Lesson:   Order of Operations, page c80 1. 23;     2.   35;     3.   23 4. (4+8)x2 or 2(4+8), or 2x(4+8), or 2(8+4) 5. 4x2+8, or 2x4+8, or 8+2x4, or8+4x2, or (4x2)+8

 "My Dear Aunt Sally" 1. Simplify, mentally if possible: a.   8 - 4 x 2 = 0 b.   3 x 3 + 4 x 5 = 29 c.   3 x 4 ÷ 2 = 6 d.   6 + 4 ÷ 2 = 8 e.   4 - 4 + 4 = 4 f.   4 ÷ 4 + 4 = 5 g.   4 + 4 ÷ 4 = 5 h.   6 + 2 ÷ 4 = 6 1/2 or 6.5 i.   6 x 2 ÷ 3 = 4 j.   6 ÷ 2 x 3 = 9 k.   2 ÷ 4 + 6 = 6 1/2 or 6.5 2. Simplify, as shown on the last page. 3. Write an expression for each. Do not simplify except to verify your answer. a.   the change from \$50 after purchasing 3 shirts at \$9 each:     50 - 3 x 9 b.   the perimeter of a 5 inch by 6 inch rectangle:     2 x 5 + 2 x 6 or 2 x (5 + 6) c.   nine increased by the product of six and eleven then decreased by half of ten:     9 + 6 x 11 - 10/2

 "Please, My Dear Aunt Sally" 1. List the marks of inclusion: ( ) and [ ] and { } and ____. 2. 1st: Check the expressions in which parentheses are not needed. 2nd: Simplify, mentally if possible:     a.   (8 - 4) x 2 = 8 x   b.   (3 x 3) + (4 x 5) = 29     c.   3 x (3 + 4) x 5 = 105     d.   3 x ([3 + 4] x 5) =105     e.   3 x [4 ÷ 2] = 6     f.   (6 + 4) ÷ 2 = 5 x   g.   (4 - 4) + 4 = 4 x   h.   (4 ÷ 4) + 4 = 5     i.   4 ÷ (4 + 4) = 1/2     j.   (4 + 4) ÷ 4 = 2 x   k.   6 + (2 ÷ 4) = 6 1/2 3. Complete the following statement. In simplifying an expression, parentheses are not needed if the operation, and the part of the expression, about which the inclusion marks are placed already has priority.

 WARM UPS from "Readily Excuse,"pg 6 1. Simplify: 9 - 4 x 5 = 9 - 20 = -11 2. Add 3 and 4 then square the result: (3+4)²= 7² = 49 3. State a number whose square is 25. (-5)(-5)=25 or (5)(5)= 25 4. State a number whose cube is -8. (-2)(-2)(-2) = -8 5. Simplify: Ans. 1 One to any power is still one. 6. Simplify: Ans. 1 Any number to the zero power other than zero is 1. 7. Simplify: Ans. 7/9

Suggestion:     Recopy whatever you do not simplify.

 Pg c80d, #4: PMDAS Order of Operations Don't think fraction. Think: There are 3 operations and the bar says treat the top as one number and treat the bottom as one number before doing the division.

 Pg c80d, #9: PMDAS Order of Operations Use parentheses to surround the computation which must be completed first.

Pg c80d, #11: PMDAS Order of Operations

Examine the table below. The last column employs the distributive law in the form of factoring.

 Situtation Restatement Justification 10% off 90% on 100%(price) - 10%(price)= 1.00(price) - .10(price)= .90(price)= .90 x the price 30% off 70% on 100%(price) - 30%(price)= 1.00(price) - .30(price)= .70(price)= .70 x the price 6% off 94% on 100%(price) - 6%(price)= 1.00(price) - .06(price)= .94(price)= .94 x the price
In summary, where p is the original price:
10% off means the price is .9 x the price
30% off means the price is .7 x the price
6% off means the price is .94 x the price
This means in question 11 that:
the sale price of a \$10 item selling for 10% off is
10% off the price of \$10 =
90% of the price of \$10 =
.90 x the price of \$10 =
.90 x 10