<h3>The Main Idea</h3> <p><strong>Small to Big = Divide. Big to Small = Multiply.</strong></p> <p>This is the single most important rule for unit conversions. When converting between units, ask yourself: "Am I going from a smaller unit to a bigger unit, or bigger to smaller?" Then apply the correct operation.</p> <h3>What is a Length Unit Conversion?</h3> <p>A length unit conversion changes a measurement from one unit to another (like inches to feet, or yards to feet) while keeping the actual length the same. The key is knowing the conversion factor and whether to multiply or divide.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — Know what unit your answer needs to be in before doing any math.</li> <li><strong>Identify your starting unit and target unit</strong> — What do you have? What do you need?</li> <li><strong>Write down the conversion factor</strong> — For example: 1 foot = 12 inches, 1 yard = 3 feet.</li> <li><strong>Determine the operation</strong> — Compare the units: small to big = divide, big to small = multiply.</li> <li><strong>Calculate and check units</strong> — Make sure your answer is in the required unit.</li> </ol> <h3>Why Does Small to Big = Divide?</h3> <p>Think of it this way: you're <strong>grouping up</strong> smaller units to make bigger ones. How many groups of 12 inches can fit in 83 inches? That's division — you're seeing how many feet you can make from the inches you have.</p> <h3>Why Does Big to Small = Multiply?</h3> <p>You're <strong>breaking apart</strong> bigger units into smaller pieces. If you have 6 feet and each foot contains 12 inches, you're multiplying to find the total number of inches.</p> <h3>Common Pitfalls</h3> <ul> <li><strong>Mixing up multiply vs divide</strong> — Always compare the unit sizes first, then pick your operation.</li> <li><strong>Forgetting to convert ALL units</strong> — If you have "3 yards and 2 feet" and need inches, convert both parts.</li> <li><strong>Not simplifying mixed units</strong> — An answer like "7 feet 17 inches" is incorrect form. Convert 12 of those inches into another foot to get "8 feet 5 inches."</li> <li><strong>Subtracting different units</strong> — You cannot subtract 96 feet from 54 yards directly. Convert first!</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Small to Big = Divide. Big to Small = Multiply.</strong></p> <p>Weight conversions follow the exact same rule as length conversions. When converting ounces to pounds, you're grouping small units into bigger ones (divide). When converting pounds to ounces, you're breaking a big unit into smaller pieces (multiply).</p> <h3>What is a Weight Unit Conversion?</h3> <p>A weight unit conversion changes a measurement from one weight unit to another (like ounces to pounds) while keeping the actual weight the same. The key conversion factor for imperial weight is: <strong>1 pound = 16 ounces</strong>.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — Know what unit your answer needs to be in.</li> <li><strong>Identify your starting unit and target unit</strong> — Ounces? Pounds? Pounds and ounces?</li> <li><strong>Write down the conversion factor</strong> — 1 pound = 16 ounces.</li> <li><strong>Determine the operation</strong> — Small to big (oz → lb) = divide by 16. Big to small (lb → oz) = multiply by 16.</li> <li><strong>Don't forget extra ounces!</strong> — If you have "6 pounds 12 ounces," convert the pounds AND add the extra ounces.</li> </ol> <h3>Working with Mixed Units (Pounds and Ounces)</h3> <p>When a problem gives you pounds AND ounces (like 6 lb 12 oz), you often need to:</p> <ul> <li><strong>Convert everything to ounces first</strong> — Multiply pounds by 16, then add the extra ounces.</li> <li><strong>Do your calculation</strong> — Multiply, divide, add, or subtract as needed.</li> <li><strong>Convert back to pounds and ounces</strong> — Divide by 16. The quotient = pounds, the remainder = ounces.