How to Solve Proportions Adjusting a Recipe

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  Ã¢â‚¬â€ is important. Mess it up, and you’ll 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 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/60 ½Ã‚   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 4/732 0/365 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.