Define the key terms. a. variable b. constant c. expression d. sum e. difference f. product g. q

step 1 We're being asked to define a budget terms. So in part A, the term is a variable. Remember, a va

Define the key terms. a. variable b. constant c. expression...

Key Concepts

base

In exponentiation, the base is the number or expression that is multiplied by itself a certain number of times as indicated by the exponent. It is the foundational component of a power expression.

order of operations

The order of operations is a set of rules that specifies the sequence in which mathematical operations should be performed to correctly evaluate an expression. It ensures consistency in calculations by prioritizing operations such as parentheses, exponents, multiplication and division, and addition and subtraction.

square root

A square root is a value that, when multiplied by itself, gives the original number. It is a specific type of radical that is commonly used to reverse the operation of squaring a number.

power

A power refers to the result of an exponentiation operation, where a base is raised to an exponent. It can also denote the exponentiation expression itself, showing the relationship between the base and the exponent.

exponent

An exponent is the number that indicates how many times the base is multiplied by itself in an exponentiation operation. It acts as a multiplier for the base in the calculation of powers.

quotient

A quotient is the result obtained when one number or expression is divided by another. It represents the division operation and indicates how many times the divisor fits into the dividend.

variable

A variable is a symbol, typically a letter, used to represent an unknown or changeable value in mathematical expressions and equations. It serves as a placeholder that can take on various values depending on the context of the problem.

difference

A difference is the result of subtracting one number or expression from another. It represents how much one quantity exceeds or falls short of another.

sum

A sum is the result of adding two or more numbers or expressions together. It represents the combined total of the values involved in the addition operation.

expression

An expression is a combination of variables, constants, and operations (such as addition, subtraction, multiplication, and division) that represents a mathematical quantity. It does not contain an equality sign and is used to denote a value or relationship that can be simplified or evaluated.

constant

A constant is a fixed value that does not change throughout the course of a mathematical problem or equation. It is used to represent a specific, unvarying number, providing a stable element in expressions and calculations.

product

A product is the result of multiplying two or more numbers or expressions together. It quantifies the outcome of the multiplication process by combining the factors.

Transcript

00:01 We're being asked to define a budget terms.

00:02 So in part a, the term is a variable.

00:05 Remember, a variable is a symbol that represents a number.

00:08 So it's a symbol that represents a number.

00:20 So that's what a variable is.

00:22 Now, for part b, we're being asked to define what a constant is.

00:26 Well, think about what the current constant means.

00:29 It means something that doesn't change.

00:31 So a constant is a term that doesn't vary.

00:34 So a term that does not vary.

00:40 And the reason why it doesn't vary is because it doesn't have a variable attached to it.

00:45 So that's what a constant is.

00:46 It's a term that doesn't vary.

00:48 Now, in part c, we're being asked for what to describe what an expression is.

00:53 Well, an expression represents the sum or difference of various terms.

00:58 So an expression is the sum or difference of terms.

01:14 Or i'll even say, i'll put that as to parentheses, because technically an expression could just contain one term.

01:20 All right, well, part d asked for what is the sum.

01:24 Well, remember, sum is when you're adding two numbers.

01:27 So you want to be thinking addition.

01:29 So, for example, if i had a plus b, i would say the sum of a plus b.

01:35 All right, in part e, we're being asked to define difference.

01:39 Well, remember, difference means subtraction.

01:42 So the word difference means subtraction.

01:46 So for example, if i said the difference of a minus b, okay, so difference is subtraction.

01:54 For part f, we wanted to find the word product.

01:56 Well, remember, the product, it happens when we multiply two numbers together.

02:00 So you want to be thinking multiplication.

02:05 So the product of, for example, 5 times 4 would be equal to 20, because you multiply those two numbers together.

02:12 All right.

02:13 Next to part g, we want to find the quotient.

02:16 Well, remember, the quotient is the answer to a division problem.

02:19 So you want to be thinking about division.

02:21 So, for example, if i wanted the quotient between 10 and 2, i would divide those numbers as i'd say that the quotient is equal to five...

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