Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d...
Transcript of Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d...
![Page 1: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/1.jpg)
Solve Proportional Relationships
![Page 2: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/2.jpg)
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 <<
![Page 3: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/3.jpg)
Use the cross products to solve proportions with variables. Which help you find missing values.
m = 3
Set up proportion.
Cross Multiply.
Divide by 15
= m5
915
EX 4) Step 1
Step 2
Step 39 x 5= 4545 ÷ 15
![Page 4: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/4.jpg)
• 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
![Page 5: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/5.jpg)
The ratio of students who ordered pizza to those that did not order pizza was 5 : 3. How many students would have pizza if 24 students ordered.
EX 6)
+ = not orderedordered Total ordered
=pizza pizza5
8 24
Xtotal total
X = 15
![Page 6: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/6.jpg)
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.
=cups Cups9
16 XX
batches batches4
9 X 4 = 36
36 ÷ 16 = 416 2 1
4 2 = Cups
EX 7)
![Page 7: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/7.jpg)
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 8)
Since you are comparing you will set up two proportions
=oz
$
oz12
1.08 X1
$
X = 0.09
X = 0.08The 16 oz. sport drink is the better buy?
![Page 8: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/8.jpg)
Essential Question
How do you solve proportions?
![Page 9: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/9.jpg)
Date _____________
Solve Proportional Relationships
![Page 10: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/10.jpg)
CROSS PRODUCT RULE
In the proportion = , the cross products,
a · d and b · c are equal.
ab
cd
EX 1) uses1.
EX 2)
2. 3.
EX 3)
![Page 11: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/11.jpg)
You can use the cross product rule to solve proportions with variables. Which help you find missing values.
=
=
1.
2.
3. =
EX 4)
![Page 12: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/12.jpg)
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) / hours
Step 2:
=
Step 1:
Step 3:
![Page 13: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/13.jpg)
The ratio of students who ordered pizza to those that did not order pizza was : . How many students would have pizza if students ordered.
EX 6)
+ =
=
![Page 14: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/14.jpg)
Sue needs cups of flour to make batches of cookies. How much flour does she need if she only wants to make a fourth of her recipe.
=
EX 7)
![Page 15: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/15.jpg)
A 12 oz sport drink cost $1.08 and a 16 oz. sport drink cost $1.28. Which drink is the better buy?
=
EX 8)
=
![Page 16: Solve Proportional Relationships. CROSS PRODUCT RULE In the proportion =, the cross products, a · d and b · c are equal. abab cdcd EX 1) = 2424 1212 44.](https://reader036.fdocuments.us/reader036/viewer/2022083009/5697bfbe1a28abf838ca26fd/html5/thumbnails/16.jpg)
Essential Question
How do you solve proportions?