**See Also**

arithmetic operations video, evaluating expressions video, expressions video, operations video, order of operations video, substitution video, substitution of variables video, variables video.

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This math video tutorial gives a step by step explanation to a math problem on "Evaluating Expressions By Substitution Of Variables Using Order Of Operations".

Evaluating expressions by substitution of variables using order of operations video involves arithmetic operations, evaluating expressions, expressions, operations, order of operations, substitution, substitution of variables, variables. The video tutorial is recommended for 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade, 6th Grade, 7th Grade, 8th Grade, 9th Grade, and/or 10th Grade Math students studying Algebra, Geometry, Trigonometry, Arithmetic, Basic Math, Pre-Algebra, and/or Advanced Algebra.

For a given combination of values for the free variables, an expression may be evaluated, although for some combinations of values of the free variables, the expression may be undefined. Thus an expression represents a function whose inputs are the values assigned the free variables and whose output is the resulting value of the expression.

An expression is a combination of numbers, operators, grouping symbols (such as brackets and parentheses) and/or free variables and bound variables arranged in a meaningful way which can be evaluated. Bound variables are assigned values within the expression (they are for internal use) while free variables can take on values from outside the expression.

If an expression has more than one operation, the order in which you do the operations becomes important.

If the expression has parentheses, you should first do the operations inside parentheses.

After taking care of parentheses, you can do all multiplication and division operations.

Finally, you can do all addition and subtraction operations.

The mnemonic "**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally" (PEMDAS) commonly used to remember the order:

**P**arentheses, **E**xponentiation, **M**ultiplication, **D**ivision, **A**ddition, **S**ubtraction.

If the expression has parentheses, you should first do the operations inside parentheses.

After taking care of parentheses, you can do all multiplication and division operations.

Finally, you can do all addition and subtraction operations.

The mnemonic "

In mathematics, substitution of variables (also called variable substitution or coordinate transformation) refers to the substitution of certain variables with other variables. Though the study of how variable substitutions affect a certain problem can be interesting in itself, they are often used when solving mathematical or physical problems, as the correct substitution may greatly simplify a problem which is hard to solve in the original variables. Under certain conditions the solution to the original problem can be recovered by back-substitution (inverting the substitution).

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