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how to show work for algebra proportions.

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4 Answers

Hi Kaela.  A proportion is simply a comparison of 2 fractions.  Like "part over whole" = "part over whole".  Whenever you are doing proportions, just make sure you "keep the top with the top and the "bottom with the bottom".  That's a nonsensical way of reminding myself - whatever "units" or quantity I use on the top of the fraction on the left side of the equals sign, that same unit or quantity has to be written on the top on the right side of the equals sign, and same for the bottom.  That's not the only way you can do it, but it's a good way of keeping it straight.

Can you be more precise with your question?

Math is Fun!

Once you get the "algebra proportion" from the wonderful tutors Krista B., and Diane S., you can make math fun, like:

Knowing that some other people call this "equivalent fraction".

Let's think about the following question:

Use ALL the nine digits, 1 to 9 (not the 0) ONLY once, to formulate an algebra proportion for 1/5.

How many such algebra proportion are there? Can you list them all? 

One answer is 2769/13845.   

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!