Learning the Basics of Pre-Algebra

For a short primer on pre-algebra, use this simple guide. Learn about basic pre-algebraic equations, and how to properly add, subtract, multiply, and divide equations.

Basic Operations

Addition and multiplication are commutative operations because a + b = b +a; ab=ba. The numbers can 'move about the operation.' For example: 3+4=7 and 4+3=7. Subtraction is not commutative because 3-2=1 while 2-3 = -1.

Properties

For all real numbers, a,b, and c, equality is reflexive, symmetric, and transitive.

An example of the reflexive property is b=b or 4=4.

If a=b, then b=a. If 6=2x, then 2x=6. This is the symmetric property.

If a=b and b=c, then a=c. This is the transitive property. For example: If y=3x, and 3x=12, then y=12.

Adding Equations

In pre-algebra, letters (such as a,b,n,x) can be used to stand for numbers. Word phrases can be translated into number phrases. For example: the word phrase (some number a added to 8) would be translated into number phrase (8 +a). If a=9, then 8+a= 8+9 or 17. The word phrase (some number b decreased by 4) would be translated into number phrase (b-4). If b=6, then b-4=6-4 or 2. The word phrase (the product of 3 and some number n) would be translated into number phrase (3 x n or 3n). if n=2, then 3n=3x2 or 6. The word phrase (15 divided by some number x) would be translated into number phrase (15/x). if x=3, then 15/x=15/3 or 5.

An equation like x+2=10 states that both x+2 and 10 name the same number. The sum of some number and 2 is 10 (x+2=10). x=8 because 8+2=10.

Twelve divided by some number is 6. 12/x = 6. X=2 because 12/2=6. Seven decreased by some number is 5. 7-x=5. X=2 because 7-2=5.

To solve an equation, you can add the same number to both sides of it.

t-3=15.To change t-3 to t, 3 was added to both sides.

t-3+3 =15. t-3=15.

+3 18-3=15.

t + 0 = 18. 15=15.

t=18

Subtracting, Multiplying, and Dividing Equations

To solve an equation, you can subtract the same number from both sides of it.

V+18=47

V+18-18=47-18 v+18=47.To change v=18 to v, 18 was subtracted from both sides.

V+0=29.29+18=47.

V=29 47=47.

To solve an equation, you can multiply both sides of it by the same number.

a/5=35

5x a/5=5x35. a/5=35. To change a/5 to a, both sides were multiplied by 5.

5xa/5=175. 175/5=35.

A=175. 35=35.

To solve an equation, you can divide both sides of it by the same non-zero number.

4m=52.

4m/4=52/4, 4m=52, To change 4m to m, both sides were divided by 4.

4m/4=52/4. 4x13=52.

m=13 52=52