6th grade

Percents are one of the types of math that we use the most in real life, which is probably why they lend themselves so nicely to word problems!

If you know how to find percents from all different angles (see our Percents Lessons), word problems are easy.  You can use a simple formula, or a proportion, fill in the items you know from the word problem, and solve.

Remember, "of" means multiplication in math.

Sometimes you are given a percent and a number, and asked to find the whole number that that percent is based on.  

There are several ways to find a whole number based on a percent.  EdBoost's preferred way to to use a proportion (not necessarily because it's the easiest way to do this operation, but because there are several related operations, and using a proportion makes it clear how to solve all kinds of percent problems).

Example: 20 is 80% of what number?

Finding a percent of a number means finding a part or portion of a number. A percent is another way to write a decimal or a fraction, so finding a percent of a number is the same as finding a fraction or decimal of a number. One great math rule to remember: the word "of" means multiply in math.

Finding a percent based on a portion of a number means figuring out what percent a specific portion represents.  When thinking about percents, remember that percent means "per 100" (think, per (each) and cent (100 as in century)).  Remember that portions do not have to be written as percents.  They can also be written as decimals or fractions (which are fairly easily converted to percents).  So 15% can also be written as .15 or $\dfrac{15}{100}$.  

Finding the square root of a perfect square is easy.  What number, times itself, equals your number?

$$\eqalign{\sqrt{81}&=9\\\sqrt{400}&=20}$$

But, what do you do when you need to find the square root of a non-perfect square.

If you have a calculator, it's simple, you use the $\sqrt{\text{  }}$ button.

If you don't have a calculator, you need to estimate.  You won't get a perfect answer by estimating but you can come close. 

It's helpful to think of square roots as the opposites of squares.

The square of a number is what you get when you multiply a number by itself.  The square of $6 = 6^2 = 36$

The square root of a number is the number that you have to multiply by itself to get another number.  So, the square root of $36 = \sqrt{36} = 6$

$6 \times 6 = 36$ so the square root of $36 = 6$.