1-2B Order of Operations Algebra 1 Glencoe McGraw-Hill Linda Stamper

In arithmetic and algebra, order of operations is used to simplify an expression involving more than one operation. ( ) , [ ] , { } First do operations within grouping symbols. Then evaluate powers. Then do multiplication and division from left to right. Finally, do addition and subtraction from left to right. A fraction bar also acts as a grouping symbol. It indicates that the numerator and denominator should each be treated as a single value.

The answer does NOT have absolute value bars! The absolute value of a number is its distance from zero on a number line. The symbol |a| represents the absolute value of a. Note: Distance cannot be negative. The answer does NOT have absolute value bars! 7 • • -1 0 1 2 3 4 5 6 7 8

The answer does NOT have absolute value bars! Evaluate the expression. The answer does NOT have absolute value bars! 12 • • -14 -12 -10 -8 -6 -4 -2 0 2 4

 Example 1 Evaluate the expression. –|3|   – 3 –|–29|   – 29

If the common sign is positive, the + is not written! Rules of Addition To add two numbers with the same sign: Step 1 ADD Step 2 ATTACH the common sign –8 + (–5) 8 + 5 – 13 13 If the common sign is positive, the + is not written!

Rules of Addition To add two numbers with the opposite signs: Step 1 SUBTRACT (to remove zero pairs) Step 2 ATTACH the sign of the number with the larger absolute value. 4 + (–7) –3

Let yellow = positive Let red = negative When you add two numbers with opposite signs, you will need to subtract (take away) the zero pairs.

Rules of Subtraction Adding the opposite of a number is equivalent to subtracting the number. Subtraction 6 – 4 = 2 Addition 6 + (– 4) = 2      

Rules for Multiplication The product of a positive number and a negative number is negative. 12(–10) = –120 The product of a negative number and a negative number is positive. –12(–10) = 120 Summary If the signs are the same, the product is positive. If the signs are not the same, the product is negative.

The Sign of a Quotient Rule The quotient of a positive number and a negative number is negative. 25 –5 –5 The quotient of a negative number and a negative number is positive. –25 –5 5 Summary If the signs are the same the quotient is positive. If the signs are not the same the quotient is negative.

White Board Practice

Evaluate.

Evaluate.

Evaluate.

Evaluate.

Evaluate. When substituting a value into an expression, use parentheses.

Evaluate. When substituting a value into an expression, use parentheses.

Evaluate.

Evaluate.

Homework 1-A4 Handout A4.