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:

• 25 4 = 6.25
• 25 4 = 6 1/4

Our remainder is what follows the whole number, what comes after the 6 in this case.

Addition and Subtraction: When adding and subtracting decimals, remember to line up your numbers by the decimal point so that all digits in each place value so that when digits are added or subtracted they are in the same place value. For example:

26.8 + 8.05 + 31

2 6 . 8 8 . 0 5 + 3 1 . 6 5 . 8 5

739.52 - 371.63

7 3 9 . 5 2 - 3 7 1 . 6 3 3 6 7 . 8 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:

37.4 x 4.3

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

		3	7	4
	x		4	3
1	6	0	8	2

Step 2: Go back to your original problem and count the decimal places behind or to the right of the decimal. In 37.4 there is one place behind the decimal, the 4. In 4.3, there is one place behind the decimal, the 3. 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 - 1 6 0 8 . 2
• Moved one more place to the left for a total of two places - 1 6 0 . 8 2
• Our answer is 160.82.

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:

3/8 + 7/16

Common denominator for 8 and 16 is 16. Therefore we need to change our fractions so that they each have 16 as their common denominator. In this case all we need to do is find an equivalent fraction for 3/8 that has 16 as its denominator. To do this we multiply both numerator and denominator by 2.

3*2/8*2 = 6/16

We can now add our fractions.

6/16 + 7/16= 13/16

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:

• 5/12 x 2/3
• 5 x 2 / 12 x 3
• 10/36

To reduce our answer to lowest terms, we need to find the greatest common factor of 10 and 36. The greatest common factor is 2, therefore we can divide both numerator and denominator by 2 and arrive at our reduced answer.

• 10 2/ 36 2
• 5/18

Division: When dividing fractions you want to remember two very important steps. The first is to take the divisor, the fraction by which you will be dividing into your fraction, and rewrite that fraction as its reciprocal. Then change the operation of division to multiplication. Then solve as multiplying fractions. For example:

• 3/7 5/8
• 3/7 x 8/5

Now multiply as above.

• 3 x 8 / 7 x 5
• 24/35

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 is to memorize the following statement where the first letter of each word represents the operation to do:

Please Excuse My Dear Aunt Sally

The rule for Order of Operations is the following:

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

For example:

6 + (15 - 8) x 14 2 - 4

Step 1: Take care of the parenthesis first.

6 + 7 x 14 2 - 4

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

6 + 98 2 - 4

Step 3: Next, division.

6 + 49 - 4

Step 4: Take care of any addition now.

55 - 4

Step 5: Finish the problem with subtraction.

51 is final answer.