STRUCTURE: APPLICATIONS

Which of the following is not an example of using the distributive property to multiply 12 times 22?

10(2 • 22)

5(4 · 3 + 3 · 4)=

120

13(10 + 2) could be used to simplify which of the following problems?

13(12)

8 + [13 - (2 + 1)]

18

6 ÷ 2 · 6 + 1 =

19

18 - 5 · 3 =

3

5(2 + 3) ÷ 25 + 8 ÷ 4

3

22·23 is equal to

440 + 66

4[(6 - 1) + 3(5 - 2)]

56

To multiply 6 26 mentally, rewrite 26 as 25 + 1 and enclose in parentheses as follows:

6 26 = 6(25 + 1) 6 25 + 6 1 = 150 + 6 = 156 (applying the distributive property).

Example 2: 8(2 + 4) ÷ 16

First, evaluate the expression in parentheses: 8(2 + 4) ÷ 16 = 8(6) ÷ 16 then, multiply: 8(6) ÷ 16 = 48 ÷ 16 then, divide: 48 ÷ 16 = 3

Example 3: 20 - 5(8 - 6)

First, evaluate the expression in parentheses: 20 - 5(8 - 6) = 20 - 5(2) then, multiply: 20 - 5(2) = 20 - 10 then, subtract: 20 - 10 = 10

Example 1: 6 ÷ 2 3 + 8 4 ÷ 2

First, multiply and divide in order from left to right: 6 ÷ 2 3 + 8 4 ÷ 2 = 9 + 16 = then, add: 9 + 16 = 25

General properties A. reflexive property B. symmetric property C. transitive property

General properties A. a = a B. if a = b, then b = a C. if a = b and b = c, then a = c

P = E = M = D = A = S =

Parentheses Exponents Multiplication Division from left to right Addition Subtraction from left to right

Properties of Multiplication H. commutative I. associative J. identity K. multiplicative inverse L. distributive M. zero

Properties of Multiplication H. a * b = b * a I. a(b * c) = (a * b)c J. a * 1 = a K. a * 1/a = 1; a =/ 0 L. a(b + c) = (a * b) + (a * c) M. a * 0 = 0

Properties of addition D. commutative E. associative F. identity G. additive inverse

Properties of addition D. a + b = b + a E. a + (b + c) = (a + b) + c F. a + 0 = a G. a + (-a) = 0

properties of axioms

The properties of axioms help us understand the operations of addition and multiplication. In this section we combine arithmetic expressions by addition and multiplication, and we justify each step by the number properties.

ORDER OF OPERATIONS

To find the value of a multi-step arithmetic expression, a definite order of operations must be followed. Expressions without parentheses: Multiply and divide left to right first; then add and subtract from left to right.

Select the number property that will justify the step in the following expression. 2(5 * 17) = (2 * 5) 17 = 10 * 17 = 170

associative - multiplication

Select the number property that will justify the step in the following expression. 6 + (14 + 70) = (6 + 14) + 70 = 20 + 70 = 90

associative= addition

Select the number property that will justify the following expression. If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?

commutative - multiplication used twice

Select the number property that will justify the step in the following expression. 4 * 13 * 25 = 4 * 25 * 13 = 100 * 13 = 1,300

identity - addition