Chapter 1: Rational Numbers

Integer Calculations

(-) x (-) results a (+) (-) x (+) results a (-) (+) x (+) results a (+)

How to prove Number Relationships

1. Convert decimals into fractions (if necessary) 2. Make both have the same denominator 3. Show that one number is greater than the other or that they are equal

An Isolated Variable

A number who has a coefficient and exponent of 1

Rational Number (definition)

Any number that can be expressed as a quotient or fraction of two integers with the denominator not equal to zero. When put into decimal form it ends at some decimal place value.

Irrational Number (definition)

Any number that can be written in fraction form and whose denominator is not equal to zero. It has a continuous remainder when put into decimal form.

Conversions

Mixed to Improper Improper to Mixed Fractions to Decimals Decimals to Fractions

Number Relationships (definition)

The relationship between two or more integers. (Greater than, Less than, Equal to). Positive integers are always greater than Negative integers. 0 is neither positive or negative.

BEDMAS

This is just a guideline to follow. Group it together as brackets and exponents, then division and multiplication, and finally addition and subtraction.

How do you calculate exponents with integer fractions?

You have to be aware if the sign is inside or outside the function of x. Inside: (-2) with the exponent outside the brackets. You would do -2x(-2)x(-2)= -8 to determine if the product is negative or positive you must know the outcome of when the two signs are multiplied. The answer is - in this case. Outside: -2 with the exponent beside the 2. You would have to ignore the sign at first and calculate 2 to the power of 3 then apply the sign. In this case the answer is also -8