<h3>The Main Idea</h3> <p><strong>The percent you apply and the result you get represent the same thing.</strong></p> <p>This is the key to every percent problem. If you're looking for the growth, use the growth percent. If you're looking for the final amount, use the final percent. Keep them matched.</p> <h3>What is a Percent?</h3> <p>A percent is a number out of 100. When you see 35%, that means 35 out of every 100, or 0.35 as a decimal. The word "of" tells you to multiply.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question first</strong> — Know what you're solving for before looking at the numbers.</li> <li><strong>Identify what you have</strong> — Find the percent and the original amount. Make sure they represent the same thing.</li> <li><strong>Set up and solve</strong> — Use the formula. Multiply to find a part, divide to find the original or percent.</li> </ol> <h3>Converting Percents</h3> <ul> <li><strong>Percent to decimal:</strong> Move the decimal point 2 places left (35% → 0.35)</li> <li><strong>Decimal to percent:</strong> Move the decimal point 2 places right (0.35 → 35%)</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>The percent you apply and the result you get represent the same thing.</strong></p> <p>If you use the discount percent, you get the discount amount. If you use the tax percent, you get the tax amount. If you want the final price, ask yourself: does my percent match what I want?</p> <h3>Discounts</h3> <p>A discount is a reduction from the original price.</p> <ul> <li><strong>Discount % × Original = Discount Amount</strong> — then subtract from original</li> <li><strong>Or use the final percent:</strong> If it's 20% off, the final price is 80% of the original. Multiply by 80% and you're done in one step.</li> </ul> <h3>Sales Tax</h3> <p>Tax is an addition to the original price.</p> <ul> <li><strong>Tax % × Original = Tax Amount</strong> — then add to original</li> <li>You could multiply by 112% for a 12% tax, but adding is usually faster than multiplying by a 3-digit number.</li> </ul> <h3>Check Yourself</h3> <p>Before you finish, ask: does the percent I used match what I'm looking for? If you used the discount percent but want the final price, you need one more step.</p>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Interest is money paid for borrowing or earned for saving.</strong></p> <p>The key is knowing whether interest is calculated once (simple) or builds on itself (compound).</p> <h3>What is Interest?</h3> <p>Interest is a percentage of the principal (starting amount) calculated over time. Banks pay you interest when you save; you pay interest when you borrow.</p> <h3>Simple Interest</h3> <p>Interest calculated <strong>only on the original principal</strong>. The amount stays the same each period.</p> <ol> <li><strong>Identify P, R, and T</strong> — Principal, Rate (as decimal), Time (in years)</li> <li><strong>Multiply:</strong> I = P × R × T</li> <li><strong>If asked for total:</strong> Add interest to principal (A = P + I)</li> </ol> <h3>Compound Interest</h3> <p>Interest calculated <strong>on principal plus previously earned interest</strong>. The amount grows each period.</p> <ol> <li><strong>Identify P, r, and n</strong> — Principal, Rate (as decimal), Number of compounding periods</li> <li><strong>Apply the formula:</strong> A = P(1 + r)<sup>n</sup></li> <li><strong>For interest earned:</strong> Subtract principal (I = A − P)</li> </ol> <p><em>Note: For more than 2 compounding periods, use a calculator — the exponent math gets tedious by hand.</em></p> <h3>Simple vs Compound: The Key Difference</h3> <ul> <li><strong>Simple:</strong> Same interest amount every period</li> <li><strong>Compound:</strong> Interest grows because you earn interest on interest</li> </ul>
Practice This Goal