Basic Algebra/Introduction to Basic Algebra Ideas/Simple Operations

Vocabulary

 * Operation
 * Equals Sign
 * Adding
 * Subtracting
 * Multiplying
 * Dividing

Lesson
An operation is a thing you do to numbers. You use signs like: +, –, ×, or ÷ for operations.

The equals sign is not an operation. You use the " = " sign for the equals sign. It is a special sign that you put between two things that are the same.

Adding
Adding is a way to put two numbers together. You use the " + " sign for the adding operation. If you have 5 apples and a friend has 6 apples, you and your friend have 11 apples. This is 5 + 6 = 11 using the signs of Mathematics, and is read "five plus six equals eleven".

Order is not important when adding. 2 + 3 is the same as 3 + 2.

Subtracting
Subtracting is a way of taking a number from another number. It is the opposite of adding. You use the " – " sign for the subtracting operation. If you have 5 apples and give 3 to a friend, you then have 2 apples left. This is 5 – 3 = 2 using the signs of Mathematics, and is read "five minus three equals two".

Order is important when subtracting. 3 – 2 is not the same as 2 – 3.

Multiplying
Multiplying is a way of adding a number many times. You use the " × ", " • " or " * " sign for the multiplying operation. If you have 4 apple trees and every tree has 25 apples, you have 100 apples. This is 4 × 25 = 100 or 25 + 25 + 25 + 25 = 100 in the signs of Mathematics. The first way is shorter and easier to use.

Multiplying 25 by 4 is the same as adding 25, 4 times or adding 4, 25 times.

4 x 25 = 100 should be read "four times twenty-five equals one hundred".

Order is not important when multiplying. 2 × 3 is the same as 3 × 2.

Dividing
Dividing is a way of subtracting a number many times. It is the opposite of multiplying. You use the " ÷ " or " / " sign for the dividing operation. If 3 friends take an equal part of a bag of 12 apples, every friend gets 4 apples. Or, you may take away (subtract) 3 apples from the bag of 12 apples, exactly 4 times until the bag is empty. This is 12 ÷ 3 = 4 or 12 – 3 – 3 – 3 – 3 = 0 in the signs of Mathematics.

12 ÷ 3 = 4 should be read "twelve divided by three equals 4".

Order is important when dividing. 3 ÷ 2 is not the same as 2 ÷ 3.

Example Problems

 * 3 + 4 = 7
 * 5 – 3 = 2
 * 6 × 2 = 12
 * 13 + 14 = 27
 * 21 – 9 = 12
 * 8 × 3 = 24

Practice Games

 * Arcademics Grand Prix (Multiplication)
 * Arcademics Jet Ski (Addition)
 * Arcademics Sailboat (Subtraction)
 * Arcademics Drag Race (Division)

Practice Problems
 {Evaluate the following expressions:}

{ 6 + 8 = { 14_2 }
 * type="{}"}

{ 3 + 4 = { 7_2 }
 * type="{}"}

{ 10 + 15 = { 25_2 }
 * type="{}"}

{ 28 + 13 = { 41_2 }
 * type="{}"}

{ 12 - 5 = { 7_2 }
 * type="{}"}

{ 16 - 3 = { 13_2 }
 * type="{}"}

{ 7 × 5 = { 35_2 }
 * type="{}"}

{ 8 × 4 = { 32_2 }
 * type="{}"}

{ 6 × 6 = { 36_2 }
 * type="{}"}

{ 14 ÷ 7 = { 2_2 }
 * type="{}"}

{ 15 ÷ 3 = { 5_2 }
 * type="{}"}

{ 40 ÷ 5 = { 8_2 }
 * type="{}"}