Tuesday, May 12, 2020

How to Solve Proportions Using a Recipe

A proportion is a set of 2 fractions that equal each other. This worksheet focuses on how to solve proportions. Real World Uses of Proportions Modifying a budget for a restaurant chain that is expanding from 3 locations to 20 locationsCreating a skyscraper from blueprintsCalculating tips, commissions, and sales tax Modifying a Recipe On Monday, you are cooking enough white rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. On Sunday, you are going to serve rice to 12 people. How would the recipe change? If youve ever made rice, you know that this ratio - 1 part dry rice and 2 parts water - is important. Mess it up, and youll be scooping a gummy, hot mess on top of your guests crawfish à ©touffà ©e. Because you are quadrupling your guest list (3 people * 4 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. These shifts in a recipe demonstrate the heart of proportions: use a ratio to accommodate lifes greater and smaller changes. Algebra and Proportions 1 Sure, with the right numbers, you can forgo setting up an algebraic equation to determine the amounts of dry rice and water. What happens when the numbers are not so friendly? On Thanksgiving, youll be serving rice to 25 people. How much water do you need? Because the ratio of 2 parts water and 1 part dry rice applies to cooking 25 servings of rice, use a proportion to determine the quantity of ingredients. Note: Translating a word problem into an equation is super important. Yes, you can solve an incorrectly set up equation and find an answer. You can also mix rice and water together to create food to serve at Thanksgiving. Whether the answer or food is palatable depends on the equation. Think about what you know: 3 servings of cooked rice 2 cups of water; 1 cup of dry rice25 servings of cooked rice ? cups of water; ? cup of dry rice3 servings of cooked rice/25 servings of cooked rice 2 cups of water/x cups of water3/25 2/x Cross multiply. Hint: Write these fractions vertically to get the full understanding of cross multiplying. To cross multiply, take the first fractions numerator and multiply it by the second fractions denominator. Then take the second fractions numerator and multiply it by the first fractions denominator. 3 * x 2 * 253x 50 Divide both sides of the equation by 3 to solve for x. 3x/3 50/3x 16.6667 cups of water Freeze- verify that the answer is correct. Is 3/25 2/16.6667?3/25 .122/16.6667 .12 Whoo hoo! The first proportion is right. Algebra and Proportions 2 Remember that x will not always be in the numerator. Sometimes the variable is in the denominator, but the process is the same. Solve the following for x. 36/x 108/12 Cross multiply: 36 * 12 108 * x432 108x Divide both sides by 108 to solve for x. 432/108 108x/1084 x Check and make sure the answer is right. Remember, a proportion is defined as 2 equivalent fractions:Does 36/4 108/12? 36/4 9108/12 9 Its right! Practice Instructions: Solve for the unknown variable. Check your answers. a/49 4/356/x 8/329/3 12/b5/60 k/652/949 s/36522.5/x 5/100a/180 4/100

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