Financial Literacy and Applied Mathematics

Currency and Calculating Change

We use currency to buy things. In many places, money is written in dollars and cents. The dollar sign is written like this: $.

When we write money, the number after the decimal point shows the cents. For example, $3.45 means 3 dollars and 45 cents.

Calculating change means finding out how much money is given back after paying for something. To find change, we subtract the cost from the amount paid.

We can write that rule like this:

$$\text{Change} = \text{Amount Paid} - \text{Cost}$$

It is very important to line up the decimal points when adding or subtracting money. This helps make sure dollars are under dollars and cents are under cents.

Main Ideas to Know

• 1 dollar = 100 cents
• Money amounts are written with two digits after the decimal point.
• To find a total cost, add the prices.
• To find change, subtract the total cost from the amount paid.
• Always check that the amount paid is greater than or equal to the cost.

Understanding Dollars and Cents

Here are some examples of money amounts:

• \($1.00\) = 1 dollar
• \($0.50\) = 50 cents
• \($2.07\) = 2 dollars and 7 cents
• \($10.25\) = 10 dollars and 25 cents

If a money amount has only one digit in the cents place, we still write two digits. For example, 5 cents is written as $0.05, not $0.5.

How to Find Total Cost

If you buy more than one item, first add the prices to find the total cost.

Example:

$$\$2.35 + \$1.20 = \$3.55$$

This means the total cost is $3.55.

How to Find Change

After finding the total cost, subtract it from the amount paid.

For example, if something costs \(\$3.55\) and you pay \(\$5.00\), then:

$$\$5.00 - \$3.55 = \$1.45$$

The change is $1.45.

Worked Example 1: One Item, Exact Change

A notebook costs $4.25. You pay with $4.25. How much change do you get?

Use subtraction:

$$\$4.25 - \$4.25 = \$0.00$$

You get $0.00 in change. This is called exact change.

Worked Example 2: One Item, Finding Change

A juice costs $2.75. You pay with $5.00. How much change do you get?

Line up the decimals and subtract:

$$\begin{aligned} &\$5.00 \\ -&\$2.75 \\ \hline &\$2.25 \end{aligned}$$

The change is $2.25.

Worked Example 3: Two Items, Then Change

You buy a pen for $1.45 and a ruler for $2.30. You pay with $5.00. How much change do you get?

Step 1: Find the total cost.

$$\begin{aligned} &\$1.45 \\ +&\$2.30 \\ \hline &\$3.75 \end{aligned}$$

The total cost is $3.75.

Step 2: Subtract from the amount paid.

$$\begin{aligned} &\$5.00 \\ -&\$3.75 \\ \hline &\$1.25 \end{aligned}$$

The change is $1.25.

Worked Example 4: More Than Two Items

You buy a snack for $1.80, a bottle of water for $1.25, and fruit for $2.15. You pay with $10.00. How much change do you get?

Step 1: Add the prices.

$$\begin{aligned} &\$1.80 \\ +&\$1.25 \\ +&\$2.15 \\ \hline &\$5.20 \end{aligned}$$

The total cost is $5.20.

Step 2: Find the change.

$$\begin{aligned} &\$10.00 \\ -&\$5.20 \\ \hline &\$4.80 \end{aligned}$$

The change is $4.80.

Tips for Success

• Always line up decimal points when adding or subtracting money.
• Write a zero if needed, like $5.00 instead of $5.
• Find the total cost first if there is more than one item.
• Then use subtraction to find the change.
• Check if your answer makes sense. The change should be less than the amount paid.

Common Mistakes to Avoid

• Forgetting to line up decimals, which can mix up dollars and cents.
• Subtracting in the wrong order. Remember: amount paid minus cost.
• Forgetting zeros in the cents place, such as writing $2.5 instead of $2.50.
• Not adding all items before finding the change.

Quick Check

1. A toy costs \(\$6.40\). You pay \(\$10.00\). What is the change?
2. You buy items that cost \(\$2.50\) and \(\$3.25\). What is the total cost?
3. If the total cost is \(\$5.75\) and you pay \(\$10.00\), what is the change?

