1 / 19

Just the facts: Order of Operations and Properties of real numbers

Just the facts: Order of Operations and Properties of real numbers. A GEMS/ALEX Submission Submitted by: Elizabeth Thompson, PhD Summer, 2008. Important things to remember. Parenthesis – anything grouped… including information above or below a fraction bar.

helmut
Download Presentation

Just the facts: Order of Operations and Properties of real numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Just the facts: Order of Operations and Properties of real numbers A GEMS/ALEX Submission Submitted by: Elizabeth Thompson, PhD Summer, 2008

  2. Important things toremember • Parenthesis – anything grouped… including information above or below a fraction bar. • Exponents – anything in the same family as a ‘power’… this includes radicals (square roots). • Multiplication- this includes distributive property (discussed in detail later). Some items are grouped!!! • Multiplication and Division are GROUPED from left to right (like reading a book- do whichever comes first. • Addition and Subtraction are also grouped from left to right, do whichever comes first in the problem.

  3. So really it looks like this….. • Parenthesis • Exponents • Multiplication and Division • Addition and Subtraction In order from left to right In order from left to right

  4. SAMPLE PROBLEM #1 Parenthesis Exponents This one is tricky! Remember: Multiplication/Division are grouped from left to right…what comes 1st? Division did…now do the multiplication (indicated by parenthesis) More division Subtraction

  5. SAMPLE PROBLEM Exponents Parenthesis Remember the division symbol here is grouping everything on top, so work everything up there first….multiplication Division – because all the work is done above and below the line Subtraction

  6. Order of Operations-BASICSThink: PEMDAS Please Excuse My Dear Aunt Sally • Parenthesis • Exponents • Multiplication • Division • Addition • Subtraction

  7. Take time to practice

  8. Assignment #1(When all assigned problems are finished – do for Homework as needed) • Remember PEMDAS and “Please Excuse My Dear Aunt Sally”? • Make up your own acronym for PEMDAS and post it on the class wiki. • Write it on White Paper and Illustrate your acronym. • Make sure it is school appropriate.

  9. Lesson Extension • Can you fill in the missing operations? • 2 - (3+5) + 4 = -2 • 4 + 7 * 3 ÷ 3 = 11 • 5 * 3 + 5 ÷ 2 = 10

  10. Assignment #2Create a Puzzle Greeting • Fold a piece of paper (white or colored) like a greeting card. • On the cover: Write an equation with missing operations (like the practice slide) • In the middle: Write the equation with the correct operations • On the back: Put your name as you would find a companies name on the back of a greeting card.

  11. Part 2: Properties of Real Numbers(A listing) • Associative Properties • Commutative Properties • Inverse Properties • Identity Properties • Distributive Property All of these rules apply to Addition and Multiplication

  12. Associative PropertiesAssociate = group It doesn’t matter how you group (associate) addition or multiplication…the answer will be the same! Rules: Associative Property of Addition (a+b)+c = a+(b+c) Associative Property of Multiplication (ab)c = a(bc) Samples: Associative Property of Addition (1+2)+3 = 1+(2+3) Associative Property of Multiplication (2x3)4 = 2(3x4)

  13. Commutative PropertiesCommute = travel (move) It doesn’t matter how you swap addition or multiplication around…the answer will be the same! Rules: Commutative Property of Addition a+b = b+a Commutative Property of Multiplication ab = ba Samples: Commutative Property of Addition 1+2 = 2+1 Commutative Property of Multiplication (2x3) = (3x2)

  14. Stop and think! • Does the Associative Property hold true for Subtraction and Division? • Does the Commutative Property hold true for Subtraction and Division? Is (5-2)-3 = 5-(2-3)? Is (6/3)-2 the same as 6/(3-2)? Is 5-2 = 2-5? Is 6/3 the same as 3/6? Properties of real numbers are only for Addition and Multiplication

  15. Inverse PropertiesThink: Opposite Rules: Inverse Property of Addition a+(-a) = 0 Inverse Property of Multiplication a(1/a) = 1 What is the opposite (inverse) of addition? What is the opposite of multiplication? Subtraction (add the negative) Division (multiply by reciprocal) Samples: Inverse Property of Addition 3+(-3)=0 Inverse Property of Multiplication 2(1/2)=1

  16. Identity Properties Rules: Identity Property of Addition a+0 = a Identity Property of Multiplication a(1) = a What can you add to a number & get the same number back? What can you multiply a number by and get the number back? 0 (zero) 1 (one) Samples: Identity Property of Addition 3+0=3 Identity Property of Multiplication 2(1)=2

  17. Distributive Property If something is sitting just outside a set of parenthesis, you can distribute it through the parenthesis with multiplication and remove the parenthesis. Rule: a(b+c) = ab+bc • Samples: • 4(3+2)=4(3)+4(2)=12+8=20 • 2(x+3) = 2x + 6 • -(3+x) = -3 - x

  18. Take time to practice

  19. Homework Log on to class wiki / discussion thread Follow the directions given: • Give an example of each of the properties discussed in class, do not duplicate a previous entry.

More Related