</li> </ul> <h3>Rate Problems with Weight</h3> <p>When you see "price per ounce" (like $0.30 per ounce), you multiply the rate by the number of ounces to get the total cost. Make sure all your weight is converted to ounces first!</p> <h3>Common Pitfalls</h3> <ul> <li><strong>Using 12 instead of 16</strong> — There are 16 ounces in a pound (not 12 like inches in a foot).</li> <li><strong>Forgetting the extra ounces</strong> — "6 pounds 12 ounces" is NOT just 6 pounds. Don't forget to add the 12!</li> <li><strong>Not simplifying</strong> — "5 pounds 20 ounces" is incorrect. Convert 16 of those ounces into another pound to get "6 pounds 4 ounces."</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Small to Big = Divide. Big to Small = Multiply.</strong></p> <p>Time conversions follow the same core rule. When converting seconds to minutes, or minutes to hours, you're grouping small units into bigger ones (divide). When going the other way, you're breaking big units into smaller pieces (multiply).</p> <h3>What is a Time Unit Conversion?</h3> <p>A time unit conversion changes a measurement from one time unit to another (like minutes to hours, or seconds to minutes). The key conversion factors are:</p> <ul> <li><strong>1 minute = 60 seconds</strong></li> <li><strong>1 hour = 60 minutes</strong></li> <li><strong>1 day = 24 hours</strong></li> <li><strong>1 week = 7 days</strong></li> </ul> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — Know what unit your answer needs to be in (hours? minutes? hours and minutes?).</li> <li><strong>Identify the keyword</strong> — "From now" means addition. "Remains" or "left" means subtraction.</li> <li><strong>Write down the conversion factor</strong> — 60 seconds/minute, 60 minutes/hour, 24 hours/day.</li> <li><strong>Determine the operation</strong> — Small to big = divide. Big to small = multiply.</li> <li><strong>Handle remainders properly</strong> — When converting to mixed units (hours and minutes), the quotient = hours, remainder = minutes.</li> </ol> <h3>Clock Time Calculations</h3> <p>When adding hours to a clock time:</p> <ul> <li><strong>Every 24 hours</strong> brings you back to the same time (next day).</li> <li><strong>Every 12 hours</strong> flips AM to PM (or PM to AM).</li> <li><strong>Adding hours doesn't change the minutes</strong> — 5:09 + 4 hours = 9:09.</li> <li><strong>Add minutes separately</strong> — Then add any extra minutes to get final time.</li> </ul> <h3>Mental Math Strategy for Time</h3> <p>When subtracting mixed time units (like 8 hours minus 2 hr 45 min minus 3 hr 30 min):</p> <ol> <li>Subtract the hours first: 8 - 2 - 3 = 3 hours</li> <li>Then subtract minutes one at a time using mental math</li> <li>Remember: 1 hour = 60 minutes (borrow if needed)</li> </ol> <h3>Common Pitfalls</h3> <ul> <li><strong>Confusing 12-hour and 24-hour cycles</strong> — 12 hours changes AM/PM, but 24 hours returns to the same time.</li> <li><strong>Adding hours and changing minutes</strong> — Adding hours alone does NOT change the minute value.</li> <li><strong>Not simplifying</strong> — "2 hours 75 minutes" is incorrect. Convert 60 minutes to 1 hour to get "3 hours 15 minutes."</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Small to Big = Divide. Big to Small = Multiply.</strong></p> <p>Volume conversions follow the same rule as all other unit conversions. Cups are smaller than quarts, quarts are smaller than gallons. Know your conversion factors and apply the rule!</p> <h3>What is a Volume Unit Conversion?</h3> <p>A volume unit conversion changes a liquid measurement from one unit to another (like cups to quarts, or gallons to quarts). The key conversion factors for imperial volume are:</p> <ul> <li><strong>1 cup = 8 fluid ounces</strong></li> <li><strong>1 quart = 4 cups</strong></li> <li><strong>1 gallon = 4 quarts</strong></li> </ul> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — Know what unit your answer needs to be in.</li> <li><strong>Write down the conversion factor</strong> — 4 cups per quart, 4 quarts per gallon.