Arecipe calls for 4 eggs, but mara only has 3. she decides to adjust the amounts of the other ingredients proportionally. the original recipe calls for 1/2 cup of sugar. which expression represents the amount of sugar, in cups, she should use? 1/2 3/4 3/4 - 1/2 1/2 x 3/4 3/4 ÷ 1/2

That ingredients have relationships to each other in a recipe is an important concept in cooking. It's also an important math concept. In math, this relationship between 2 quantities is called a ratio. If a recipe calls for 1 egg and 2 cups of flour, the relationship of eggs to cups of flour is 1 to 2. In mathematical language, that relationship can be written in two ways:

Both of these express the ratio of eggs to cups of flour: 1 to 2. If you mistakenly alter that ratio, the results may not be edible.

Working with proportion

All recipes are written to serve a certain number of people or yield a certain amount of food. You might come across a cookie recipe that makes 2 dozen cookies, for example. What if you only want 1 dozen cookies? What if you want 4 dozen cookies? Understanding how to increase or decrease the yield without spoiling the ratio of ingredients is a valuable skill for any cook.

Let's say you have a mouth-watering cookie recipe:

1 cup flour
1/2 tsp. baking soda
1/2 tsp. salt
1/2 cup butter
1/3 cup brown sugar
1/3 cup sugar
1 egg
1/2 tsp. vanilla
1 cup chocolate chips

This recipe will yield 3 dozen cookies. If you want to make 9 dozen cookies, you'll have to increase the amount of each ingredient listed in the recipe. You'll also need to make sure that the relationship between the ingredients stays the same. To do this, you'll need to understand proportion. A proportion exists when you have 2 equal ratios, such as 2:4 and 4:8. Two unequal ratios, such as 3:16 and 1:3, don't result in a proportion. The ratios must be equal.

Going back to the cookie recipe, how will you calculate how much more of each ingredient you'll need if you want to make 9 dozen cookies instead of 3 dozen? How many cups of flour will you need? How many eggs? You'll need to set up a proportion to make sure you get the ratios right.

Start by figuring out how much flour you will need if you want to make 9 dozen cookies. When you're done, you can calculate the other ingredients. You'll set up the proportion like this:

You would read this proportion as "1 cup of flour is to 3 dozen as X cups of flour is to 9 dozen." To figure out what X is (or how many cups of flour you'll need in the new recipe), you'll multiply the numbers like this:

Now all you have to do is find out the value of X. To do that, divide both sides of the equation by 3. The result is X = 3. To extend the recipe to make 9 dozen cookies, you will need 3 cups of flour. What if you had to make 12 dozen cookies? Four dozen? Seven-and-a-half dozen? You'd set up the proportion just as you did above, regardless of how much you wanted to increase the recipe.

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