Simplifying Expressions With Exponents And Decimals With Order Of Operations Video Tutorial
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Simplifying Expressions With Exponents And Decimals With Order Of Operations
This math video tutorial clip shows how to simplify expressions by following the rules of order of operations, distributive property and combining like terms.
Decimal exponents in the problem require decimal multiplication. After two decimal multiplications, we reach the solution using subtraction of two decimal numbers.
Simplifying expressions with exponents and decimals with order of operations involves algebra, algebraic expressions, arithmetic, arithmetic operations, decimals, exponents, expressions, number sense, operations, order of operations, simplifying algebraic expressions, simplifying expressions.
Algebra
Algebra is a branch of mathematics concerning the study of structure, relation and quantity.
Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.
Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.
Algebraic Expressions
An algebraic expression is an expression that is written using one or more variables.
Examples:
2x x – 6 3b + 4 p + q
Exponents
Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication:
a1 = a
a2 = a × a
a3 = a × a × a
a4 = a × a × a × a
and so on.
Expressions
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.
Order Of Operations
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 "Please Excuse My Dear Aunt Sally" (PEMDAS) commonly used to remember the order:
Parentheses, Exponentiation, Multiplication, Division, Addition, Subtraction.
Simplifying Expressions
Simplifying expressions requires a lot of practice. First, you need to have a clear and thorough understanding of the properties of integers and real numbers. Even though these properties may look obvious, it becomes difficult to identify them in given expressions.
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