Business Math: Arithmetic, Percentages, and Core Small-Business Calculations

Why Business Math Matters

Every decision a small-business owner makes has a number behind it. Whether you are pricing a product, paying a supplier invoice, tracking your bank account, or deciding how many units you must sell to cover your costs, accurate arithmetic is the foundation. Errors in business math cost real money. This lesson builds the core calculation skills you will use every day and that are tested on both the NFTE and Certiport ESB credentials.

Whole Numbers, Fractions, and Decimals

Small-business records use all three forms. A purchase order might list 144 units at $3.75 each. Multiply 144 × $3.75 to find the total cost: $540.00. When dividing, keep track of remainders — a supplier that sells in cases of 12 means you order in multiples of 12, so rounding up protects you from running short.

Fractions appear in recipes, material cuts, and commission splits. Convert fractions to decimals before entering them in a spreadsheet: ¾ = 0.75. Decimals appear in every dollar amount, so align decimal points when adding or subtracting by hand.

Percentages: Tax, Tip, Discount, and Markup

A percentage is a ratio out of 100. To convert: 18% = 18/100 = 0.18.

Sales tax is added to a selling price. If a product sells for $50.00 and the local sales tax rate is 8%, the customer pays $50.00 × 1.08 = $54.00. (Always verify your local rate; it changes by jurisdiction.)

Tip works the same way. A 20% tip on a $35.00 restaurant bill is $35.00 × 0.20 = $7.00.

Discount reduces a price. A 15% discount on a $200 item means the customer saves $200 × 0.15 = $30.00, paying $170.00. You can also calculate the sale price directly: $200 × (1 − 0.15) = $200 × 0.85 = $170.00.

Markup is the amount added to cost to create a selling price. Markup can be expressed as a percentage of cost (cost-based markup) or of selling price (margin). For cost-based markup: Selling Price = Cost × (1 + Markup %). If you pay $40 for an item and apply a 60% markup on cost, the selling price is $40 × 1.60 = $64.00.

Markdown is a reduction from the original selling price, used during sales or clearance. Markdown % = (Original Price − Sale Price) / Original Price × 100.

Ratios and Proportions

A ratio compares two quantities: if you spend $3 on materials for every $10 of revenue, your cost-to-revenue ratio is 3:10 or 0.30 (30%). Proportions let you scale: if 5 pounds of coffee makes 80 cups, how much coffee makes 200 cups? Set up the proportion: 5/80 = x/200; cross-multiply: x = (5 × 200)/80 = 12.5 pounds.

Break-Even Analysis

The break-even point is the number of units you must sell so that total revenue equals total costs — you neither profit nor lose money. Understanding break-even helps you set prices and sales targets.

Key terms:

• Fixed Costs (FC): Costs that stay the same regardless of how many units you sell (rent, insurance, loan payments).
• Variable Costs per Unit (VC): Costs that change with each unit produced or sold (materials, packaging, shipping).
• Selling Price per Unit (SP): What the customer pays for one unit.
• Contribution Margin per Unit (CM): SP − VC. This is the amount each sale contributes toward covering fixed costs.

Break-Even Quantity (BEQ): BEQ = FC ÷ CM

Break-Even Revenue (BER): BER = BEQ × SP

In a spreadsheet, label separate cells for FC, VC, and SP. Enter the formula for CM as =SP−VC, and BEQ as =FC/CM. If you change any input, the output updates instantly — this is the power of a formula-driven model.

Gross Profit and Net Cash Flow

Gross Profit = Total Revenue − Cost of Goods Sold (COGS). It measures how much you earn from sales before paying operating expenses.

Net Cash Flow = Total Cash In − Total Cash Out for a period. A positive net cash flow means more money came in than went out. A negative result signals a potential problem even if the business looks profitable on paper — timing of payments matters.

When reading a bank statement, add all deposits for the month (cash in) and all withdrawals and payments (cash out). The difference should match the ending balance change on the statement. If it does not, find the discrepancy before moving on — small errors compound quickly.

Simple Interest

When a small business borrows money or earns interest on a savings account, simple interest applies in many short-term situations. The formula is: I = P × r × t, where I = interest, P = principal (the amount borrowed or deposited), r = annual interest rate as a decimal, and t = time in years. If you borrow $5,000 at 6% for 6 months (0.5 years): I = $5,000 × 0.06 × 0.5 = $150.00. Total repaid = $5,150.00.

Accuracy and Safety in Financial Calculations

In business math, accuracy is a safety issue for your finances. Verify totals independently — enter data, calculate by hand or with a calculator, then compare to your spreadsheet output. Keep backup copies of all financial files. Never share spreadsheets containing sensitive cost or pricing data publicly. Protect files with passwords when they contain proprietary business information. Fraudulent invoices exist; always cross-reference invoice totals against purchase orders and receiving records before authorizing payment.