Whenever you show work, you want to show every step in solving the problem. So lets get and example problem:

A cookie recipe that makes 24 cookies requires 2 eggs. How many eggs would you need to make 192 cookies?

So start with the original information given by the problem:

Original recipe: 2 eggs for every 24 cookies. This is the proportion for the original recipe.

**2 per 24 **or **2/24**

In the new recipe, we want to make 192 cookies. So we use a proportion to make sure that the amount of eggs is the same fore each recipe. Because we don't know how many eggs we need, we substitute variable x in place of the number of eggs.

New recipe: x eggs for every 192 cookies

**x per 192 **or **x/192**

Then we need to make the two proportions equal which is done with the equation symbol.

**2/24 = x/192**

Now we have a problem to solve. To solve for proportions we need to multiply the numerator of one proportion by the denominator of the other, and we do this for both proportions:

**2/24 = x/192**

**2*192 = 24*x**

Next we simplify the equation:

**2*192 = 24*x**

**2*192= 384 and 24*x is simplified to 24x**

**384 = 24x**

Next we want to get x by itself to find out how many eggs. To do this we divide both sides by 24.

**384 =24x**

**384/24 =24x/24**

Then we simplify the equation to get our answer:

**384/24 =24x/24**

**16 = x**

So our x value is 16, which means that we need 16 eggs in order to make 192 cookies.

If you would like to check your work, and easy way is to do this is to divide the numerators by the denominators and each side should get the same number. or simplify both proportions and you should get the same basic simplification.

Just remember that showing your work requires that you show each intermittent step to solving the problem. Good Luck!