Proportions

PROPORTIONS 🙌

6th Grade Math

📚 Learning Objectives

• Know: What a ratio is and the 3 ways to write a ratio

• Understand: The two methods to identifying proportions

• Do: Find the missing number of a proportion

Multiple Choice

What is a ratio?

• A comparison of two or more numbers by division

• A race between two or more cars

Multiple Select

What are the three ways to write a ratio?

• word form 'to'

• word form 'and'

• fraction form /

• question mark form ?

• colon form :

LESSON REVIEW 😎

• A proportion is an equation of two equivalent ratios.

• We learned two ways tell whether two ratios form a proportion.

✅ METHOD #1

To tell whether two ratios are proportional,
you simplify both ratios and see if they are equal.

Equal ( $=$ ) .................. PROPORTIONAL
Not Equal ( $\ne$ ) .................... NOT PROPORTIONAL

SIMPLIFYING METHOD

Multiple Choice

Using the simplifying method, tell whether the ratios form a proportion.

 $\frac{3}{12}\ ,\ \frac{2}{8}$  

• Proportional 

• Not Proportional

Multiple Choice

Using the simplifying method, tell whether the ratios form a proportion.

 $\frac{21}{28}\ ,\ \frac{75}{100}$  

• Proportional 

• Not Proportional

Multiple Choice

Using the simplifying method, tell whether the ratios form a proportion.

 $\frac{5}{10}\ ,\ \frac{3}{8}$  

• Proportional 

• Not Proportional

Poll

Do you understand how the SIMPLIFYING METHOD works? 😮

• YES 😁

• NO 😖

✅ METHOD #2

To tell whether two ratios are proportional,
you multiply the diagonals of the ratios and see if their cross products are equal.

Equal ( $=$ ) .................. PROPORTIONAL
Not Equal ( $\ne$ ) .................... NOT PROPORTIONAL

CROSS PRODUCT METHOD

Multiple Choice

Using the cross product method, tell whether the ratios form a proportion.

 $\frac{8}{3}\ ,\ \frac{5}{2}$  

• Proportional 

• Not Proportional

Multiple Choice

Using the cross product method, tell whether the ratios form a proportion.

 $\frac{6}{9}\ ,\ \frac{5}{7}$  

• Proportional 

• Not Proportional

Multiple Choice

Using the cross product method, tell whether the ratios form a proportion.

 $\frac{6}{4}\ ,\ \frac{9}{6}$  

• Proportional 

• Not Proportional

Poll

Do you understand how the 'CROSS PRODUCT' method works? 😮

• YES 😁

• NO 😖

SOLVING PROPORTIONS USING THE 'CROSS PRODUCT' METHOD

Pre-Algebra 😎

Multiple Choice

Solve the proportion using cross product.

  $\frac{y}{4}=\frac{4}{8}\ \$  

•  $y=2$  

•  $y=4$  

•  $y=8$  

•  $y=16$  

Multiple Choice

Solve the proportion using cross product.

  $\frac{7}{12}=\frac{21}{a}\ \$  

•  $a=7$  

•  $a=21$  

•  $a=36$  

•  $a=45$  

Multiple Choice

Solve the proportion using cross product.

  $\frac{4}{5}=\frac{m}{25}\ \$  

•  $m=15$  

•  $m=20$  

•  $m=25$  

•  $m=30$  

Multiple Choice

Solve the proportion using cross product.

  $\frac{3}{v}=\frac{18}{42}\ \$  

•  $v=3$  

•  $v=6$  

•  $v=7$  

•  $v=9$  

Multiple Choice

The speed limit on Guam is 35 miles per hour.

You drive a total of 5 hours from Yigo to Merizo and back.

How many miles did the trip take?

• 35 miles per 5 hours

• 75 miles per 5 hours

• 105 miles per 5 hours

• 140 miles per 5 hours

• 175 miles per 5 hours

Multiple Choice

A small plane is traveling at a rate of 40 meters for every 2 seconds. How many meters will the plane travel in 20 seconds?

• 100 meters

• 200 meters

• 300 meters

• 400 meters

Multiple Choice

For every dollar Ms. Cruz spends at Ross, she earns two customer points in her Ross card. If Ms. Cruz spends $225 at Ross, how many customer points will she earn in her card?

• 300 points

• 350 points

• 400 points

• 450 points