How do properties help me simplify algebraic expressions?
Also in solving arithmetic expression, you will use the order of operations including exponents.
|Who can edit:||Vignette In the Classroom In this vignette, students use associative, commutative, and distributive properties to generate equivalent algebraic expressions for the area of a rectangle. Today's task is to generate as many expressions as you can to represent the area of this rectangle.|
|Factors and the Distributive Property||Then evaluate the expression. Slide 2 Example b Use the Distributive Property to write as an equivalent expression.|
Intuitive Approach to Addition and Subtraction: What is my net worth? To find the answer: My net worth will be indicated by 40 - Since I owe more than I have, the answer has to be a negative number.
Intuitive Rule for combining numbers with unlike signs: Find the difference subtraction of the two numbers and use the sign of the larger number. A way to use this rule is to cover the signs of the numbers.
Find the difference between the numbers with the signs covered. Use the sign of the larger number. My net worth is indicated by - Since I am in debt and I owe you money, my net worth has to be Negative. Intuitive Rule for combining numbers with like signs: Add the two numbers and use the common sign.
Make a note card with the rules for adding and subtracting like and unlike signed numbers. Review note cards at least twice a week as part of your homework routine. The product is the answer to a multiplication problem. The quotient is the answer to a division problem. How much money will I lose?
Since I am losing money, the answer has to be a negative number. In the example above, is the product. The factors are the numbers being multiplied. The product or quotient of two numbers with unlike signs is always negative. How much more money did I have 7 days ago?
Since I had more money 7 days ago, the answer has to be a positive number. The product or quotient of two numbers with like signs is always positive. Divide Since the numerator and denominator are both negative, the quotient must be positive. Make note cards for all of the rules and vocabulary in the course.
Multiplication problems can be expressed in several ways: Division problems can be expressed in several ways: Zero in a Division Problem Division can be checked using multiplication.simplest form simplifying an expression term two-step equation.
Use the Distributive Property to write each expression as an equivalent expression.
Then evaluate the expression, if possible. 1. 3(8 2) Use the Distributive Property to write each expression as an equivalent expression. After discussing an expression, have students write the correct property and how it was applied to simplify each expression on their paper.
3 + (17 + ) Use associative property . Use the Distributive Property to write an equivalent expression for the following questions. 7. (2 + x)(2 + 3x) 8. Write an equivalent expression in factored form.
Explain how you can use the Distributive Property to write equivalent expressions. Use an example to demonstrate.
Algebraic expressions are the phrases used in algebra to combine one or more variables (represented by letters), constants, and the operational (+ - x /) symbols. Algebraic expressions, however, don't have an equals (=) sign. Like terms can be combined as is stated in the distributive property $$3x+7x=\left (3+7 \right)x=10x$$ Expressions like 3x+7x and 10x are equivalent expressions since they denote the same number.
Equations, Inequalities, and Problem Solving Simplifying Algebraic Expressions 74 CHAPTER 2 Equations, Inequalities, and Problem Solving As we explore in this section, an expression such as is not as simple as Next, we simplify this expression.
Use the distributive property.