Download Ch. 6.3 Proportions Ratio – a fraction, or quotient of two quantities

Ch. 6.3 Proportions
Ratio – a fraction, or quotient of two quantities with the same units.
A ratio of length to width would be calculated by finding
length/width (also can be calculated by doing length ÷ width)
A ratio of 16 oz to 2 lbs would first have to be converted to the
same units.
16 oz = 1 lb.
16 oz to 2 lbs = 1 lb to 2 lbs = 1 lb / 2 lbs = ½
Rate – a ratio of two quantities with different units.
60 miles/ 2 hours , $500/2 weeks, etc…
A unit rate is a rate with 1 as the denominator.
Example 1 Find the unit rate of miles per hour.
60miles/2 hours can be converted to a unit rate by doing the division
60/2 = 30.
60 miles /2 hours = 30 miles/1 hour = 30mph
Example 2 Find the unit cost of a pound of fruit
$3 for 2 pounds of fruit.
$3
2lbs
3 $
2 lb
1.5
$
lb
1.5 $
1 lbs
$1.50
lb
$1.50 per pound
Proportion – a statement with two ratios set equal to one another.
Ratios are “proportional” if they are equal.
1
2
136
272
How do we know they are equal? Cross-multiply to prove it.
2*136 = 272 ? Yes.
Solving Proportions
Use cross-multiplication to solve an equation where one
fraction equals another.
3
7
12
x
3 x 12 7 84
84
x
28
3
Check: Put x = 28 into the original proportion.
3 12
7 28
Are these ratios equivalent ? Do cross - multiplying to check.
3 28 12 7
84 84
Example 3
a)
21 n
12 8
If possible, simplify the fractions first to make the cross - multiplication easier.
21 7
12 4
7 n
4 8
7 8 4n
56 4n
56 4n
4
4
14 n
Check : put n 14 back into the original proportion.
21 14
12 8
21 8 12 14
If you don' t want to do the math,
break all the numbers down into their
prime - factored form and compare.
3 7 2 2 2 2 2 3 2 7
When doing application problems, make sure to write down the units that go
along with the numbers.
Example 5
Yusef can wash 6 windows in 21 minutes. How many minutes will it take him to
wash 10 windows?
What are we being asked to find? How many minutes.
Let m = number of minutes to wash 10 windows.
Put given info into a mathematical proportion.
6 windows in 21 minutes
6 windows
21 minutes
10 windows in ? Minutes.
10 windows
Let m = the unknown number of minutes. m minutes
Set up a proportion and solve it.
6 windows 10 windows
21 minutes m minutes
6 10
21 m
Simplify, then solve
2 10
7 m
Cross - multiplication :
2m 7 10
2m 70
2m 70
2
2
m 35
Check :
6 10
21 35
6 35 21 10
210 210
UNIT ABBREVIATIONS
Money
Volume
dollars $
cents ¢ or $0._ _
teaspoon tsp
tablespoon tbsp
Time
cup c
years yr
pint pt
months wks
quart qt
weeks wks
gallon gal
days dys
liter l
hours hr
milliliter ml
minutes min
cubic feet ft3
seconds sec or s
Area
square miles mi2
Length
miles mi
square feet ft2
yards yd
Weight
feet ft
inches in. or “
meters m
pounds lb
ounces oz
grams g
kilometers km
kilograms kg
Rates are usually stated with the word “per” in between two
quantities with different units.
Miles per Hour = miles/hours = mph
Feet per second = feet/seconds = ft/s
Dollars per pound = $/lb
Dollars per ounce = $/oz
Inches per week = in./wk