<h3>The Main Idea</h3> <p><strong>Read the question sentence first.</strong></p> <p>Before reading any details, find the question sentence and understand what the problem wants you to find. This tells you where the story wants you to end up — and often hints at what math you'll need to do.</p> <h3>What is an Operation Word Problem?</h3> <p>An operation word problem gives you information and asks you to combine it using basic operations: addition, subtraction, multiplication, or division. The challenge is figuring out <em>which</em> operations to use and <em>in what order</em>.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — What are you solving for? Look for keywords like "how many more," "how many total," "how many remain," or "how many complete."</li> <li><strong>Identify what you have</strong> — List the given numbers and what they represent.</li> <li><strong>Match operations to keywords:</strong> <ul> <li>"Total" or "altogether" → Add or multiply</li> <li>"More," "left," or "remain" → Subtract</li> <li>"Each" with a total → Multiply (to find grand total) or divide (to find number of groups)</li> <li>"Complete" or "full" → Often involves a limiting factor</li> </ul> </li> <li><strong>Execute in order</strong> — Work through each operation step by step.</li> </ol> <h3>Special Case: Limiting Factor Problems</h3> <p>When a problem asks for "complete" sets that require multiple resources:</p> <ol> <li>Calculate how many sets you can make from <em>each</em> resource separately</li> <li>The answer is the <strong>minimum</strong> — you can only make as many complete sets as your most limited resource allows</li> </ol> <h3>Special Case: Time Overlap Problems</h3> <p>When a problem asks how long multiple things happen "at the same time":</p> <ol> <li>Draw a timeline or blocks for each time interval</li> <li>Find where the blocks overlap</li> <li>Add up all the overlapping intervals</li> </ol>
Practice This Goal<h3>The Main Idea</h3> <p><strong>"Of" means multiply — even with decimals and fractions.</strong></p> <p>When you see "2/3 of 12.6" or "18.50 per hour for 6.5 hours," you're multiplying. Don't let the decimals intimidate you — the operations are the same as with whole numbers.</p> <h3>What is a Decimal Word Problem?</h3> <p>A word problem where the given values include decimals (like $18.50 or 6.5 hours). The math is the same — you just need to keep track of decimal places in your calculations.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — What are you solving for?</li> <li><strong>Identify the operation</strong> — Look for keywords: <ul> <li>"Of" → Multiply</li> <li>"Out of" → Divide</li> <li>"Total," "altogether" → Add</li> <li>"Left," "remaining" → Subtract</li> <li>"Per" with a quantity → Multiply (rate × time, price × quantity)</li> </ul> </li> <li><strong>Line up decimals for addition/subtraction</strong> — Stack the numbers so decimal points align.</li> <li><strong>Count decimal places for multiplication</strong> — The answer has as many decimal places as the total in both factors.</li> </ol> <h3>Multiplying by a Fraction</h3> <p>When multiplying a decimal by a fraction like 2/3:</p> <ol> <li>Multiply by the numerator (top number)</li> <li>Divide by the denominator (bottom number)</li> </ol> <p>Example: 2/3 × 12.6 → (12.6 × 2) ÷ 3 = 25.2 ÷ 3 = 8.4</p> <h3>Breaking Up Complex Multiplication</h3> <p>For problems like 18.50 × 14.75, split the multiplier:</p> <ul> <li>18.50 × 14 = 259.00</li> <li>18.50 × 0.75 = 18.50 × 3/4 = 13.875</li> <li>Add them: 259.00 + 13.875 = 272.875</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Read the question first to identify the operation, then make the denominators match (for add/subtract) or flip (for divide).</strong></p> <h3>What is a Fraction Word Problem?</h3> <p>A word problem where the given quantities are fractions or mixed numbers. The key is identifying the operation from context clues, then applying the correct fraction rules.</p> <h3>Identifying the Operation</h3> <ul> <li><strong>"Remains," "left," "how much more"</strong> → Subtraction</li> <li><strong>"Total," "altogether," "combined"</strong> → Addition</li> <li><strong>"Of"</strong> → Multiplication</li> <li><strong>"How many can be made," "how many fit," "each"</strong> → Division</li> </ul> <h3>Adding and Subtracting Fractions</h3> <ol> <li><strong>Find the Least Common Denominator (LCD)</strong> — the smallest number both denominators divide into</li> <li><strong>Convert both fractions</strong> to have the LCD</li> <li><strong>Add or subtract the numerators</strong> — keep the denominator the same</li> <li><strong>Simplify if needed</strong></li> </ol> <h3>Multiplying Fractions</h3> <ol> <li><strong>Convert mixed numbers to improper fractions</strong> — multiply whole by denominator, add numerator</li> <li><strong>Multiply numerators together, multiply denominators together</strong></li> <li><strong>Simplify or convert back to mixed number</strong></li> </ol> <h3>Dividing Fractions: Keep-Change-Flip</h3> <ol> <li><strong>Keep</strong> the first fraction the same</li> <li><strong>Change</strong> division to multiplication</li> <li><strong>Flip</strong> the second fraction (take the reciprocal)</li> <li>Then multiply as usual</li> </ol> <p><em>Tip:</em> Write whole numbers as fractions over 1 (e.g., $48 = \frac{48}{1}$)</p> <h3>Converting Mixed Numbers</h3> <p>To convert a mixed number like $3\frac{1}{2}$ to an improper fraction:</p> <ul> <li>Multiply whole number × denominator: $3 \times 2 = 6$</li> <li>Add the numerator: $6 + 1 = 7$</li> <li>Keep the same denominator: $\frac{7}{2}$</li> </ul>
Practice This Goal