Answers

1. $$\$10.00 - \$6.40 = \$3.60$$
2. $$\$2.50 + \$3.25 = \$5.75$$
3. $$\$10.00 - \$5.75 = \$4.25$$

Summary

To work with currency, remember that money is written in dollars and cents. Add prices to find the total cost, and subtract the cost from the amount paid to find the change.

When solving money problems, line up decimal points carefully and always write two digits for cents. With practice, you can quickly find total costs and exact change in real-life shopping situations.

Unit Prices and Better Buys

Have you ever seen two different-sized products at a store and wondered which one is the better deal? A bigger package does not always mean a better price. To compare fairly, we use unit price.

A unit price tells the cost for one unit of something. The unit could be 1 item, 1 ounce, 1 pound, 1 bottle, or 1 pack. Finding the unit price helps us decide which choice gives us more for our money.

When we compare two or more products using unit price, we are looking for the better buy. Usually, the better buy is the one with the lower unit price.

How to find unit price

To find unit price, divide the total cost by the number of units.

$$\text{Unit Price} = \frac{\text{Total Cost}}{\text{Number of Units}}$$

For example, if 4 apples cost \(\$2.00\), then the cost for 1 apple is:

$$2.00 \div 4 = 0.50$$

So the unit price is \(\$0.50 per apple\).

Why unit price matters

• It helps you compare products of different sizes.

• It helps you spend money wisely.

• It helps you notice when a larger size is or is not a better deal.

Steps for finding the better buy

1. Look at the price of each product.

2. Look at the amount in each product, such as ounces or number of items.

3. Divide the price by the amount to find the unit price.

4. Compare the unit prices.

5. The product with the smaller unit price is the better buy.

Important tip: Make sure the units match. If one item is priced by ounces and another is priced by ounces, you can compare them. If the units are different, you need to change them so they match first.

Worked Example 1: Comparing packs of pencils

Pack A has 6 pencils for \(\$1.50\). Pack B has 10 pencils for \(\$2.00\). Which is the better buy?

First, find the unit price for Pack A.

$$1.50 \div 6 = 0.25$$

Pack A costs \(\$0.25 per pencil\).

Now find the unit price for Pack B.

$$2.00 \div 10 = 0.20$$

Pack B costs \(\$0.20 per pencil\).

Now compare: \(\$0.20\) is less than \(\$0.25\).

Pack B is the better buy.

Worked Example 2: Comparing snack bags by ounces

A 5-ounce bag of pretzels costs \(\$2.25\). An 8-ounce bag costs \(\$3.20\). Which is the better buy?

Find the unit price for the 5-ounce bag.

$$2.25 \div 5 = 0.45$$

The 5-ounce bag costs \(\$0.45 per ounce\).

Find the unit price for the 8-ounce bag.

$$3.20 \div 8 = 0.40$$

The 8-ounce bag costs \(\$0.40 per ounce\).

Compare the unit prices: \(\$0.40\) is less than \(\$0.45\).

The 8-ounce bag is the better buy.

Worked Example 3: When the bigger package is not the better buy

Soap Pack A has 12 bars for \(\$9.00\). Soap Pack B has 20 bars for \(\$16.00\). Which is the better buy?

Find the unit price for Pack A.

$$9.00 \div 12 = 0.75$$

Pack A costs \(\$0.75 per bar\).

Find the unit price for Pack B.

$$16.00 \div 20 = 0.80$$

Pack B costs \(\$0.80 per bar\).

Compare: \(\$0.75\) is less than \(\$0.80\).

Pack A is the better buy, even though it has fewer bars. This shows that a bigger package is not always the cheapest choice for each unit.

Worked Example 4: Finding unit price with money and decimal answers

A pack of 3 notebooks costs \(\$4.50\). What is the unit price?

Divide the total cost by the number of notebooks.

$$4.50 \div 3 = 1.50$$

The unit price is \(\$1.50 per notebook\).

If another store sells 5 notebooks for \(\$8.00\), then:

$$8.00 \div 5 = 1.60$$

That store charges \(\$1.60 per notebook\).

Compare: \(\$1.50\) is less than \(\$1.60\).

The first store is the better buy.

What to watch out for

• Do not compare total prices only. A lower total price may be for a much smaller amount.

