Using the Distributive property

Learning Targets I can recognize a common factor given two addends. (Example 21+14; Common factor of 7) I can express a sum of two whole numbers (1-100) with a common factor as a multiple of a sum of two whole numbers with no common factors (Example 21+14 = 7(3+2)). I can understand that the sum of two addends (or terms) can also be represented as the product of two terms, the GCF and the sum of relatively prime numbers, if the original addends have a common factor.

Can You Solve it Quickly? 512 x 5 Please solve the following problem. Is there a way to make this problem simpler? Today, we will learn how to write this problem as a multiplication problem using two factors. 2,560 500 x 5 12 x 5 + 2,500 60

Does This Make Sense? Is 8 x 5 the same as (5 x 5) + (3 x 5)? Why or why not? 8 x 5 is the same as (5 x 5) + (3 x 5) because 40 and 25 + 15 = 40

Notation There are many symbols that can be used for multiplication: The times sign (x) is probably what you are used to using. Computers often use the asterisk (*) The raised dot ( ) is an easy symbol to write and it prevents confusion when we use variables. Parentheses outside(inside) mean that the amount inside the parentheses is multiplied by the amount outside the parentheses.

Another Way of Writing a Number as the Sum of Two or More Numbers We can write 27 in many different ways: 15 + 12 20 + 7 15 + 5 + 7 These are all equivalent expressions because they have the same numerical value (answer). We can say that 3(5+4) = 15 + 12 = 27

Sometimes a Factor is More Than Just a Single Number of Quantity You know you can rename 9 as 5 + 4. So we can write 27 = 3(5+4). In this example, we are writing 27 as the product of two factors, 3 and (5+4).

New Ideas and Vocabulary Numerical Expression: A mathematical phrase that uses numbers and operations. Equivalent Expressions: Mathematical phrases that have the same value. You can use parentheses, a raised dot, or an asterisk to show multiplication. Factors can be more than just a single number because a number can be written as the sum or two or more numbers. Getting Ready for the Problem