Solving Problems Using Proportional Reasoning

Proportional Problem Solving

A method for solving problems by maintaining proportional relationships between variables. It involves using ratios and proportions to find solutions.

Understanding Proportions

• Proportions are a way to compare two or more quantities.
• They are expressed as ratios or fractions.
• Proportions help solve problems involving scaling, equivalent ratios, and direct variation.
• They are used in various fields like mathematics, science, and finance.

Multiple Choice

What are proportions used for?

• Comparing quantities

• Solving scaling problems

• Analyzing direct variation

• Calculating finance ratios

Proportions: Comparing Quantities

Proportions are used to compare quantities. They help us understand the relationship between different amounts. By using proportions, we can determine if two quantities are equal or if one is larger or smaller than the other. Proportions are a fundamental concept in mathematics and are used in various fields such as science, finance, and engineering.

Multiple Choice

Janet is writing a book. She writes 3 pages every 2 days. If she continues at the same pace, how long will it take her to write a 400-page book?

Which proportion could be used to solve this problem?

• $$\frac{3}{x}=\frac{400}{2}$$
  

• $$\frac{x}{400}=\frac{3}{2}$$

• $$\frac{x}{2}\ =\ \frac{3}{400}$$

• $$\frac{3}{2}=\frac{400}{x}$$

Math Response

Solve for x

$$\frac{3}{4}=\frac{x}{8}$$  

Type Number Only!

Type answer here

Correct Answer: 6

Deg^°

Rad

Math Response

Solve for a

$$\frac{a}{45}=\frac{3}{15}$$  

Type number only!

Type answer here

Correct Answer: 9

Deg^°

Rad

Multiple Choice

Solve the proportion below:

• 42
• 6
• 2
• 28

Multiple Choice

• 3
• 5.3
• 1.08
• 27

Multiple Choice

Solve the proportion.

• 1
• 3
• 6
• 5

Multiple Choice

Solve for x 

• x = 6
• x = 25
• x = 28
• x = 17

Multiple Choice

Solve the proportion:

$$\frac{c}{12}\ =\ \frac{5}{3}$$  

• $$c=36$$

• $$c=7.2$$  

• $$c\ =\ 20$$  

• $$c\ =\ 12$$  

Multiple Choice

Solve for x 

• x = 16
• x = 28
• x = 1/26
• x = 26

Math Response

Solve the proportion below:

$$\frac{1.6}{21}\ =\ \frac{8}{d}$$

Type number only. Remember to simplify

Type answer here

Correct Answer: 105

Deg^°

Rad

Multiple Choice

What is the missing number for this proportion?

• 1
• 3
• 9

Multiple Choice

What is the new equation after you cross multiply?

• 4 $$\cdot$$  x = 25

• 25x

• 5 $$\cdot$$  x = 20

• 4/25