Science, Tech, Math › Math How to Solve Proportions to Adjust a Recipe Practical Applications of Proportion Problems Share Flipboard Email Print A practical application of a math proportions problem is adjusting a recipe to double or quadruple it. Betsie Van Der Meer, Getty Images Math Math Tutorials Geometry Arithmetic Pre Algebra & Algebra Statistics Exponential Decay Functions Worksheets By Grade Resources View More By Jennifer Ledwith Math Expert B.B.A., Finance and Economics, University of Oklahoma Jennifer Ledwith is the owner of tutoring and test-preparation company Scholar Ready, LLC and a professional writer, covering math-related topics. our editorial process Jennifer Ledwith Updated March 03, 2018 A proportion is a set of 2 fractions that equal each other. This article 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 Use Proportions to Modify 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 you’ve ever made rice, you know that this ratio — 1 part dry rice and 2 parts water — is important. Mess it up, and you’ll be scooping a gummy, hot mess on top of your guests' crawfish étouffée. 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 life's 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, you'll 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 fraction's numerator and multiply it by the second fraction's denominator. Then take the second fraction's numerator and multiply it by the first fraction's denominator.3 * x = 2 * 253x = 50Divide both sides of the equation by 3 to solve for x.3x/3 = 50/3x = 16.6667 cups of waterVerify that the answer is correct.Is 3/25 = 2/16.6667?3/25 = .122/16.6667= .12The 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 = 108xDivide both sides by 108 to solve for x.432/108 = 108x/1084 = xCheck 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 = 9It’s right! Answers and Solutions to Solving Proportions 1. a/49 = 4/35Cross multiply:a *35 = 4 * 4935a = 196Divide both sides of the equation by 35 to solve for a.35a/35 = 196/35a = 5.6Verify that the answer is correct.Does 5.6/49 = 4/35?5.6/49 = .1142857144/35 = .114285714 2. 6/x = 8/32Cross multiply:6 * 32 = 8*x192 = 8xDivide both sides of the equation by 8 to solve for x.192/8 = 8x/824 = xVerify that the answer is correct.Does 6/24 = 8/32?6/24 = ¼8/32 = ¼3. 9/3 = 12/bCross multiply:9 * b = 12 * 39b = 36Divide both sides of the equation by 9 to solve for b.9b/9 = 36/9b = 4Verify that the answer is correct.Does 9/3 = 12/4?9/3 = 312/4 = 34. 5/60 = k/6Cross multiply.5 *6 = k * 6030 = 60kDivide both sides of the equation by 60 to solve for k.30/60 = 60k/60½ = kVerify that the answer is correct.Does 5/60 = (1/2)/ 6?5/60 = .08333(1/2)/ 6 = .08333.5. 52/949 = s/365Cross multiply.52 *365 = s * 94918,980 = 949sDivide both sides of the equation by 949 to solve for s.18,980/949 = 949s/94920 = sVerify that the answer is correct.Does 52/949 = 20/365?<br/>52/949 = 4/7320/365 = 4/736. 22.5/x = 5/100Cross multiply.22.5 * 100 = 5 * x2250 = 5xDivide both sides of the equation by 5 to solve for x.2250/5 = 5x/5450 = xVerify that the answer is correct.Does 22.5/x = 5/100?22.5/450 = .055/100 = .057. a/180 = 4/100Cross multiply.a * 100 = 4 * 180100a = 720Divide both sides of the equation by 100 to solve for a.100a/100 = 720/100a = 7.2Verify that the answer is correct.Does 7.2/180 = 4/100?7.2/180 = .044/100 = .04 Edited by Anne Marie Helmenstine, Ph.D.