Solve Proportions. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are...
-
Upload
jared-gilmore -
Category
Documents
-
view
218 -
download
4
Transcript of Solve Proportions. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are...
Solve Proportions
CROSS PRODUCT RULE
In the proportion = , the cross products,
a · d and b · c are equal.
ab
cd
EX 1)= 2
412
44uses
1. Prove proportionality
EX 2) = 57
35
2521 2. Disprove proportionality3. Compare fractions
EX 3) 57
35
2521 <<
You can use the cross product rule to solve proportions with variables. Which help you find missing values.
15m
15m15
= 4515
m = 3
Set up proportion.
Cross Multiply.
Divide each side by 15 to isolate the variable.
= m5
915
This is called the extreme and means ratio.
= 45
EX 4)
• Unit rate : a rate whose denominator is 1. It may not always look like a number; watch for words like per or each.
milesEX 5) 200 / 4 hours
How many miles traveled per hour?
Step 2: set up proportion=
Step 1: highlight rates
Miles Miles
Hours Hour
200
4
X1 Step 3: Cross multiply
and divide
200 X 1 = 200 ÷ 4 = 50 X = 50 mph
gallonsmilesEX 6) 160
/ 5
How many miles per gallon?
Step 2: set up proportion=Step 1: highlight rates
Miles Miles
Gal Gal
160
5
X1 Step 3: Cross multiply
and divide
160 X 1 = 160 ÷ 5 = 32 X = 32 mpg
Length
12 inches (in)= 1 foot (ft)3 feet = 1 yard (yd)
5,280 feet = 1 mile (mi)
Weight
16 ounces (oz) = 1 pound (lb) 2000 pounds = 1 ton
Capacity
8 fluid ounces (fl oz) = 1 cup (c)2 cups = 1 pint (pt)
2 pints = 1 quart (qt)4 quarts = 1 gallon (gal)
Convert 5,000 pounds to tons.
1: Set up Proportion= pounds tons
2,000 1
2000x = 5,000
5,000 m x
x = 2.5
EX 7)
2: Solve Proportion
Cross multiply
Divide
Convert 24 pints to cups.
= cups pints
2 1
1 • c = 2 • 24
c = 48
c 24
EX 8)
Sue needs 9 cups of flour to make 16 batches of cookies. How much flour does she need if she only wants to make a fourth of her recipe.
Set up proportion.
Cross Multiply.
Divide
=cups Cups9
16 XX
batches batches4
9 X 4 = 36
36 ÷ 16 = 416 2 1
4 2 = Cups
Determine Ratios.
EX 5)
Ralph has a paper clip with a mass of 9g and a volume of 3cm3. What is the density?
Set up proportion.
Cross Multiply.
Divide
=Mass mass9 g
3 cm 3
X
1Volume cm3
9 X 1 = 9
9 ÷ 3 =
Determine Ratios.
EX 6)
Density – is a comparison of how much mass is in a unit of volume. Written – mass / unit volume
3
Density = 3g/cm3
A 12 oz sport drink cost $1.08 and a 16 oz. sport drink cost $1.28. Which drink is the better buy?
Step 2: set up proportion
=
Step 1: highlight rates
oz
$$
oz16
1.28 X1 Step 3: Cross multiply
and divide
EX. 7)
Since you are comparing you will set up two proportions
=oz
$
oz12
1.08 X1
$
Solve
Solve
161.28
12 oz drink that cost $1.08 is $0.09 / oz
$1.08 X 1 = 1.08 ÷ 121.08 12.0 0 9
Back
16 oz drink that cost $1.28 is $0.08 / oz
$1.28 X 1 = 1.28 ÷ 16.0 0 8
The better buy is the cheaper drinkThe 16 oz is the better buy
A car travels 480 miles in 8 hours and uses 16 gallons of gas. What is the average speed? ( miles per hour)What is the average gas mileage? ( miles per gallon)
Try this on your own
Notes start here
Solve Proportions
CROSS PRODUCT RULE
In the proportion = , the cross products,
a · d and b · c are equal.
ab
cd
EX 1)= 2
412
uses1.
EX 2) = 57
35
2. 3.
EX 3)
You can use the cross product rule to solve proportions with variables. Which help you find missing values.
=
=
1.
2.
3.
= m5
915
This is called the extreme and means ratio.
=
EX 4)
How many miles traveled per hour?
miles
• Unit rate : a rate whose denominator is 1. It may not always look like a number; watch for words like per or each.
EX 5) 200
/ 4 hours
Step 2:
=
Step 1:
Step 3:
gallonsmilesEX 6) 160
/ 5
How many miles per gallon?
=
Convert 5,000 pounds to tons.
1: Set up = pounds tons
=
=
EX 7)
2: _____ Proportion
C
D
Convert 24 pints to cups.
= cups pints
=
=
EX 8)
Sue needs 9 cups of flour to make 16 batches of cookies. How much flour does she need if she only wants to make a fourth of her recipe.
=
EX 9)
Ralph has a paper clip with a mass of 9g and a volume of 3cm3. What is the density?
=
EX 10)
Density – is a comparison of how much mass is in a unit of volume. Written – mass / unit volume
A 12 oz sport drink cost $1.08 and a 16 oz. sport drink cost $1.28. Which drink is the better buy?
=
EX 11)
=
A car travels 480 miles in 8 hours and uses 16 gallons of gas. What is the average speed? ( miles per hour)What is the average gas mileage? ( miles per gallon)
Try this on your own