</li> <li><strong>Determine the operation</strong> — Small to big = divide. Big to small = multiply.</li> <li><strong>Handle mixed units carefully</strong> — If you have "4 gallons 1 quart," you may need to convert everything to quarts first.</li> </ol> <h3>Working with Mixed Volume Units (Gallons and Quarts)</h3> <p>When a problem gives you gallons AND quarts (like 4 gal 1 qt):</p> <ul> <li><strong>Convert gallons to quarts first</strong> — Multiply gallons by 4, then add the extra quarts.</li> <li><strong>Do your calculation</strong> — Add, subtract, etc.</li> <li><strong>Convert back if needed</strong> — Divide by 4. Quotient = gallons, remainder = quarts.</li> </ul> <h3>Common Pitfalls</h3> <ul> <li><strong>Confusing cups with quarts</strong> — 4 cups = 1 quart (not 2 or 8).</li> <li><strong>Forgetting extra quarts</strong> — "4 gallons 1 quart" is NOT the same as "4 gallons."</li> <li><strong>Not simplifying</strong> — "3 gallons 6 quarts" is incorrect. Convert 4 quarts to 1 gallon to get "4 gallons 2 quarts."</li> <li><strong>Converting in the wrong direction</strong> — Don't convert at the end if it makes subtraction harder. Sometimes it's easier to keep mixed units and convert only when needed.</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Plug in, calculate, and finish the problem.</strong></p> <p>Temperature conversions between Fahrenheit and Celsius use a formula. You substitute the given temperature into the formula and solve. The most common mistake is stopping too early — make sure you complete all the arithmetic!</p> <h3>What is a Temperature Conversion?</h3> <p>A temperature conversion changes a measurement from one temperature scale to another (Celsius to Fahrenheit, or Fahrenheit to Celsius). Unlike length or weight conversions that use a simple multiply/divide, temperature uses a formula because the scales have different starting points (0°C = 32°F, not 0°F).</p> <h3>The Formulas</h3> <p>There are two ways to write the same formulas. They give identical results — use whichever you find easier:</p> <ul> <li><strong>Celsius to Fahrenheit:</strong> F = (9/5)C + 32 <em>or</em> F = 1.8C + 32</li> <li><strong>Fahrenheit to Celsius:</strong> C = (5/9)(F - 32) <em>or</em> C = (F - 32) ÷ 1.8</li> </ul> <p><strong>Why are they the same?</strong> Because 9 ÷ 5 = 1.8 and 5 ÷ 9 ≈ 0.556. The fraction form (9/5 and 5/9) is exact; the decimal form (1.8) is often easier for mental math.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question sentence first</strong> — Are you solving for F (Fahrenheit) or C (Celsius)?</li> <li><strong>Identify what you're given</strong> — Don't confuse the given value with what you're solving for! "If C = 25" means you HAVE C and need to find F.</li> <li><strong>Choose the correct formula</strong> — Use the formula that solves for your unknown.</li> <li><strong>Substitute carefully</strong> — Replace the variable with the given value.</li> <li><strong>Complete ALL the arithmetic</strong> — Don't stop after multiplication. Add or subtract 32!</li> </ol> <h3>Why Temperature is Different</h3> <p>For length, weight, time, and volume, converting is just multiply or divide. Temperature is different because:</p> <ul> <li>The scales start at different places (water freezes at 0°C but 32°F)</li> <li>The degree sizes are different (a Celsius degree is bigger than a Fahrenheit degree)</li> <li>So you need BOTH multiplication AND addition/subtraction</li> </ul> <h3>Common Pitfalls</h3> <ul> <li><strong>Stopping too early</strong> — After multiplying (9/5) × 25 = 45, you MUST add 32 to get the final answer.</li> <li><strong>Confusing what you're solving for</strong> — "If C = 25" means C is given, not what you're finding. Read carefully!</li> <li><strong>Order of operations errors</strong> — When going F to C, subtract 32 FIRST, then multiply by 5/9.</li> <li><strong>Using the wrong formula</strong> — Make sure you use the formula that has your unknown isolated.</li> </ul>
Practice This Goal