Arithmetic Operations Study Guide for McGraw-Hill's ASVAB

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

1. Perform operations shown within Parentheses
2. Attend to Exponents and Square Roots
3. Perform Multiplication or Division from left to right
4. 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.

123,756

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.

123,456

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.

123.456

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

Result = 123.46