This is an arithmetic progression. Therefore you must add or subtract a number to the number before it to arrive at the next number.

We must first find the difference between each number.

To start, take the second number and subtract the first number

In this case it yields .

Then take the third number and subtract the second number which results in

If the resulting number is the same you now know the difference between each number in the sequence and can apply the difference to each break in the arithmetic sequence.

Again the difference is .

So we take the final number and add the difference to it resulting with 

"2 pints in a quart, 4 quarts in a gallon"

To get the prime factorization of a number we must factor it in the most reduced version of prime numbers that multiplied together produce the number.

Prime numbers are numbers that are only divisible by themselves and 1. 1,2,3,5,7. . .

In this example we first divide the number by because its 3 and odd number which gives us 

We now know that 3 is at least one of the prime factors.

Then we divide the result by 3 again to get 

We then combine all of the prime numbers to get the answer of .

If we have a right angle triangle and a value for two of the three side lengths use the Pythagorean Theorem to solve for the length of the third side.

The two side lengths that meet to form the right angle are labeled  and  which are interchangeable for each side length. The long side connecting them is labeled  and is known as the hypotenuse.

The Pythagorean Theorem states .

Take 3 and 4 and plug them into the equation as  and  to yield 

First square the numbers .

After squaring the numbers add them together 

Once you have the sum, take the square root of both sides 

After calculating our answer is .

This is a geometric progression. Therefore you must multiply or divide a number by the number before it to arrive at the next number.

We must first find the ratio between each number.

To start, take the second number and divide the first number yielding 

Then take the third number and divide the second number which results in 

If the resulting number is the same you now know the ratio between each number in the sequence and can apply the ratio to each resulting number.

In this case the number is .

So we then take the final number and multiply it by 3 we received to get the answer of .

This is an arithmetic progression. Therefore you must add or subtract a number to the number before it to arrive at the next number.

We must first find the difference between each number.

To start, take the second number and subtract the first number.

In this case it yields 

Then take the third number and subtract the second number which results with .

If the resulting number is the same you now know the difference between each number in the arithmetic sequence and can apply the difference to each number.

Again the difference is .

So we take the final number and add the difference to it resulting with

Then we do the same with the answer to get 

The answer is .

 is a geometric progression. Therefore you must multiply or divide a number by the number before it to arrive at the next number.

We must first find the ratio between each number.

To start, take the second number and divide the first number yielding 

Then take the third number and divide the second number which results in 

If the resulting number is the same you now know the ratio between each number in the sequence and can apply the ratio to each resulting number.

In this case the number is .

So we then take the final number and multiply it by the ratio we received to get the answer of .

The formula for the number of diagonals in a figure is:

where is the number of sides in the figure.

A pentagon is a five-sided figure, so we plug 5 in for .

There are 5 diagonals in a pentagon.

The least common multiple is the smallest number that both of the numbers multiply to.

For example, for 2 and 6 it would be 6 because and . For 2 and 5 it would be 10 because  and . For 3 and 8 it would be 24.

Multiply the numbers in the sequence 1,2,3,4 to find their multiples.

So for 15 the multiples are:  .

And for 25 the multiples are: .

The least common multiple is .

A yard equals 3 feet.