• Always divide to find the cost for one unit.

• Make sure the units are the same before comparing.

• The lower unit price means the better buy.

Quick check thinking

Ask yourself:

• What is the price?

• How many units are there?

• What is the cost for 1 unit?

• Which choice has the smaller unit price?

Summary

Unit price helps us compare prices fairly. To find unit price, divide the total cost by the number of units. Then compare the unit prices to find the better buy. The item with the lower cost for one unit is usually the best choice.

Budgeting and Expenses means making a plan for how to use money. A budget helps you see how much money comes in and how much money goes out.

When you know your budget, you can make better choices. You can decide what you need, what you want, and how much money you can save.

In this lesson, you will learn how to:

• identify income and expenses
• tell the difference between fixed and variable expenses
• find out if a budget has money left over or not enough money
• use addition and subtraction with money

1. What is income?

Income is money that comes in. For a child, income might be allowance, birthday money, money earned from doing extra chores, or money from a lemonade stand.

For example, if you get \(\$12.00\) for allowance and \(\$8.00\) for helping a neighbor, your total income is:

$$\$12.00 + \$8.00 = \$20.00$$

So your income is \(\$20.00\).

2. What are expenses?

Expenses are money that goes out. Expenses are things you spend money on, like snacks, games, school supplies, or gifts.

If you buy a notebook for \(\$3.50\) and a snack for \(\$2.25\), your total expenses are:

$$\$3.50 + \$2.25 = \$5.75$$

3. What is a budget?

A budget is a plan for your money. It shows your income, your expenses, and how much money is left.

A simple budget can be written like this:

$$\text{Money Left} = \text{Income} - \text{Expenses}$$

If the answer is positive, you have money left over. If the answer is \(0\), you used all your money. If your expenses are greater than your income, you do not have enough money.

4. Fixed and variable expenses

Not all expenses are the same. Some stay the same, and some change.

Fixed expenses are costs that stay the same each time or happen regularly in the same amount.

• a weekly music lesson that costs \(\$15\)
• a monthly club fee of \(\$10\)
• a bus pass that costs the same each month

Variable expenses are costs that can change. You may spend more one time and less another time.

• snacks
• toys
• books
• video game items

For example, if you always pay \(\$10\) each month for a club, that is a fixed expense. If you spend \(\$4\) on snacks one week and \(\$7\) the next week, snacks are a variable expense.

5. Needs and wants

When making a budget, it helps to think about needs and wants.

• Needs are things that are important to have, like school supplies or lunch.
• Wants are things you would like to have, like candy or a new toy.

If your money is limited, you should usually pay for needs first. Then you can decide how much to spend on wants and how much to save.

6. How to make a simple budget

1. Find your total income.
2. List all your expenses.
3. Separate fixed expenses and variable expenses.
4. Add the expenses.
5. Subtract expenses from income.
6. Decide whether you should spend less or save more.

Worked Example 1: Finding money left over

Mia earns \(\$25.00\) from allowance and chores. She spends \(\$6.00\) on markers and \(\$4.50\) on a snack.

Step 1: Add the expenses.

$$\$6.00 + \$4.50 = \$10.50$$

Step 2: Subtract expenses from income.

$$\$25.00 - \$10.50 = \$14.50$$

Answer: Mia has \(\$14.50\) left over.

Worked Example 2: Fixed and variable expenses

Jalen gets \(\$30.00\) this month. He pays \(\$12.00\) for an art class every month. He also spends \(\$5.00\) on a comic book and \(\$3.50\) on juice.

Step 1: Identify the fixed expense.

The art class costs \(\$12.00\) every month, so it is a fixed expense.

Step 2: Identify the variable expenses.

The comic book and juice can change, so they are variable expenses.

Step 3: Add all expenses.

$$\$12.00 + \$5.00 + \$3.50 = \$20.50$$

Step 4: Find the money left.

$$\$30.00 - \$20.50 = \$9.50$$

Answer: Jalen has \(\$9.50\) left after paying his fixed and variable expenses.

Worked Example 3: Not enough money

Sara has \(\$18.00\). She wants to buy a book for \(\$9.75\), a game for \(\$7.50\), and a pen set for \(\$3.25\).

