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Master Percentages for the Digital SAT

🎯 Digital SAT Math • Percentages

Master Percentages for the Digital SAT

Percentages are simply another way to write fractions. This Digital SAT lesson focuses on percent conversions, decimal conversions, and finding percentages of quantities that frequently appear in College Board SAT Math practice tests. On the SAT, many problems become much easier when you can switch naturally between fractions, decimals, and percentages. This lesson will help you recognize equivalent forms, avoid common percentage traps, and solve confidently without guessing.

⏩

Quick Check (45 Seconds)

Can you answer these without a calculator?

  1. Write 50% as a fraction.
  2. Write 25% as a decimal.
  3. Write 0.8 as a percentage.
  4. Which is greater: 40% or 2/5?
  5. What is 10% of 80?
If these feel easy, skim the explanations and spend more time on the SAT Practice section.
📋

Essential Rules

A percent simply means “out of 100.”

The word percent literally means per hundred.

For example:

$$50\% = \frac{50}{100} = \frac12$$

The number has not changed. Only the way we write it has.

🧠

First Thought

Whenever you see a percentage, ask yourself:

Would this problem become easier as a fraction or a decimal?

Strong SAT students choose the representation that makes the work easiest.
📊

Three Ways to Write the Same Number

Fraction Decimal Percent
1/20.550%
1/40.2525%
3/40.7575%
1/50.220%
2/50.440%
3/50.660%
4/50.880%
Notice something? You already know almost everything in this table. The only new language is the percentage.
🔄

Three Conversion Methods

Percent → Decimal

Divide by 100.

$$75\% \rightarrow 0.75$$

Decimal → Percent

Multiply by 100.

$$0.37 \rightarrow 37\%$$

Fraction → Percent

$$\frac34 \rightarrow 0.75 \rightarrow 75\%$$
$$\frac14 = \frac{25}{100} = 25\%$$
🌟

SAT Habit #8

  • Sometimes percentages are easiest.
  • Sometimes fractions are easier.
  • Sometimes decimals save time.
The strongest SAT students switch naturally between all three.
🎯

Guided Example 1 — Percent to Decimal

Convert 35% to a decimal.

$$35\% = \frac{35}{100} = 0.35$$
Answer: 0.35
🎯

Guided Example 2 — Decimal to Percent

Convert 0.125 to a percentage.

$$0.125 \times 100 = 12.5$$
Answer: 12.5%
🎯

Guided Example 3 — Finding a Percentage of a Number

What is 25% of 80?

$$25\% = \frac14$$
$$\frac14 \text{ of } 80 = 20$$
$$0.25 \times 80 = 20$$
Both methods are equally correct. Choose whichever feels more natural.
## SATMath800 — Percentages Chapter (Part 2) Paste this **directly below Part 1**. This part follows the uploaded document and continues with: * Quick Practice * SAT-Style Practice Set A * Full Solutions * SAT Strategy Spotlight — “`html
✏️

Quick Practice

Try these before looking at the answers.

Question Answer
Convert 60% to a decimal. 0.6
Convert 0.45 to a percentage. 45%
Convert 3/5 to a percentage. 60%
Convert 12.5% to a decimal. 0.125
📝

SAT-Style Practice Set A

These questions are designed to feel similar to the short calculator and non-calculator percentage questions that appear in recent Digital SAT Math practice tests.

Question 1

What decimal is equivalent to 62%?

  • A) 0.062
  • B) 0.62
  • C) 6.2
  • D) 62

Question 2

What percentage is equivalent to 0.375?

  • A) 3.75%
  • B) 37.5%
  • C) 375%
  • D) 0.375%

Question 3

Which fraction is equivalent to 40%?

  • A) 1/5
  • B) 2/5
  • C) 3/5
  • D) 4/5

Question 4

What is 15% of 200?

