MODULE A - 2 DECIMALS AND ORDER OF OPERATION

OBJECTIVES At the end of this module, the student will be able to…  List the rules for working with decimals.  Given a mathematical problem involving decimals, add, subtract, multiply or divide decimals with and without a calculator and derive the correct answer.  List the rules for order of operation when performing calculations.  Given a mathematical problem, determine the proper order of operation for problems containing addition, subtraction, multiplication and division with and without a calculator and derive the correct answer.

Decimals THE RULES: Addition Subtraction Multiplication Division

ADDITION When working without a calculator  Line up the decimals  Round to the appropriate number of decimal places  Add: = 54.0  Round to the correct number of places

PRACTICE = =

SUBTRACTION When working without a calculator  Line up the decimals  Round to the appropriate number of decimal places  Subtract: = 158

PRACTICE 7.23 – = – =

MULTIPLICATION Multiply the numbers as if they are whole numbers without decimals. Count the number of decimal places in the original numbers. That total will be the number of decimal places in the answer x (4 places) = 506 x 2 = 1012 =.1012 (4 places)

PRACTICE 98.7 X = 0.23 x 1000 =

DIVISION Top Number is theNumerator Bottom Number is theDenominator  Make the denominator a whole number by moving the decimal place to the right.  Move the decimal in the numerator to the right by the same amount.  Divide.

PRACTICE (moved 1 places) = (moved 1 places)

PRACTICE

TIME FOR PRACTICE See practice assignment

Order of Operation Three Rules First Rule: Order - Multiplication & Division from left to right Second Rule: Order - Addition & Subtraction from left to right 12 x 6 – 2 = (12 x 6) – 2 = 72 – 2 = 70

PEMDAS - "Please Excuse My Dear Aunt Sally"

Practice What will you do first?  70 x 4 – 40 = ______  850 x 2 x 30 = ______  / 2 = ______  / 5 = ______  945 – 9 x 5 = ______

Order of Operation Third Rule:  Simplification - Work inside outside Parenthesis ( ) Brackets [ ] Braces { } 194 – {[20 x (9-5)] + 14} =

Clinical Example The Alveolar Air Equation – pressure of O 2 in the alveoli  P A O 2 = F I O 2 (P Baro – P H 2 O ) – P A CO 2 [F I O 2 + (1-F I O 2 )] R  P A O 2 = 0.5 (760 – 47) – 40 [0.5 + (1 – 0.5 )] 0.8  Parentheses: P A O 2 = 0.5 (713) – 40 [0.5 + (0.625)]  Brackets: P A O 2 = 0.5(713) – 40 [1.125]  Multiply left to right:P A O 2 = 357 – 45  Subtract left to right: P A O 2 = 312 mm Hg

PRACTICE 100 – {[10 x (6 - 5)] + 25} = ______ 1289 – {[120 x (23 – 13)] + 4} = ______ 82 – [34 x (33 – 11)] + 76 = ______

ASSIGNMENTS Self-Assessment:  Decimals  Order of Operation Answers will be posted on website