Division: When dividing whole numbers and a remainder is a result of that division, the remainder may be written as a decimal or even as a simple fraction. For example:

• 9 5 = 1.8
• 9 5 = 1 ⁴/₅

Our remainder is what is in addition to the whole number 1 in this case.

Addition and Subtraction: When adding or subtracting decimals, line up the digits by lining up the decimal point so that all digits are in their correct place value. For example:

13.2 + 4.06 + 22

1 3 . 2       4 . 0 6 + 2 2 .       3 9 . 2 6

648.52 - 239.43

6 4 8 . 5 2 - 2 3 9 . 4 3   4 0 9 . 0 9

Multiplication: When multiplying decimals, remember to multiply just as you would any two whole numbers. Once you have an answer then count the decimal places behind the decimal in each of the numbers being multiplied. In the answer count that number of places to the left from the end of your answer. For example:

23.4 x 2.5

Step 1: Multiply as if the decimal points weren't there.

	2	3	4
x		2	5
5	8	5	0

Step 2: Go back to your original problem and count the decimal places behind or to the right of the decimal. In 23.4 there is one place behind the decimal, the 4. In 2.5, there is one place behind the decimal, the 5. Adding up the number of places together equals 2 decimal places.

Step 3: Take the number of decimal places found in step 2, which is 2 places, and count that many places to the left in our answer. Therefore we have the following:

• Moved one place to the left - 5 8 5 . 0
• Moved one more place to the left for a total of two places - 5 8 . 5 0
• Our answer is 58.50.

Addition and Subtraction: Remember that in order to add or subtract fractions there must be common denominators. If the problem doesn't give you the fractions with common denominators, then you will need to find the common denominator by finding the least common multiple of the denominators and changing the fractions to equivalent fractions with common denominators. Once you have common denominators, add the numerators and keep the denominator the same as the common denominator. Always check to see if you can reduce your final answer as well. For example:

3/4 + 5/8

Common denominator for 4 and 8 is 8. Therefore we need to change our fractions so that they each have 8 as their common denominator. In this case all we need to do is find an equivalent fraction for 3/4 that has 8 as its denominator. To do this we multiply both numerator and denominator by 2.

3*2/4*2 = 6/8

We can now add our fractions.

6/8 + 5/8 = 11/8

Remember to check if you can reduce. Since this is an improper fraction we may need to put our answer in mixed number form, which is 1 3/8.

Multiplication: When multiplying fractions you need to multiply the numerators together and then multiply the denominators together. Unlike in addition and subtraction, you don't have to have common denominators in order to multiply fractions. Once you have an answer, always be sure to see if you fraction can be reduced into lowest terms. To reduce you, you will want to find the greatest common factor of the numerator and denominator and divide by that factor. For example:

• 7/8 x 2/5
• 7 x 2 / 8 x 5
• 14/40

To reduce our answer to lowest terms, we need to find the greatest common factor of 14 and 40. The greatest common factor is 2, therefore we can divide both numerator and denominator by 2 and arrive at our reduced answer.

• 14 2 / 40 2
• 7/20

Division: When dividing fractions you want to remember two very important steps. The first is to take the divisor, the second fraction, and rewrite that fraction as its reciprocal. Then change the operation of division to multiplication. Then solve as multiplying fractions. In other words, simply "flip the second fraction and multiply the two fractions".

For example:

• 2/3 3/7
• 2/3 x 7/3

Now multiply as above.

• 2 x 7 / 3 x 3
• 14/9

Reduce to a mixed number if requested would be 1 5/9.

When given a mathematical sentence with different operations it is very important to know which operations or steps to do first through the solution of the problem. One way to remember the correct order of operations is to memorize the following statement where the first letter of each word represents the operation to be completed.

Please Excuse My Dear Aunt Sally

The correct order of operations is:

• Parenthesis - whatever may be in parenthesis is taken care of first.
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

For example:

3 + (12 - 5) x 10 2 - 5

Step 1: Take care of the parenthesis first.

3 + 7 x 10 2 - 5

Step 2: There are no exponents so we move down to multiplication.

3 + 70 2 - 5

Step 3: Next, division.

3 + 35 - 5

Step 4: Take care of any addition now.

38 - 5

Step 5: Finish the problem with subtraction.

33 is final answer.