Section 1.7 Properties of Real Numbers and Simplifying Expressions 79 612 32. 612 32 6122 6132 12 18 30 612 32 6152 30 Distributive Property of Multiplication over Addition If a, b, and c are real numbers, then a1b c2 ab ac and 1b c2a ab ac Applying the Distributive Property Example 5 Apply the distributive property: Solution: 21a 6b 72 Apply the distributive property. Simplify. 21a 6b 72 21a 6b 72 21a2 216b2 2172 2a 12b 14 Skill Practice Apply the distributive property. 10. 71x 4y z2 Answer 10. 7x 28y 7z 4. Distributive Property of Multiplication over Addition The operations of addition and multiplication are related by an important property called the distributive property of multiplication over addition. Consider the expression The order of operations indicates that the sum 2 3 is evaluated first, and then the result is multiplied by 6: Notice that the same result is obtained if the factor of 6 is multiplied by each of the numbers 2 and 3, and then their products are added: The factor of 6 is distributed to the numbers 2 and 3. The distributive property of multiplication over addition states that this is true in general. TIP: The mathematical definition of the distributive property is consistent with the everyday meaning of the word distribute. To distribute means to “spread out from one to many.” In the mathematical context, the factor a is distributed to both b and c in the parentheses.
miller_beginning_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above