simplify and evaluate algebraic expressions honors math grade 7

Simplify and Evaluate Algebraic ExpressionsHonors Math – Grade 7

Get Ready for the LessonThe Cortez and Marshall families went to the planetarium together. There are 2

adults and 3 children in the Cortez family and 1 adult and 2 children in the Marshall family. They bought adult and child tickets, and made a donation of $20 for both families at the entrance. How much did the two families pay in all?

To find how much, write and simplify an algebraic expression.

Define the variables for the unknown quantities.

A term of an algebraic expression is a number, a variable or a product or quotient of numbers and variables.

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The numerical part of a term that contains variables is the numerical coefficient.

Numerical coefficient

The variable, or variables, of a term is called the literal coefficient.

Literal coefficient

A term that does not have variables is called a constant.

5 terms

Identify the number of terms in each expression. Then name the numerical and literal coefficients and the constant of each expression.

163 2 xxy 534 3 rt

Terms that have exactly the same literal coefficients and are raised to the same power such as 2a and a are called like terms.

Terms that do not have the same variables or the corresponding variables are not raised to the same powers are called unlike terms.

To combine like terms…use the Distributive Property.

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Simplify each expression by combining like terms.

fggf 463 rssrs 61213

Simplify each expression by combining like terms.

22 1142 nnn yxxy 22 547

To evaluate an algebraic expression, you substitute numbers for the variables in the expression and then compute using the Order of Operations.

KEY CONCEPT The Substitution PrincipleFor any numbers a and b, if a = b, then a may be replaced with b.

THINK…

PLUG IT IN! PLUG IT IN!

Evaluate each expression when r = 10, s = 8 and t = 3.5

56 t 485 ts rt 32

Before evaluating some algebraic expressions, you can simplify them by combining like terms.

Evaluate when p = 0.5, q = -0.75 and r = 6.

qrpqrp 1224 22

Evaluate the expression for the given values of the variables.

3.026 42

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nnnm 5.1325.35.1 when m = 5 and n = -4