# BASIC MATH RULES

Basic Math Rules :

In this section, we are going to learn some basic rules in math which will be much useful for the middle grade students to become master in math.

Rule 1 :

The result will be positive

Example :

2 + 1  =  3

Rule 2 :

The result will be negative

Example :

-3 + (-5)  =  -8

## Subtraction Rules

Rule 1 :

Negative + Positive  =  Subtract

Take sign of number with largest absolute value

Example :

-3 + 5  =  2

Rule 2 :

Positive + Negative  =  Subtract

Take sign of number with largest absolute value

Example :

3 + (-5)  =  -2

## Multiplication Rules

Rule 1 :

Positive x Positive  =  Positive

Example :

3 x 5  =  15

Rule 2 :

Negative x Negative  =  Positive

Example :

(-3) x (-5)  =  15

Rule 2 :

Positive x Negative  =  Negative

Example :

3 x (-5)  =  -15

Rule 2 :

Negative x Positive  =  Negative

Example :

-3 x 5  =  -15

## Division Rules

Rule 1 :

Positive ÷ Positive  =  Positive

Example :

20 ÷ 4  =  5

Rule 2 :

Negative ÷ Negative  =  Positive

Example :

(-20) ÷ (-4)  =  5

Rule 2 :

Positive ÷ Negative  =  Negative

Example :

20 ÷ (-4)  =  -5

Rule 2 :

Negative ÷ Positive  =  Negative

Example :

-20 ÷ 4  =  -5

## Exponent Rules

Rule 1 :

xm ⋅ xn  =  xm+n

Example :

34 ⋅ 35  =  34+5

34 ⋅ 35  =  39

Rule 2 :

xm ÷ xn  =  xm-n

Example :

37 ÷ 35  =  37-5

37 ÷ 35  =  32

Rule 3 :

(xm)n  =  xmn

Example :

(32)4  =  3(2)(4)

(32)4  =  38

Rule 4 :

(xy)m  =  xm ⋅ ym

Example :

(3 ⋅ 5)2  =  32 ⋅ 52

(3 ⋅ 5)2  =  9 ⋅ 25

(3 ⋅ 5)2  =  225.

Rule 5 :

(x / y)m  =  xm / ym

Example :

(3 / 5)2  =  32 / 52

(3 / 5)2  =  9 / 25

Rule 6 :

x-m  =  1 / xm

Example :

3-2  =  1 / 32

3-2  =  1 / 9

Rule 7 :

x0  =  1

Example :

30  =  1

Rule 8 :

x1  =  x

Example :

31  =  3

Rule 9 :

xm/n  =  y -----> x  =  yn/m

Example :

x1/2  =  3

x  =  32/1

x  =  32

x  =  9

Rule 10 :

(x / y)-m  =  (y / x)m

Example :

(5 / 3)-2  =  (3 / 5)2

(5 / 3)-2  =  32 /  52

(5 / 3)-2  =  9 / 25

Rule 11 :

ax  =  ay -----> x  =  y

Example :

3m  =  35 -----> m  =  3

Rule 12 :

xa  =  ya -----> x  =  y

Example :

k3  =  53 -----> k  =  5

## Order of Operations (PEMDAS)

This rule can be used to simplify or evaluate complicated numerical expressions with more than one binary operation easily.

Very simply way to remember  PEMDAS rule :

P -----> Parenthesis

E -----> Exponents

M -----> Multiplication

D -----> Division

S -----> Subtraction

Important notes :

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Multiplication does not always come before division. We have to do one by one in the order from left to right.

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.

Examples :

16 ÷ 4 x 3  =  4 x 3  =  12

18 - 3 + 6   =  15 + 6  =  21

In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next.

So we do division first and multiplication next.

## Percent Equation  ## Percent Decrease / Increase

The formula given below can be used to find the percent increase or decrease of a value. The change may be an increase or a decrease.

Here, the original amount is the value before increase or decrease.

## Place Value Place value of a digit in a number is the digit multiplied by thousand or hundred or whatever place it is situated.

For example,

In 25486, the place value of 5 is

=  5 ⋅ 1000

=  5000

Here, to get the place value of 5, we multiply 5 by 1000.

Because 5 is at thousands place.

## Face Value

Face value of a digit in a number is the digit itself.

More clearly, face value of a digit always remains same irrespective of the position where it is located.

For example,

In 25486, the face value of 5 is 5.

## The difference between place value and face value

The difference between place value and face has been illustrated in the picture shown below. ## Angles

Acute Angle : Less than 90°

Obtuse Angle : More than 90°

Right Angle : 90°

Straight Angle : 180°

Complementary Angles :

Two angles the sum of whose measures is 90 degrees.

Supplementary Angles :

Two angles the sum of whose measures is 180 degrees.

## Triangles

Triangles :

1. The sum of the lengths of any two sides of a triangle is greater than the third side.

2. The sum of all the three angles of a triangle is 180°.

Isosceles Triangle :

Two sides equal ; two equal angles

Equilateral Triangle :

Three sides equal ; three equal angles

Right Triangles :

Pythagorean Theorem :

a2 + b2  =  c2

where a and b are the measures of the legs of the triangle and c is the hypotenuse.

## Statistics

Mean (Average) :

Sum of all values divided by number of values.

Median :

Middle value when the values are arranged numerically.

Mode :

The data value that occurs most frequently.

## Probability

Probability of the event A :

P(A)  =  The frequency of A / Total sample size

## Converting Mixed Number to Improper fraction ## Converting Improper fraction to Mixed Number  Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 