What is Ratios, Proportions, and Percents?

Master ratio problems and percent calculations on SAT

How can I study Ratios, Proportions, and Percents effectively?

Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 21 problems provided, checking solutions as you go. Regular review and active practice are key to retention.

Is this Ratios, Proportions, and Percents study guide free?

Yes — all study notes, flashcards, and practice problems for Ratios, Proportions, and Percents on Study Mondo are free to access. No account is needed.

What course covers Ratios, Proportions, and Percents?

Ratios, Proportions, and Percents is part of the SAT Prep course on Study Mondo, specifically in the Problem Solving and Data Analysis section. You can explore the full course for more related topics and practice resources.

Are there practice problems for Ratios, Proportions, and Percents?

Yes, this page includes 21 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Ratios, Proportions, and Percents

Loading…

Situation	Multiplier
20% increase	$\times 1.20$
15% decrease	$\times 0.85$
8% sales tax	$\times 1.08$
30% discount	$\times 0.70$

Ratios, Proportions, and Percents | Study Mondo

Fraction	Decimal	Percent
$\frac{1}{2}$	0.50	50%
$\frac{1}{3}$	0.333...	33.3%
$\frac{1}{4}$	0.25	25%
$\frac{1}{5}$	0.20	20%
$\frac{1}{8}$	0.125	12.5%
$\frac{3}{4}$	0.75	75%
$\frac{2}{3}$	0.667...	66.7%

📚 Practice Problems

1Problem 1easy

❓ Question:

What is 15% of 200?

💡 Show Solution

Solution:

Convert to decimal and multiply: $0.15 \times 200 = 30$

Answer: $30$

SAT Tip: 15% = 0.15 (move decimal two places left)

2Problem 2easy

❓ Question:

What is 15% of 200?

💡 Show Solution

Solution:

Convert to decimal and multiply: $0.15 \times 200 = 30$

Answer: $30$

3Problem 3medium

❓ Question:

A price increased from $\$ 80 $to$ $100$. What is the percent increase?

💡 Show Solution

Solution:

Use percent change formula: $\text{Percent Change} = \frac{100 - 80}{80} \times 100\%$

4Problem 4medium

❓ Question:

A price increased from $\$ 80 $to$ $100$. What is the percent increase?

💡 Show Solution

Solution:

Use percent change formula: $\text{Percent Change} = \frac{100 - 80}{80} \times 100\%$

5Problem 5hard

❓ Question:

In a class, the ratio of boys to girls is $3:5$ . If there are 40 students total, how many are girls?

💡 Show Solution

Solution:

Total ratio parts: $3 + 5 = 8$

6Problem 6hard

❓ Question:

In a class, the ratio of boys to girls is $3:5$ . If there are 40 students total, how many are girls?

💡 Show Solution

Solution:

Total ratio parts: $3 + 5 = 8$

7Problem 7easy

❓ Question:

The ratio of boys to girls in a class is $3:5$ . If there are 24 students in the class, how many girls are there?

💡 Show Solution

Step 1: Total parts = $3 + 5 = 8$

8Problem 8easy

❓ Question:

The ratio of boys to girls in a class is $3:5$ . If there are 24 students in the class, how many girls are there?

💡 Show Solution

Step 1: Total parts = $3 + 5 = 8$

9Problem 9easy

❓ Question:

The ratio of boys to girls in a class is $3:5$ . If there are 24 students in the class, how many girls are there?

💡 Show Solution

Step 1: Total parts = $3 + 5 = 8$

10Problem 10medium

❓ Question:

A shirt originally priced at $45 is on sale for 20% off. Sales tax of 8% is applied after the discount. What is the total cost?

💡 Show Solution

Step 1: Apply the 20% discount using a multiplier: $\$45 \times 0.80 = \$36$

Step 2: Apply 8% sales tax:

11Problem 11medium

❓ Question:

A shirt originally priced at $45 is on sale for 20% off. Sales tax of 8% is applied after the discount. What is the total cost?

💡 Show Solution

Step 1: Apply the 20% discount using a multiplier: $\$45 \times 0.80 = \$36$

Step 2: Apply 8% sales tax:

12Problem 12medium

❓ Question:

A shirt originally priced at $45 is on sale for 20% off. Sales tax of 8% is applied after the discount. What is the total cost?

