7. Algebra Flashcards
What is a term?
One or more numbers and/or letters all connected by multiplication or division.
What is an Algebraic expression?
An algebraic expression is one more terms in a phrase. It’s not a whole “sentence,” so an expression doesn’t include an equal sign. here’s an example: 4x+2y+38c.
What is an equation?
An equation is a mathematical statement that states that two mathematical expressions are equal. An equation always includes an equal sign, like this example: 7a + 3b = 588.
What is a variable?
A variable is a number in disguise. In this expression, x and y are the variables: 7x + 10y = 27. The are called variables because the numbers they represent can vary from problem to problem. When you write your own equations, you can use any letters that make sense to you.
If the same letter appears more than once in a given equation or expression, it stands for the same number in all instances in that equation/expression. In 3x +2x =10, the first x doesn’t represent a different number from the second x. In this case, x = 2 (both times).
What is a coefficient?
A coefficient is the number part of an algebraic term. In this equation, 8 and 12 are the coefficients: 8a -12b = -4.
What is a constant?
A constant is a term in an algebraic expression that contains only a number; it’s a term without a variable attached to it. In this equation, 5 is the constant:14d +12a +5.
What are real numbers?
Real number are actual quantities, like amounts, ages, distances, and temperatures. A real number can be an integer, fraction, or decimal, and it can be rational or irrational. They’re numbers that appear on a number line, like this:
What are rational numbers?
Rational numbers are the set of real numbers, fractions, and terminating decimals. Rational numbers can always be written as the ratio or quotient of two integers. These are examples of rational numbers: 1/2, 5, 0.25.
What are irrational numbers?
Irrational numbers can’t be expressed as a quotient or ration of two integers. With irrational numbers, the decimal form is nonrepeating and nonterminating, like pi. You can’t write pi as a quotient of two integers, and its decimal form goes on forever. The same goes for square roots and other roots.
What are exponents? & What should you know about exponents?
An exponent tells you how many times to use a value (its base ) in multiplication. In this equation, 2 and x are both exponents: s2 + 3x = 470.
- Any base raised to the power of one equals itself: x1 = x.
- Any base raised to the zero power (except 0) equals 1: x0=1
- To multiply terms with the same base, add the exponents: x2 (x3) = x2+3 = x5
- If a base has a negative exponent, it’s equal to its reciprocal (inverse) with a positive exponent: x-3 = 1/x3
- When a product has an exponent, each factor is raised to that power: (xy)3 = x3y3.
What is a polynomial?
A polynomial is an expression that contains one or more terms, like constants, variables, and exponents. The exponents on the variables in a polynomial are always whole numbers. Here’s an example of a polynomial of a polynomial: 3ab - 2x2 + 2y3 - 7. Other special names for polynomials signal whether they have one, two, or three terms. For example, 2ab7 is a monomial because it has one term. 6x - 3 is a binomial because it has two terms, and 4a + 7b3 is a trinomial because it has three terms..
What are like terms?
In algebra, you combine like terms — terms that have matching variables in the expression or equation. The variables must have the same power to be like terms. These are all like terms: 4xy, 7xy, 32xy. Because xy is the same, you can combine them if you’re working with an equation, like this:
4xy + 7xy + 32xy = 215
43xy = 215
Why should you do the same thing on what you did on either side of an equation?
Because this proportional calculation keeps the equation equal.
Can you combine like terms?
If like terms are on the same side of the equation, yes!
When you transpose a term on the opposite side of the equal sign to find x, you always have to use an inverse operation.
True or false
True
How do you solve a multistep equation?
(equations with two same variables on the opposite side e.g., 3x + 3 = 9 + x)
INVERSE OPERATIONS!
How to simplify an expression?
- Remove whatever parentheses you can by multiplying factors
- Use exponent rules to remove any remaining parentheses (if applicable).
- Combine like terms
- Combine constants
- 3(2+x)+4(4x+3)-(x2)2
- 6+3x+16x+3-x4
- 6+19x+12-x4
- 19x+18-x4
Create an equation for the following problems
- Kathy sold 10 more carnival tickets than Bonnie did. Together, they sold 480 tickets. How many tickets did Bonnie sell?
- t + (t + 10) = 480
You can perform any calculation on either side of an equation as long as…
you do the same thing to both sides of the equation.
How do you solve one-step equations involving addition and subtraction?
- x + 47,372 = 50,000
- Isolate x on one side of the equal sign (x = 50,000 - 47,372).
Why do you get a negative number when you divide or multiply by:
negative and positive?
and get a positive number when you divide or multiply by:
negative and negative?
To balance each side of the equation.
One variable is always equal to one times that variable.
True or False
True
Describe the FOIL method.
Foil is a technique for distributing two binomials in algebra. FOIL stands for First, Outer, Inner, and Last, and it refers to problems like this one: (x+2) (x+5).
What are two-variable equations?
Two-variable equations are what you see when working with graphs and in some other instances, they are usually multiple solutions (x + 3 = y).
When you have two or more of these equations and they all have exponents of 1, the equations are called linear systems, and to solve them, you either have to use substitution or combine equations.