Mathematics

Adding two negative numbers results in

a negative number (-8) + (-6) = -14

Subtracting a positive number from a negative number results in

a negative value (-12) - 7 is the same as (-12) + (-7) with a solution of -19

For multiplication and division of integers and rational numbers, if one number is positive and another number is negative, the result is

a negative value (-15) / 5 has a solution of -3 since there is one negative number

Integer

a number that does not have a fractional part the whole numbers together with their negatives counting numbers, their opposites, and zero ... -3, -2, -1, 0, 1, 2, 3, ...

Irrational number

a number that is a never-ending, non-repeating decima

Base-10 system

a place value system in which each digit is 10 times greater than the digit to the right of it.

Subtracting a negative number from a positive number results in

a positive value 12 - (-7) is the same as 12 + 7 with a solution of 19

Adding two positive numbers results in

a positive value 3.3 + 4.8 = 8.1

Place value system

a system of writing numbers in which the quantity is determined by its place in the written string

Conjugate

a technique used to change the complex number into a real number the conjugate of 4 - 3i is 4 + 3i multiplying (4 - 3i) ( 4 + 3i) = 16 + 12i - 12i + 9 = 25

Adding one positive and one negative number requires taking the

absolute values and finding the difference between them then, the sign of the number that has the higher absolute value for the final solution is used (-9) + 11 has a difference of absolute values of 2 the final solution is 2 because 11 has the higher absolute value 9 + (-11) has a difference of absolute values of 2 the final solution is -2 because 11 has the higher absolute value

Subtracting two positive numbers is the same as

adding one positive and one negative number 4.9 - 7.1 is the same as 4.9 + (-7.1) the solution is -2.2 since the absolute value of -7.1 is greater 8.5 - 6.4 is the same as 8.5 + (-6.4) the solution is 2.1 since the absolute value of 8.5 is greater

Real numbers

are used in normal settings

Numerator

the top number in a fraction

Rational number

A number that can be written as a fraction using integers every integer is also a rational number inclusive of integers, fractions, and decimals that terminate, or end or repeat

Denominator

The bottom number in a fraction

Ordering numbers (decimal ordering)

assuming that any numbers to the left of the decimal point are equal, the next numbers to be compared are those immediately to the right of the decimal point if those are equal, then move on to compare the values in the next decimal place to the right ex. Which number is greater, 12.35 or 12.38? check that the values to the left of the decimal point are equal 12 = 12 next, compare the values of the decimal place to the right of the decimal 12.3 = 12.3 finally, compare the value of the numbers in the next decimal place to the right of both numbers 12.35 and 12.38 here the 5 is less than the 8, so the final way to express this inequality is 12.35 < 12.38

When subtracting integers and negative rational numbers, one has to

change the problem to adding the opposite and then apply the rules of addition

Complex numbers

composed of both a real number and an imaginary one imaginary numbers are the result of taking the square root of -1, and sqrt -1 = i

Sum

cumulative value

Whole numbers

only includes positive integers and 0 include all counting numbers and zero 0, 1, 2, 3, 4, ...

Natural numbers

only positive integers

For multiplication and division of integers and rational numbers, if both numbers are positive or both numbers are negative, the result is a

positive value (1.7)(-4) has a solution of 6.8 since both numbers are negative values

Addition also holds the associative property, which means

that the groups of numbers don't matter in an addition problem (a + b) + c = a + (b+ c)

Addition holds the commutative property, which means

that the numbers in an addition equation can be switched without altering the result a + b = b + a

The number before the division sign is called

the dividend, or, if expressed as a fraction, then its the numerator in a /b, a is the dividend or the numerator

The number after the division sign is called

the divisor, or, if expressed as a fraction, then it's the denominator in a/b, b is the divisor or the denominator

Counting numbers

the first numbers learned as a child 1, 2, 3, 4, and so on

A number line

typically consists of integers and is used to visually represent the value of a rational number

Ordering Numbers (all real numbers)

whether the question asks to order the numbers from greatest to least or least to greatest, the crux of the question is the same - convert the numbers into a common format generally its easiest to write the numbers as whole numbers and decimals so they can be placed on a number line 1. Order the following rational numbers from greatest to least: sqrt 36, 0.65, 78%, 3/4, 7, 90% 5/2 of the seven numbers, the whole number (7) and the decimal (0.65) are already in an accessible form the square root of 36 equals 6 (if the test asks for the root of a non-perfect root, determine which two whole numbers the root lies between). Next, convert the percentages to decimals. A percentage means "per hundred," so this conversion requires moving the decimal point two places to the left, leaving 0.78 and 0.90. Lastly, focus on fractions: 3/4 = 0.75; 5/2 = 2.5 Now, the only step left is to list the numbers in the requested order: 7, sqrt 36, 5/2, 90%, 78%, 3/4, 0.65 2. Order the following rational numbers from least to greatest: 2.5, sqrt 9, -10.5, 0.853, 175%, sqrt 4, 4/5 sqrt 9 = 3 175% = 1.75 sqrt 4 = 2 4/5 = .8 from least to greatest, the answer is: -10.5, 4/5, 0.853, 175%, sqrt 4, 2.5, sqrt 9

Fraction

written as x/y and represents the quotient of x being divided by y