Step 1: Add the expenses.

$$\$9.75 + \$7.50 + \$3.25 = \$20.50$$

Step 2: Compare expenses to income.

Her expenses are \(\$20.50\), but her income is only \(\$18.00\).

Step 3: Subtract to find how much more she needs.

$$\$20.50 - \$18.00 = \$2.50$$

Answer: Sara does not have enough money. She needs \(\$2.50\) more, or she must choose to spend less.

Worked Example 4: Planning a budget

Leo has \(\$40.00\). He wants to save \(\$10.00\). He also has a fixed expense of \(\$8.00\) for a club fee. Then he wants to buy snacks for \(\$6.50\) and a small toy for \(\$9.00\).

Step 1: Add the money he plans to save and spend.

$$\$10.00 + \$8.00 + \$6.50 + \$9.00 = \$33.50$$

Step 2: Compare with his income.

Leo has \(\$40.00\), and his total planned amount is \(\$33.50\).

Step 3: Find the money left over.

$$\$40.00 - \$33.50 = \$6.50$$

Answer: Leo can save \(\$10.00\), pay his expenses, and still have \(\$6.50\) left.

Tips for smart budgeting

• Write down all income and expenses.
• Check prices carefully.
• Add decimals neatly, lining up the decimal points.
• Pay fixed expenses and needs first.
• Be careful with small purchases because they can add up.
• Try to save some money if you can.

Common mistakes to avoid

• Forgetting an expense
• Mixing up income and expenses
• Not lining up decimal points when adding or subtracting money
• Spending more than the amount of money you have

Quick check

If you have \(\$22.00\), and you spend \(\$5.50\) on lunch and \(\$8.25\) on a book, how much is left?

First add the expenses:

$$\$5.50 + \$8.25 = \$13.75$$

Then subtract from income:

$$\$22.00 - \$13.75 = \$8.25$$

So, \(\$8.25\) is left.

Summary

A budget is a plan for money. Income is money coming in, and expenses are money going out. Some expenses are fixed, which means they stay the same, and some are variable, which means they can change.

To use a budget, add your expenses and subtract them from your income. This helps you see whether you have money left over, need to spend less, or can save more.

Taxes, Tips, and Discounts are all about changing a price by a percent.

Sometimes the price goes up, like when tax or tip is added. Sometimes the price goes down, like when a discount is taken off. Learning how to find these amounts helps you understand shopping, restaurants, and real-life money choices.

In this lesson, you will learn what taxes, tips, and discounts are, how to find them, and how to find the final price.

First, remember what percent means.

The word percent means out of 100. So:

• 10% means 10 out of 100
• 25% means 25 out of 100
• 50% means 50 out of 100

You can also write a percent as a decimal.

• 10% = 0.10
• 25% = 0.25
• 8% = 0.08

To change a percent into a decimal, move the decimal point two places left.

For example:

• 12% = 0.12
• 5% = 0.05
• 30% = 0.30

What is tax?

Tax is extra money added to the cost of something you buy. A sales tax is usually a percent of the price.

If an item costs \(\$20\) and the tax is 5%, you do not just pay \(\$20\). You pay the original price plus the tax.

What is a tip?

A tip is extra money given for a service, like at a restaurant or after a haircut. A tip is also often a percent of the original cost.

Like tax, a tip is added to the original amount.

What is a discount?

A discount is money taken off the original price. Stores use discounts during sales.

If a shirt costs \(\$30\) and it is 20% off, you pay less than \(\$30\).

The big idea:

• Tax and tip are added.
• Discount is subtracted.

How to find a tax, tip, or discount

There are two main steps:

1. Find the percent amount.
2. Add it to the original price for tax or tip, or subtract it for a discount.

Step 1: Find the percent amount

Use this rule:

$$\text{Percent amount} = \text{original price} \times \text{decimal form of percent}$$

Step 2: Find the final price

• For tax or tip:

$$\text{final price} = \text{original price} + \text{percent amount}$$

• For discount:

$$\text{sale price} = \text{original price} - \text{discount amount}$$

Worked Example 1: Finding tax

A toy costs \(\$12\). The sales tax is 10%. How much tax is added, and what is the final price?