💡 Show Solution

Step 1: Apply the 20% discount using a multiplier: $\$45 \times 0.80 = \$36$

Step 2: Apply 8% sales tax:

13Problem 13medium

❓ Question:

A population increased from 12,000 to 15,600 over 5 years. What was the percent increase?

💡 Show Solution

Use the percent change formula: $\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

14Problem 14medium

❓ Question:

A population increased from 12,000 to 15,600 over 5 years. What was the percent increase?

💡 Show Solution

Use the percent change formula: $\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

15Problem 15medium

❓ Question:

A population increased from 12,000 to 15,600 over 5 years. What was the percent increase?

💡 Show Solution

Use the percent change formula: $\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100$

16Problem 16hard

❓ Question:

After a 15% discount, a laptop costs $680. What was the original price?

💡 Show Solution

Step 1: A 15% discount means the customer pays 85% of the original price. $\text{Original} \times 0.85 = 680$

Step 2: Solve for the original price:

17Problem 17hard

❓ Question:

After a 15% discount, a laptop costs $680. What was the original price?

💡 Show Solution

Step 1: A 15% discount means the customer pays 85% of the original price. $\text{Original} \times 0.85 = 680$

Step 2: Solve for the original price:

18Problem 18hard

❓ Question:

After a 15% discount, a laptop costs $680. What was the original price?

💡 Show Solution

Step 1: A 15% discount means the customer pays 85% of the original price. $\text{Original} \times 0.85 = 680$

Step 2: Solve for the original price:

19Problem 19expert

❓ Question:

The value of an investment increases by 10% in the first year and decreases by 10% in the second year. If the initial investment was $1,000, what is the value after two years, and what is the net percent change?

💡 Show Solution

Step 1: After year 1 (10% increase): $\$1{,}000 \times 1.10 = \$1{,}100$

20Problem 20expert

❓ Question:

💡 Show Solution

Step 1: After year 1 (10% increase): $\$1{,}000 \times 1.10 = \$1{,}100$

21Problem 21expert

❓ Question:

💡 Show Solution

Step 1: After year 1 (10% increase): $\$1{,}000 \times 1.10 = \$1{,}100$

\$36 \times 1.08 = \$38.88

\$36 \times 1.08 = \$38.88

\$36 \times 1.08 = \$38.88

Original = \frac{680}{0.85} = $ 800

\text{Original} = \frac{680}{0.85} = \$800

Original = \frac{680}{0.85} = $ 800

\text{Original} = \frac{680}{0.85} = \$800

Original = \frac{680}{0.85} = $ 800

\text{Original} = \frac{680}{0.85} = \$800

Ratios, Proportions, and Percents

Try the Interactive Version!

Ratios, Proportions, and Percents on the SAT

Why This Topic Matters

Ratios

Ratio Problems Strategy

Part-to-Part vs. Part-to-Whole

Proportions

Setting Up Proportions

Unit Conversions

Percents

Key Formulas

Percent Change

Multiplier Method (SAT Shortcut!)

Successive Percent Changes

SAT Question Types

Type 1: Direct Proportion

Type 2: Percent of a Number

Type 3: Percent Change

Type 4: Working Backward

Type 5: Scale and Maps

Common SAT Mistakes

Conversion Quick Reference

📚 Practice Problems

1Problem 1easy

❓ Question:

2Problem 2easy

❓ Question:

3Problem 3medium

❓ Question:

4Problem 4medium

❓ Question:

5Problem 5hard

❓ Question:

6Problem 6hard

❓ Question:

7Problem 7easy

❓ Question:

8Problem 8easy

❓ Question:

9Problem 9easy

❓ Question:

10Problem 10medium

❓ Question:

11Problem 11medium

❓ Question:

12Problem 12medium

❓ Question:

13Problem 13medium

❓ Question:

14Problem 14medium

❓ Question:

15Problem 15medium

❓ Question:

16Problem 16hard

❓ Question:

17Problem 17hard

❓ Question:

18Problem 18hard

❓ Question:

19Problem 19expert

❓ Question:

20Problem 20expert

❓ Question:

21Problem 21expert

❓ Question:

Practice Lab

Practice with Flashcards

Browse All Topics

📌 Related Topics in Problem Solving and Data Analysis

❓ Frequently Asked Questions