  • A) 15
  • B) 20
  • C) 30
  • D) 40
✅

Solutions

Question 1 Solution

Percent means divide by 100.

$$62\% = \frac{62}{100} = 0.62$$
Answer: B) 0.62

Question 2 Solution

Multiply by 100.

$$0.375 \times 100 = 37.5$$
Answer: B) 37.5%

Question 3 Solution

Convert the percent to a fraction.

$$40\% = \frac{40}{100}$$

Simplify by dividing by 20.

$$\frac{40}{100} = \frac25$$
Answer: B) 2/5

Question 4 Solution

Convert 15% to a decimal.

$$15\% = 0.15$$

Multiply by 200.

$$0.15 \times 200 = 30$$
Answer: C) 30
💡

SAT Strategy Spotlight

Notice that every question above can be solved using the same pattern:

$$\text{Percent} \leftrightarrow \text{Decimal} \leftrightarrow \text{Fraction}$$

The SAT often hides a simple idea behind unfamiliar wording.

Fast SAT Habit: Whenever you see a percentage, immediately think “divide by 100”. This single habit prevents many common SAT errors.
## SATMath800 — Percentages Chapter (Part 3) Paste this **directly below Part 2**. This part follows the uploaded document and continues with: * Finding a Percentage of a Quantity * Guided Examples 4–6 * Mental Math Shortcuts * SAT Strategy Spotlight * Quick Practice Set B — “`html
🔢

Finding a Percentage of a Quantity

This is one of the most common SAT percentage tasks.

General Formula

$$\text{Part} = \text{Percent} \times \text{Whole}$$

For SAT problems, convert the percent to a decimal or fraction first.

🎯

Guided Example 4 — Using a Decimal

What is 18% of 250?

Step 1: Convert the percent to a decimal.

$$18\% = 0.18$$

Step 2: Multiply by the whole.

$$0.18 \times 250$$
$$= 45$$
Answer: 45
🎯

Guided Example 5 — Using a Fraction

What is 75% of 64?

Step 1: Convert the percent to a fraction.

$$75\% = \frac34$$

Step 2: Multiply.

$$\frac34 \times 64$$

Divide first:

$$64 \div 4 = 16$$

Then multiply:

$$16 \times 3 = 48$$
Answer: 48
🎯

Guided Example 6 — SAT Word Problem

A school has 320 students. If 35% of them participate in a club, how many students participate?

Step 1: Convert the percent.

$$35\% = 0.35$$

Step 2: Multiply by the total number of students.

$$0.35 \times 320$$

A quick way:

$$35 \times 32 = 1120$$

Then place the decimal correctly:

$$0.35 \times 320 = 112$$
Answer: 112 students
⚡

Mental Math Shortcuts

The SAT often rewards recognizing common percentage patterns.

Percent Fraction Shortcut
50% 1/2
25% 1/4
75% 3/4
20% 1/5
10% divide by 10
5% half of 10%
Example:
$$5\% \text{ of } 240$$
First find 10%:
$$24$$
Then take half:
$$12$$
💡

SAT Strategy Spotlight

Many students automatically use decimals for every percentage problem.

Sometimes fractions are much faster:

$$25\% \text{ of } 84$$

Decimal method:

$$0.25 \times 84$$

Fraction method:

$$\frac14 \times 84 = 21$$
SAT Rule: If the percent is 25%, 50%, or 75%, check whether the fraction form makes the arithmetic easier.
✏️

Quick Practice Set B

Try these on your own before checking the answers in the next section.

  1. What is 30% of 150?
  2. What is 12% of 250?
  3. What is 75% of 28?
  4. What is 5% of 360?
Answers: 45, 30, 21, 18
## SATMath800 — Percentages Chapter (Part 4) Paste this **directly below Part 3**. This part follows the uploaded document and continues with: * SAT-Style Practice Set B * Full Solutions * Challenge Problem * Common SAT Trap Alert * Transition to Percent Increase and Decrease — “`html
📝

SAT-Style Practice Set B

These questions focus on finding a percentage of a quantity, which is one of the most frequently tested percentage skills on the Digital SAT.

Question 5

What is 30% of 150?

  • A) 30
  • B) 45
  • C) 50
  • D) 60

Question 6

What is 12% of 250?

  • A) 12
  • B) 25
  • C) 30
  • D) 32

Question 7

What is 75% of 28?

  • A) 18
  • B) 20
  • C) 21
  • D) 24

Question 8

What is 5% of 360?