Step 1: Change 10% to a decimal.

$$10\% = 0.10$$

Step 2: Find the tax.

$$12 \times 0.10 = 1.20$$

The tax is \(\$1.20\).

Step 3: Add the tax to the original price.

$$12.00 + 1.20 = 13.20$$

Answer: The tax is \(\$1.20\), and the final price is \(\$13.20\).

Worked Example 2: Finding a tip

A family’s restaurant bill is \(\$25\). They leave a 20% tip. How much is the tip, and how much do they pay in all?

Step 1: Change 20% to a decimal.

$$20\% = 0.20$$

Step 2: Find the tip.

$$25 \times 0.20 = 5.00$$

The tip is \(\$5.00\).

Step 3: Add the tip to the bill.

$$25.00 + 5.00 = 30.00$$

Answer: The tip is \(\$5.00\), and the total cost is \(\$30.00\).

Worked Example 3: Finding a discount

A backpack costs \(\$40\). It is on sale for 15% off. How much is the discount, and what is the sale price?

Step 1: Change 15% to a decimal.

$$15\% = 0.15$$

Step 2: Find the discount.

$$40 \times 0.15 = 6.00$$

The discount is \(\$6.00\).

Step 3: Subtract the discount from the original price.

$$40.00 - 6.00 = 34.00$$

Answer: The discount is \(\$6.00\), and the sale price is \(\$34.00\).

Worked Example 4: Discount and then tax

A game costs \(\$50\). It is 20% off, and then 8% tax is added to the sale price. What is the final cost?

This example has two changes, so go one step at a time.

Step 1: Find the discount.

$$20\% = 0.20$$

$$50 \times 0.20 = 10.00$$

The discount is \(\$10.00\).

Step 2: Find the sale price.

$$50.00 - 10.00 = 40.00$$

The sale price is \(\$40.00\).

Step 3: Find the tax on the sale price.

$$8\% = 0.08$$

$$40 \times 0.08 = 3.20$$

The tax is \(\$3.20\).

Step 4: Add the tax to the sale price.

$$40.00 + 3.20 = 43.20$$

Answer: The final cost is \(\$43.20\).

Helpful shortcuts with friendly percents

Some percents are easy to find in your head.

• 10%: move the decimal one place left.
  10% of \(\$30\) is \(\$3\).
• 5%: find 10%, then divide by 2.
  5% of \(\$30\) is \(\$1.50\).
• 50%: half of the amount.
  50% of \(\$18\) is \(\$9\).
• 25%: one fourth of the amount.
  25% of \(\$20\) is \(\$5\).

How to know whether to add or subtract

Ask yourself this question: Is the price going up or down?

• If money is being added, like tax or tip, add.
• If money is being taken away, like a discount, subtract.

Common mistakes to avoid

• Do not add the percent number directly to the price.
  For example, with \(\$20\) and 8% tax, do not do \(20 + 8\). You must first find 8% of 20.
• Change the percent to a decimal correctly.
  For example, 8% is \(0.08\), not \(0.8\).
• For discounts, subtract the discount from the original price.
• If there is more than one step, do them in order.

Let’s compare

If a bike helmet costs \(\$24\):

• With 10% tax, the tax is \(24 \times 0.10 = 2.40\), so the final price is \(\$26.40\).
• With 10% discount, the discount is \(24 \times 0.10 = 2.40\), so the sale price is \(\$21.60\).

The percent amount is the same in both cases, but one is added and one is subtracted.

Quick steps to remember

1. Read carefully: Is it tax, tip, or discount?
2. Change the percent to a decimal.
3. Multiply to find the percent amount.
4. Add for tax or tip.
5. Subtract for discount.

Summary

Taxes and tips make a price go up. Discounts make a price go down.

To solve these problems, first find the percent amount by multiplying the original price by the decimal form of the percent. Then add or subtract that amount to get the final price.

With practice, you will be able to find sale prices, restaurant totals, and shopping costs with confidence.

Gross vs. Net Income

When people earn money from a job, they do not always keep all of it. Some money may be taken out for things like taxes or other deductions. That means there are two different amounts to understand: gross income and net income.

