How to find the Percent of a Number

math joke

Let’s start with a little math joke. What did 2 say as he left the party? …..

Peace out!

Ok, so hopefully that made you smile a little. Now let’s get down to business.

how to find the percent of a number

A fundamental concept your middle school student should know how to do is how to find the percent of a number.

In a recent post, I showed How to Change a Percent to a Fraction.  Go there first if you need a refresher on how to do that, but recall that the % sign means to divide by 100.

So for example, 35% is equal to 35/100 = 7/20.

But what if I wanted to find the percent of a number.  For example, what if you are asked to find 35% of 12.  How should you begin?

Steps to Finding the Percent of a Number

To find the percent of a number do the following:

  1. Realize that the word of means to multiply in math.  If your child is struggling in math, go back and make sure that he knows the meanings of commonly used words in math.  Of is used a lot in math, so definitely make sure that he knows the meaning of that word.
  2. Change your percent to either a fraction or a decimal.  So here we will change 35% to either a fraction OR a decimal.  I’m going to choose to change 35% to a fraction.  Remembering that the % signs means to divide by 100, I get 35% = 35/100.  You don’t have to reduce 35/100, but I recommend getting in the habit of reducing anytime you can so that you can work with smaller numbers.  Here 35/100 reduces to 7/20 because the Greatest Common Factor between 35 and 100 is 5.
  3. Then multiply the two numbers.  So here we multiply 7/20 times 12.  To multiply fractions, we multiply the NUMERATORS and then we multiply the DENOMINATORS.  So here we’d do 7 times 12 which is 84, and then we’d do 20 times 1 to get 20. (Remember there’s an imaginary 1 under 12 so that 12 = 12/1.)  So we get 84/20.  Now we reduce, this.  The easiest way to reduce this is to do 84 ÷ 20, because remember that the fraction bar means to divide.  When do 84 ÷ 20, we get 4 and 1/5 or written as a decimal 4.2.  So 35% of 12 is 4.2.

Tips:

When you multiply 7/20 by 12, BEFORE you multiply the numerators and the denominators, use the shortcut to reduce any numbers you can before multiplying.  You do that by seeing if numbers on the diagonals have any common factors other than 1.  Here the greatest common factor between 20 and 12 is 4, so we can reduce 20 to make it 5, and we reduce 12 to make it 3.  So then we multiply 7/5 by 3.  Then you multiply the numerators and denominators.  So we’d have 7 times 3 which is 21, and 5 times 1 is 5, so overall, we have 21/5. Then we reduce this to get  21/5 is 4 and 1/5 or 4.2.  Using the shortcut enables you to work with smaller numbers before multiplying your fractions.

So there you go. Those are the steps to finding 35% of 12.  Did you struggle to do this problem because of other things not explained thoroughly? For example, do you need an explanation of how to find the greatest common factor between numbers, or more information on how we changed 84/20 or 21/5 to 4.2?  Let me know in the comments below any other how tos you’d like me to do.

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