Ramos on Math

May 4, 2021

MSM1 Proportional Rates/ Unit Rates

<ul> <li><strong>Definition: </strong>Proportion is an equation which defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. &nbsp;When two ratios are equal in value, then they are said to be in proportion.<br> </li> <li>When you have a fraction and &nbsp;multiply the numerator and the denominator by the same number or divide each by the same number the fraction are proportional.<br> </li> <li>Examples: ½ is proportional to 2/4 because you multiply the numerator and the denominator by 2. ⅓ is proportional to 2/6 because you multiply the numerator and the denominator by 2. ¼ is proportional to 3/6 &nbsp;because you multiply the numerator and the denominator by three.<br> </li> <li>We can compare these ratios in &nbsp;a chart for easy comparison and formulating missing value to create proportional ratios.<br> </li> <li><strong>A unit rate: </strong>&nbsp;A <strong>unit rate</strong> is a <strong>rate</strong> with 1 in the denominator. If you have a <strong>rate</strong>, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate <strong>unit rate</strong> or price per <strong>unit</strong> by completing the division operation: numerator divided by denominator.<br> <ul> <li>Example: You walk 24 miles in 6 minutes, divide 24 by 6=4, the unit rate is 4 miles per minute. We divided the numerator and denominator by 4<br> </li> <li>This helps when comparing things like cars; The mustang gets 22 gallon per mile and the Corolla gets 55 miles per 2 gallons. If we convert the Corolla to a unit rate we can compare and see which car gets more per gallon. Divide the numerator and denominator by 2, and you see the Corolla get 27.5 miles per gallon (which is better gas mileage).<br> </li> <li>Here is a unit rate calculator: <a href="https://www.calculatorsoup.com/calculators/math/unit-rate-calculator.php#:~:text=A%20unit%20rate%20is%20a,operation%3A%20numerator%20divided%20by%20denominator"><u>https://www.calculatorsoup.com/calculators/math/unit-rate-calculator.php#:~:text=A%20unit%20rate%20is%20a,operation%3A%20numerator%20divided%20by%20denominator</u></a>.<br> </li> <li><strong>Some real world examples we use in our daily life:<br> </strong> <ul> <li>Price per pound<br> </li> <li>Heart beats per minute<br> </li> <li>Calories per serving<br> </li> <li>Steps per Day</li> </ul> </li> </ul> </li> </ul> <p><br></p>