  • A) 15
  • B) 18
  • C) 20
  • D) 36
✅

Solutions

Question 5 Solution

$$30\% = 0.30$$
$$0.30 \times 150 = 45$$
Answer: B) 45

Question 6 Solution

$$12\% = 0.12$$
$$0.12 \times 250 = 30$$
Answer: C) 30

Question 7 Solution

Use the fraction shortcut:

$$75\% = \frac34$$
$$\frac34 \times 28$$
$$28 \div 4 = 7$$
$$7 \times 3 = 21$$
Answer: C) 21

Question 8 Solution

Use the mental math shortcut.

First find 10%:

$$10\% \text{ of } 360 = 36$$

Then take half:

$$5\% \text{ of } 360 = 18$$
Answer: B) 18
🧩

Challenge Problem

A jacket costs $240. A store advertises a 25% discount. What is the amount of the discount?

Step 1: Convert 25% to a fraction.

$$25\% = \frac14$$

Step 2: Find one fourth of 240.

$$240 \div 4 = 60$$
Discount Amount: $60

Notice that the question asked for the discount, not the final price.

⚠️

Common SAT Trap

Students often confuse these two questions:

Question A: What is 25% of 240?

$$60$$

Question B: What is the price after a 25% discount?

$$240 – 60 = 180$$
SAT Tip: Read the final sentence carefully. Determine whether the question asks for the part, the discount amount, or the new total.
📈

What Comes Next?

So far, we have focused on:

  • Converting between percentages, decimals, and fractions
  • Finding a percentage of a quantity
  • Using mental math shortcuts for common percentages

The next major SAT skill is Percent Increase and Percent Decrease. These problems appear frequently in:

  • price changes,
  • population growth,
  • salary changes,
  • test score changes,
  • and data analysis questions.
Before moving on, make sure you can quickly solve problems such as 15% of 200, 75% of 64, and 5% of 360 without writing many steps.
## SATMath800 — Percentages Chapter (Part 5) Paste this **directly below Part 4**. This part follows the uploaded document and continues with: * Percent Increase * Percent Decrease * Guided Examples 7–10 * SAT Trap Alert * Quick Practice Set C — “`html
📈

Percent Increase

A percent increase compares the amount of increase to the original amount.

Formula

$$\text{Percent Increase} = \frac{\text{Increase}}{\text{Original}} \times 100\%$$
🎯

Guided Example 7 — Basic Increase

A price increases from $50 to $65.

Step 1: Find the increase.

$$65 – 50 = 15$$

Step 2: Divide by the original value.

$$\frac{15}{50} = 0.3$$

Step 3: Convert to a percentage.

$$0.3 \times 100\% = 30\%$$
Answer: 30% increase
📉

Percent Decrease

A percent decrease compares the amount of decrease to the original amount.

Formula

$$\text{Percent Decrease} = \frac{\text{Decrease}}{\text{Original}} \times 100\%$$
🎯

Guided Example 8 — Basic Decrease

A population decreases from 200 to 170.

Step 1: Find the decrease.

$$200 – 170 = 30$$

Step 2: Divide by the original value.

$$\frac{30}{200} = 0.15$$

Step 3: Convert to a percentage.

$$0.15 \times 100\% = 15\%$$
Answer: 15% decrease
🎯

Guided Example 9 — Finding the New Price After an Increase

A concert ticket costs $80 and increases by 25%.

Method 1: Find the increase first

$$25\% \text{ of } 80 = 0.25 \times 80 = 20$$
$$80 + 20 = 100$$

Method 2: Use the multiplier directly

$$1 + 0.25 = 1.25$$
$$80 \times 1.25 = 100$$
New Price: $100
🎯

Guided Example 10 — Finding the New Price After a Decrease

A jacket costs $120 and is discounted by 30%.

Method 1: Subtract the discount

$$30\% \text{ of } 120 = 36$$
$$120 – 36 = 84$$

Method 2: Use the multiplier directly

$$1 – 0.30 = 0.70$$
$$120 \times 0.70 = 84$$
Sale Price: $84
⚠️

SAT Trap Alert

A number increases from 40 to 50. Many students answer 10% because the increase is 10.

