicine
Ounces of water Ounces of 6 water
m
5 36 8 m 8
8
36
8
5 m
22.5 m
22.5 ounces of medicine would be needed.
m8180 8 8
Find the cross products. Multiply both sides of the proportion by the denominator of the fraction containing the unknown
Jane drives her delivery van 800 miles in 3 days. At this rate, how far will she drive in 15 days?
Jane drives her delivery van 800 miles in 3 days. At this rate, how far will she drive in 15 days?
Jane would drive 4000
Miles in 15 days
d800
3 15
Find the cross products. Multiply both sides of the proportion by the denominator of the fraction containing the unknown
Distance in 3 days
Distance in 15 days
time time
800 x 15 = 3d
3 3 800 x 15 = 12000
12000 3
d=4000
Definition Percent can be defined as “of one hundred.”
a) Find decimal notation by division.b) Convert the decimal notation to percent notation. To do so, multiply by 100 to move the decimal point two places to the right, and write a % symbol.
5.
80.625
8 5.000
48
20
16
40
40
0
162.5% o
50.625 r 62 %
28
Slide 4- 34
Translate: What is 19% of 82?
What is 19% of 82? | | | | a = 19% x 82 19/100 = .19 .19 x 82 = 15.58
The sales tax rate in Ohio is 6%. How much tax is charged on the purchase of 4 books at $15.95 each? What is the total price?
Slide 4- 42
The sales tax rate in Ohio is 6%. How much tax is charged on the purchase of 4 books at $15.95 each? What is the total price?Solution a) We first find the cost of the books. 4 × $15.95 = $63.80b) The sales tax on items costing $63.80 is Sales tax rate × Purchase price 0.06 × $63.80 or $3.83