The basic operations of arithmetic are addition, subtraction, multiplication, and division.

** Addition** There are two ways to show addition:

In either case, you need to add the two numbers to get the sum.

** Subtraction** There are also two ways to show subtraction:

Subtraction of Whole Numbers with Renaming Sometimes you have to "rename" numbers in order to complete subtraction.

To subtract the 5 from the 1 in the ones place, "rename" the "31" in the top number as "2 tens and 11 ones." Write "2" above the 3 in the tens place and "11" above the 1 in the ones place. Subtract 5 from 11 to get 6.

Next, you need to subtract the 6 from the (new) 2 in the tens place, so rename "72" as "6 hundreds and 12 tens." Write "6" above the 7 in the hundreds place and "12" above the 3 in the tens place. Subtract 6 from 12 to get 6. Then subtract 4 from 6 in the hundreds place to get 2, completing the subtraction.

** Multiplication** Multiplication is a bit more complicated in that it can be shown in various ways.

- 10 × 3 = 30

- 10(3) = 30

- (10)3 = 30

- 10 · 3 = 30

- (10)(3) = 30

** Division** Division can also be shown in more than one way.

** Order of Operations** If addition, subtraction, multiplication, and division are all in the same mathematical statement, the order of operations (what you do first, second, third, and so on) is

- Perform operations shown within Parentheses
- Attend to Exponents and Square Roots
- Perform Multiplication or Division from left to right
- Perform Addition or Subtraction from left to right

You can use the sentence "Please Excuse My Dear Aunt Sally" to help you remember the order of operations.

Example

** Rounding** Often you will be asked to round to the nearest 10, 100, or 1,000 or to the nearest tenth, hundredth, or thousandth. A good way to do this is to underline the number in the place to which you are rounding. Identify the number immediately to the right. If it is 5 or greater, round up by 1. If it is 4

*Examples*

Round 123,756 to the nearest thousand.

- Underline the number in the thousands place.

- 12

__3__,756

Look at the number in the place immediately to the right.

7 is greater than 5, so round the underlined number to 4 and change the rest to zeros.

- Result = 124,000

Round 123,456 to the nearest thousand.

- Underline the number in the thousands place.

- 12

__3__,456

Look at the number in the place immediately to the right.

4 is less than 5, so keep the number in the thousands place as it is and change all numbers to the right to zeros.

- Result = 123,000

Round 123.456 to the nearest hundredth.

- Underline the number in the hundredths place.

- 123.4

__5__6

6 is greater than 5, so change the 5 to 6 and make all numbers to the right zeros.

- Result = 123.46

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