Solve proportions

Learning Objectives Define a proportion and identify proportional relationships. Set up proportions correctly from given information or word problems. Apply the cross-multiplication property to solve proportions for an unknown variable. Solve proportions using scaling or unit rate methods. Check the validity of their solutions to proportions. Solve real-world problems by setting up and solving proportions. Ever wonder how chefs scale up a recipe for a big party, or how maps accurately represent real distances? 🗺️ It's all thanks to proportions! In this lesson, you'll learn what proportions are and master powerful techniques to solve them, especially when there's a missing piece of information. Understanding proportions is crucial for everything from cooking t...

TermDefinitionExample RatioA comparison of two quantities by division. It can be written as a:b, a/b, or 'a to b'.The ratio of 3 apples to 5 oranges can be written as 3:5 or 3/5. RateA ratio that compares two quantities with different units.Driving 60 miles in 2 hours is a rate of 60 miles/2 hours. Unit RateA rate where the second quantity (denominator) is 1 unit.If you drive 60 miles in 2 hours, the unit rate is 30 miles per hour (30 miles/1 hour). ProportionAn equation stating that two ratios are equivalent.The equation 1/2 = 3/6 is a proportion because both ratios represent the same value. Equivalent RatiosRatios that represent the same relationship or value, even if the numbers are different.1/2 and 5/10 are equivalent ratios because they both simplify to 0.5. Cross-Multipli...

Definition of a Proportion A proportion is an equation that states that two ratios are equal: $\frac{a}{b} = \frac{c}{d}$ This rule defines what a proportion is. For the equation to be true, the ratio of 'a' to 'b' must be the same as the ratio of 'c' to 'd'. 'b' and 'd' cannot be zero. Cross-Multiplication Property If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$. This is the primary method for solving proportions. You multiply the numerator of the first ratio by the denominator of the second, and set it equal to the product of the denominator of the first ratio and the numerator of the second. This transforms the proportion into a linear equation that can be solved for an unknown variable.