User:MathMan64~enwikibooks/Current Work

User:MathMan64/Arithmetic

= Addition =

Addition is based on counting. For example, Pat and Chris each have a few rocks in their collections. Pat counts her rocks and finds that she has 3 rocks. Chris counts his collection and he has 5 rocks. When they combine their collections and count them all, the total they get is 8 rocks. 3 rocks plus 5 rocks equals 8 rocks.

The total is also call the sum. When counting the total, it obviously does not matter whether Pat counts hers first or Chris counts his first. 5 + 3 = 8 as well as 3 + 5 = 8. This concept works for any addition situation.


 * When adding, it does not matter which number is first.

One-digit numbers
Knowing the basic addition facts for all the one-digit numbers is crucial for doing arithmetic efficiently. Adding any number to zero always gives the original number. No matter how many rocks Pat has, if Chris has none, together they have a sum thatis the same as Pat's amount.

The addition of digits other than zero must be memorized. Use the table below to review these facts. Find one number to be added, in the left column; find the other in the top row. The sum is where the column and row meet.

Multi-digit numbers
Pat went on a day trip. In the morning she traveled for 3 hours. In the afternoon she traveled 8 miles. How long was her trip altogether?

This question cannot be answered (unless there is more information available, such as an average travel speed.)


 * Only the same kind of things can be added.

This concept is used in adding multi-digit numbers. (It is also used in adding fractions, and letters in algebra.)

When adding multi-digit numbers, the digits must be aligned so that the digits in the same place values are one under another.

Example: 14 + 36