Learning the difference helps us understand how much money a person earns in total and how much money they actually take home.

What is gross income?

Gross income is the total amount of money earned before anything is taken out.

If someone works and earns money, the full amount they earned is their gross income.

What is net income?

Net income is the amount of money a person actually gets after deductions are taken away.

A deduction is money subtracted from the gross income. For this lesson, think of deductions as money taken out before the person gets paid.

The basic idea

The relationship between gross income, deductions, and net income is:

$$\text{Gross Income} - \text{Deductions} = \text{Net Income}$$

You can also think of it like this:

• Gross income = all the money earned
• Deductions = money taken out
• Net income = money left over

Why does this matter?

If a person only looks at gross income, they may think they have more money to spend than they really do.

Net income is usually the better amount to use when planning spending, saving, or budgeting, because it shows the money the person actually receives.

Important words to know

• Income: money earned
• Gross income: total money earned before deductions
• Deduction: money taken out
• Net income: money left after deductions

How to find net income

1. Find the gross income.
2. Find the total deductions.
3. Subtract the deductions from the gross income.

In math form:

$$\text{Net Income} = \text{Gross Income} - \text{Deductions}$$

How to find gross income

Sometimes you know the net income and the deductions, but you need to find the gross income.

Then you can use:

$$\text{Gross Income} = \text{Net Income} + \text{Deductions}$$

Worked Example 1: Whole numbers

Mia earns \(\$80\) for helping at a shop. \(\$12\) is taken out. What is her net income?

Step 1: Gross income = \(\$80\)

Step 2: Deductions = \(\$12\)

Step 3: Subtract

$$80 - 12 = 68$$

Mia's net income is \(\$68\).

Worked Example 2: Using decimals

Jordan earns \(\$145.50\). Deductions are \(\$18.25\). What is the net income?

Use the formula:

$$\text{Net Income} = \text{Gross Income} - \text{Deductions}$$

Substitute the numbers:

$$145.50 - 18.25 = 127.25$$

Jordan's net income is \(\$127.25\).

When subtracting decimals, line up the decimal points carefully.

Worked Example 3: Finding gross income

Sara takes home \(\$92.40\) after \(\$7.60\) is taken out. What was her gross income?

We know:

• Net income = \(\$92.40\)
• Deductions = \(\$7.60\)

Use the formula:

$$\text{Gross Income} = \text{Net Income} + \text{Deductions}$$

$$92.40 + 7.60 = 100.00$$

Sara's gross income is \(\$100.00\).

Worked Example 4: More than one deduction

Leo earns \(\$200.00\). Two deductions are taken out: \(\$15.00\) and \(\$9.50\). What is his net income?

First, find the total deductions:

$$15.00 + 9.50 = 24.50$$

Now subtract from the gross income:

$$200.00 - 24.50 = 175.50$$

Leo's net income is \(\$175.50\).

Thinking carefully about the difference

Here is a quick way to remember:

• Gross means the bigger amount first
• Net means the amount left after money is taken out

So, gross income is usually greater than or equal to net income.

In symbols:

$$\text{Gross Income} \geq \text{Net Income}$$

Common mistakes to avoid

• Do not mix up gross and net.
• Do not forget to subtract all deductions.
• When working with money, line up decimal points.
• If finding gross income, add deductions back to net income instead of subtracting.

Try to reason it out

If someone earns \(\$50\) and takes home \(\$50\), then the deductions must be \(\$0\).

If someone earns \(\$50\) and takes home \(\$45\), then \(\$5\) was taken out.

This helps us see that the net income tells us what the person really receives.

Real-life connection

Imagine two people compare their pay:

• Person A has a gross income of \(\$120\)
• Person B has a net income of \(\$110\)

We cannot tell right away who actually takes home more unless we know the deductions for Person A.

That is why it is important to know whether a number is gross or net.

Summary

Gross income is the total amount earned before money is taken out.

Net income is the amount left after deductions.

Use these formulas:

$$\text{Net Income} = \text{Gross Income} - \text{Deductions}$$

$$\text{Gross Income} = \text{Net Income} + \text{Deductions}$$

When you understand gross and net income, you can better tell how much money a person really gets to use.

