# Commutative law of multiplication to write an equivalent expression

Math Video Transcript We will also learn how to find them. Equivalent fractions are fractions that have the same value. What does this means? How much would you receive on the 30th day? The double of an amount is the same as multiplying an amount by two. So, the daily amounts in cents for each day would be: We use exponents to write the problem for each day in a shorter form. This says that we would need to multiply 29 two's to find the amount of money in cents for the thirtieth day.

Determine this amount then decide which choice would be the best choice. Solution The above problem motivates why exponents are used as a shortcut to setup problems.

We now give more examples involving exponents. Exponents Definition of an Exponent: The expressionwhich is n factors of b used for n — 1 multiplications, can be written as bn. The b is called the base and the n is called the exponent. A coin is flipped three times. How many outcomes are possible?

To solve the above problem in Session 9 Old Session 9we completed a tree diagram as illustrated below to solve the problem to motivate the Fundamental Counting Principle.

We have eight possible outcomes when a coin is flipped three times. What if we were to flip a coin four times? There would be sixteen possible outcomes if a coin is flipped four times. We would have 8, different possible outcomes if a coin is flipped thirteen times.

Note that as the number of times we have to repeat the multiplication becomes larger, the notation of using only multiplication becomes cumbersome. So, we use the short-cut notation with exponents to represent this type of repeated multiplication.

Use repeated multiplication to find 53,and On the menu there are three wines, three salads, three entrees, and three desserts. There are also three credit cards in his wallet. How many ways can he choose a meal choosing exactly one of each type of item and pay fo it with a credit card?

Dino has choices for a meal and paying for it. Self-Check Problem A standard die is rolled five times. Write the problem in exponential form and then solve it. Solution Exponents and Cartesian Product Since exponents represent repeated multiplication, exponents may also be used to represent Cartesian products of sets the set of ordered pairs. See Session 9 Old Session 9. A coin is flipped twice. What are the possible outcomes?

We may solve this problem as a Cartesian product question by giving the set all the possible ordered pairs. Determine the number of elements in B2, check the solution by finding B2, and then plot B2 on a coordinate plane.

Let D be the set of possible outcomes when rolling one 6-sided die. Write D using roster notation. Write out D2 using roster notation. What does D2 represent?

## Arithmetic properties

How many elements are in D2? Self-Check Problem Write the Cartesian Product for the possible outcomes of a person twice choosing one number between 1 and 3, inclusive.equivalent expressions, p. 16 Expressions with the same value, like 12 + 7 and 7 + 12, are equivalent expressions.

The commutative and associative properties can be used to write equivalent expressions. a. Simplify the expression 7 + (12 + x). 7 + (12 + x) = (7 + 12) + x . Since everything in this expression is multiplied, we use the commutative and associative properties of multiplication with the definition of exponent to find the product: Example: Multiply (4 x)(2 x)(x).

All three of these properties can also be applied to Algebraic Expressions. Which of the following statements illustrate the distributive, associate and the commutative property? Directions: Click on each question mark to see what property goes with the statement on the left.

Choose 3 expression from the blue box that have the same value as expressions 1, 2, and 3 shown in the pink box. 7(4+2) = (7 x 4) + (7 x 2) = 7 x 6 Together we will discover ways to show or Model. Most of algebra involves either simplifying expressions (by writing equivalent expressions) or solving equations (by writing equivalent equations).

We can use the addition and multiplication principles to produce equivalent equations, like x = 5 from which the solution - in this case, 5- is obvious.

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