Put it Together

While the forgotten food in your fridge may not be what you spend your work day dreaming about devouring when you get home, those jumbled bits and pieces can be used to create something tasty enough to satisfy your hunger. Hopefully this module offered you enough tidbits to keep you full long enough to get to the next section, where you will learn how to put these forgotten skills to work as you continue to grow your mathematical prowess. Remember, you can come back to this review any time throughout the course for practice dividing fractions, simplifying with square roots, or whatever you might need to help you learn the concepts in this course more easily.

Glossary

algebraic expression constants and variables combined using addition, subtraction, multiplication, and division

associative property of addition the sum of three numbers may be grouped differently without affecting the result; in symbols, [latex]a+\left(b+c\right)=\left(a+b\right)+c[/latex]

associative property of multiplication the product of three numbers may be grouped differently without affecting the result; in symbols, [latex]a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c[/latex]

base in exponential notation, the expression that is being multiplied

commutative property of addition two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[/latex]

commutative property of multiplication two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\cdot b=b\cdot a[/latex]

constant a quantity that does not change value

distributive property the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, [latex]a\cdot \left(b+c\right)=a\cdot b+a\cdot c[/latex]

equation a mathematical statement indicating that two expressions are equal

exponent in exponential notation, the raised number or variable that indicates how many times the base is being multiplied

exponential notation a shorthand method of writing products of the same factor

identity property of addition there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, [latex]a+0=a[/latex]

identity property of multiplication there is a unique number, called the multiplicative identity, 1, which, when multiplied by a number, results in the original number; in symbols, [latex]a\cdot 1=a[/latex]

integers the set consisting of the natural numbers, their opposites, and 0: [latex]\{\dots ,-3,-2,-1,0,1,2,3,\dots \}[/latex]

inverse property of addition for every real number [latex]a[/latex], there is a unique number, called the additive inverse (or opposite), denoted [latex]-a[/latex], which, when added to the original number, results in the additive identity, 0; in symbols, [latex]a+\left(-a\right)=0[/latex]

inverse property of multiplication for every non-zero real number [latex]a[/latex], there is a unique number, called the multiplicative inverse (or reciprocal), denoted [latex]\frac{1}{a}[/latex], which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, [latex]a\cdot \frac{1}{a}=1[/latex]

natural numbers the set of counting numbers: [latex]\{1,2,3,\dots \}[/latex]

order of operations a set of rules governing how mathematical expressions are to be evaluated, assigning priorities to operations

rational numbers the set of all numbers of the form [latex]\frac{m}{n}[/latex], where [latex]m[/latex] and [latex]n[/latex] are integers and [latex]n\ne 0[/latex]. Any rational number may be written as a fraction or a terminating or repeating decimal.

real number line a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.

real numbers the sets of rational numbers and irrational numbers taken together

variable a quantity that may change value

whole numbers the set consisting of 0 plus the natural numbers: [latex]\{0,1,2,3,\dots \}[/latex]