Profit and Loss Foundations

Have you ever thought about what happens when someone sells lemonade, bookmarks, cookies, or handmade crafts? They collect money from customers, but they also spend money to make or buy the items first. To understand whether they are doing well, they need to know if they made a profit or had a loss.

In this lesson, you will learn how to compare the money earned with the money spent. This helps us understand simple business situations in real life.

Important Words to Know

• Revenue: the total money earned from selling something.
• Cost: the total money spent to make, buy, or run the business.
• Profit: the money left after costs are taken away from revenue.
• Loss: when costs are more than revenue.

You can find profit or loss using subtraction.

$$\text{Profit or Loss} = \text{Revenue} - \text{Cost}$$

After you subtract, the answer tells you what happened:

• If the answer is greater than 0, there is a profit.
• If the answer is less than 0, there is a loss.
• If the answer is 0, the business broke even. That means it did not make money or lose money.

Step-by-Step Method

1. Find the revenue.
2. Find the cost.
3. Subtract cost from revenue.
4. Decide whether the answer shows a profit, loss, or break-even.

Worked Example 1: Finding a Profit

A student sells pencils and earns \(\$18\). The pencils and supplies cost \(\$11\).

Use the rule:

$$\text{Profit or Loss} = \text{Revenue} - \text{Cost}$$

Substitute the numbers:

$$18 - 11 = 7$$

The answer is \(\$7\). Since the answer is greater than 0, the student made a profit of \(\$7\).

Worked Example 2: Finding a Loss

A bake sale earns \(\$25\). The ingredients and packaging cost \(\$31\).

Subtract cost from revenue:

$$25 - 31 = -6$$

The answer is \(-6\), which means the sale had a loss of \(\$6\).

You can also think of it this way: the costs were \(\$6\) more than the money earned.

Worked Example 3: Break-Even

A child makes friendship bracelets. They earn \(\$14\) from sales. The string and beads cost \(\$14\).

Subtract:

$$14 - 14 = 0$$

The answer is \(0\). This means the child broke even. They did not make a profit, and they did not have a loss.

Worked Example 4: Using Decimals

A lemonade stand earns \(\$32.50\). The lemons, sugar, cups, and signs cost \(\$18.75\).

Subtract carefully with the decimal points lined up:

$$32.50 - 18.75 = 13.75$$

Since the answer is positive, the lemonade stand made a profit of \(\$13.75\).

How to Find Revenue

Sometimes revenue is not given directly. You may need to find it by multiplying the number of items sold by the price of each item.

$$\text{Revenue} = \text{Number Sold} \times \text{Price of Each Item}$$

For example, if 8 notebooks are sold for \(\$3\) each, then:

$$8 \times 3 = 24$$

The revenue is \(\$24\).

If the cost was \(\$17\), then:

$$24 - 17 = 7$$

So the profit is \(\$7\).

Comparing Profit and Loss

Here is a simple way to remember:

• If revenue is bigger than cost, there is a profit.
• If cost is bigger than revenue, there is a loss.
• If they are equal, the business breaks even.

Common Mistakes to Avoid

• Do not subtract in the wrong order. Use revenue minus cost.
• Make sure you include all costs, not just one cost.
• Line up decimal points when subtracting money amounts.
• Check whether the final answer means profit, loss, or break-even.

Quick Practice Thinking

If a stand earns \(\$40\) and costs are \(\$28\), then:

$$40 - 28 = 12$$

That is a profit of \(\$12\).

If a craft table earns \(\$19\) and costs are \(\$23\), then:

$$19 - 23 = -4$$

That is a loss of \(\$4\).

Why This Matters

Knowing profit and loss helps people make smart decisions. A seller can see whether their business idea is working. They can also decide if they should spend less, sell more, or change the price.

Summary

Profit and loss help us understand money earned and money spent. First, find the revenue. Then subtract the cost.

$$\text{Profit or Loss} = \text{Revenue} - \text{Cost}$$

If the answer is positive, it is a profit. If the answer is negative, it is a loss. If the answer is zero, it is break-even. With careful subtraction, you can solve many real-world money problems.