Percent Applications

🛍️ Percent Applications

Part 1 of 5 — Concept Introduction

Every time you see a "30% OFF" sign, add sales tax at the register, or leave a tip at a restaurant, you are doing percent math in the real world. In this lesson you will learn one core idea and then use it to handle discounts, tax, tips, and percent change like a pro.

The Big Idea: Percent of a Number

A percent is just a fraction out of $100$. The word percent literally means "per hundred." So $25\%$ means $25$ out of $100$, which is the decimal $0.25$.

To find a percent of a number, you multiply:

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

The trick is to first turn the percent into a decimal by dividing by $100$ (move the decimal point two places left).

Worked Example: Find a Percent of a Number

Find $25\%$ of $80$.

Step 1 — Change the percent to a decimal. $25\% = 0.25$

Step 2 — Multiply by the whole. $0.25 \times 80 = 20$

So $25\%$ of $80$ is $20$. ✅

That single skill — multiply the decimal by the whole — is the engine behind discounts, tax, and tips. You will reuse it again and again.

Percent Change 📈📉

Sometimes a value goes up (a price increase, a raise) or down (a sale, a price drop). Percent change measures how big that change is compared to where you started:

$\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%$

• A positive answer means an increase.
• A negative answer means a decrease.

Example: A plant grows from $10$ cm to $13$ cm. $\frac{13 - 10}{10} \times 100\% = \frac{3}{10} \times 100\% = 30\%$

The plant grew by $30\%$ — a positive number, so it is an increase. 🌱

Concept Check 🎯

Make sure you can find a percent of a number.

🧮 Worked Examples

Part 2 of 5 — Step-by-Step

Discounts: Paying Less

A discount lowers the price. If something is "$20\%$ off," you do not pay that $20\%$ — so you keep paying the other $80\%$. There are two ways to find the final price:

Method 1 — Subtract the discount: $\text{Discount} = 0.20 \times 50 = 10 \qquad \text{Final} = 50 - 10 = \$40$

Method 2 — Multiply by what is left (the shortcut): $50 \times (1 - 0.20) = 50 \times 0.80 = \$40$

Both give $40. The shortcut, original price $\times (1 - \text{discount rate})$, is faster once you trust it.

Tax and Tips: Paying More

Sales tax is an extra amount added on top of the price. Because you pay $100\%$ of the price plus the tax, you multiply by $(1 + \text{tax rate})$.

Example — $30 item with $8\%$ tax: $30 \times (1 + 0.08) = 30 \times 1.08 = \$32.40$

A tip is money you give for good service, usually a percent of the bill. To find the tip amount by itself, just multiply:

Example — $15\%$ tip on a $40 bill: $40 \times 0.15 = \$6$

Your Turn ✏️

A jacket costs $60 and is on sale for $25\%$ off. Work through it step by step.

• Box 1: The discount amount: $0.25 \times 60 = ?$ (dollars)
• Box 2: The sale price: $60 - \text{discount} = ?$ (dollars)
• Box 3: Using the shortcut, $60 \times 0.75 = ?$ (dollars — it should match Box 2!)

🤝 Guided Practice

Part 3 of 5

Apply the discount, tax, and tip rules to these two questions.

Choose the Right Multiplier 🔽

For each situation, pick the calculation that finds the correct answer.

🌎 Application & Word Problems

Part 4 of 5

Real receipts often combine several steps. Read carefully and figure out whether each percent makes the price go up or down.

Maya's Restaurant Bill

Maya and her friends order food that comes to a $40 bill. Their server is great, so they leave a $20\%$ tip. To find the total Maya pays, she needs two pieces:

1. The tip amount: $40 \times 0.20 = 8$, i.e. $8
2. The total: bill + tip $= 40 + 8 = 48$, i.e. $48

Notice this is the same idea as tax — money added on top — so the shortcut $40 \times 1.20 = 48$, i.e. $48 also works. 🍽️

Word Problem Practice ✏️

A video game normally costs $80. During a sale it is $15\%$ off, and then $5\%$ sales tax is added to the sale price.

• Box 1: The sale price: $80 \times 0.85 = ?$ (dollars)
• Box 2: The tax on the sale price: $0.05 \times \text{sale price} = ?$ (dollars)
• Box 3: The final total: sale price $+$ tax $= ?$ (dollars)

Percent Change in the Real World 📊

🏆 Review & Challenge

Part 5 of 5

You now have a full toolkit for percent applications. Here is everything in one place:

Summary Table

Remember the direction: discounts go down ($1 - \text{rate}$), while tax and tips go up ($1 + \text{rate}$). Percent change is positive for an increase and negative for a decrease. Now show what you know! 💪

Mixed Challenge 🎯

These questions blend everything together. Take your time.