The correct calculation is:

$$\frac{10}{40} = 0.25$$
$$0.25 \times 100\% = 25\%$$
Always divide by the ORIGINAL value, not the increase itself.
✏️

Quick Practice Set C

  1. Increase from 40 to 52 → ?% increase
  2. Decrease from 90 to 72 → ?% decrease
  3. $200 increased by 15% → new price?
  4. $150 decreased by 20% → new price?
Answers: 1) 30%  •  2) 20%  •  3) $230  •  4) $120
## SATMath800 — Percentages Chapter (Part 6) Paste this **directly below Part 5**. This is the **final part** of the chapter and includes: * SAT Thinking Habits * Successive Percent Changes * Mixed SAT Practice * Chapter Challenge * Final Review Checklist * SAT Speed Tricks * Footer and Closing HTML Tags — “`html
🧠

Think Like the SAT

The SAT rarely asks, “Convert 25% to a decimal.” Instead, it hides percentage ideas inside:

  • discounts,
  • taxes,
  • population growth,
  • salary changes,
  • test score comparisons,
  • and data analysis tables.
Whenever you see words such as increase, decrease, discount, tax, more than, or less than, immediately think:
$$\text{Original} \times \text{Multiplier}$$
⚡

Successive Percent Changes

A price increases by 20% and then decreases by 20%. Is the final price the same as the original price?

Assume the original price is $100.

Increase by 20%

$$100 \times 1.20 = 120$$

Decrease the new price by 20%

$$120 \times 0.80 = 96$$
The final price is $96, not $100. The overall change is a 4% decrease.

This is a classic SAT trap. Consecutive percentage changes usually do not cancel each other out.

📝

Mixed SAT Practice

Question 1

A $120 jacket is discounted by 25%. What is the sale price?

  • A) $80
  • B) $90
  • C) $95
  • D) $100

Question 2

A value increases from 240 to 300. What is the percent increase?

  • A) 20%
  • B) 25%
  • C) 30%
  • D) 60%

Question 3

What is 12.5% of 64?

  • A) 6
  • B) 7
  • C) 8
  • D) 10
✅

Solutions

Question 1

$$120 \times 0.75 = 90$$
Answer: B) $90

Question 2

$$300 – 240 = 60$$
$$\frac{60}{240} = 0.25$$
$$0.25 \times 100\% = 25\%$$
Answer: B) 25%

Question 3

$$12.5\% = \frac18$$
$$\frac18 \times 64 = 8$$
Answer: C) 8
🏆

Chapter Challenge

A store increases the price of a $240 laptop by 15%. During a sale, the new price is reduced by 20%. What is the final price?

Step 1: Increase by 15%

$$240 \times 1.15 = 276$$

Step 2: Decrease by 20%

$$276 \times 0.80 = 220.8$$
Final Price: $220.80

Notice that we used multipliers for both changes. This is the fastest and safest SAT method.

📚

Final Review Checklist

Make sure you can do each of these confidently:

  • ☐ Convert percentages to decimals
  • ☐ Convert decimals to percentages
  • ☐ Convert common fractions to percentages
  • ☐ Find a percentage of a quantity
  • ☐ Use 25%, 50%, and 75% fraction shortcuts
  • ☐ Find percent increase
  • ☐ Find percent decrease
  • ☐ Find the new total after a percentage change
  • ☐ Solve consecutive percentage change problems
If you can complete every item above without looking at the formulas, you are performing at a strong SAT foundation level for percentage questions.
⚡

SAT Speed Tricks

Memorize these shortcuts:

Percent Fast SAT Shortcut
10% move decimal one place left
5% half of 10%
1% move decimal two places left
25% divide by 4
50% divide by 2
75% divide by 4, then multiply by 3
These shortcuts can save 30–60 seconds per module, which is often the difference between finishing comfortably and rushing through the last few SAT questions.

Percentages Become Easy When You See the Pattern

The Digital SAT constantly moves between fractions, decimals, percentages, discounts, increases, and decreases. The strongest students recognize equivalent forms immediately and choose the representation that makes the problem easiest.

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