Mastering Math: Properties & Operations Guide

1. Commutative PropertyAddition-the addition of terms in any order obtains the same sum. (a+b+c=d, a+c+b=d)Multiplication- the multiplication of terms in any order obtains the same product. (abc=d, bca=d)

2. Distributive PropertyA rule or method that states that every term inside grouping symbols may be multiplied by a term outside grouping to yield an equivalent expression. Ex) 10(3+7) = (10*3)+(10*7)=100

3. Associative PropertyAddition- changing the grouping of terms in a sum without changing the sum. (4+2=2+4)Multiplication- changing the grouping of factors in a product without changing the product. (4*2=2*4)

4. Identity PropertyAddition- the rule that recognizes that a given number remains unchanged after the addition of a zero. (4+0=4)Multiplication- the rule that recognizes that a given number remains unchanged after multiplication with the number one. (4*1=4)

5. Inverse Property

6. (P.E.M.D.A.S F.L.T.R.) Order of Operations

7. P.E.M.D.A.S. • “ ”= Parenthesis “()” • “”= Exponent “22” • “”= Multiplication “6x8” • “ ”= Division “9÷3” • “”= Addition “7+5” • “”= Subtraction “10-4” • FLTR

8. P.E.M.D.A.S.F.L.T.R is also know as the Order of Operations. Order of Operations is the order in which you perform mathematical operations to solve an equation. We need P.E.M.D.A.S.F.L.T.R because it helps us solve equations properly and always the same way. Remember: Calculate an equation in the wrong order and you will get the wrong answer. What is P.E.M.D.A.S.F.L.T.R and why do we need it?

9. arenthesis “( )” • Used to group equations. • Parenthesis can also be shown as brackets. ”[ ] or { }”. • An example of an equation with parenthesis is: 6 (5+3) • Choose the proper way to solve the equation: • A. 6x5 =30 30 + 3 = 33 • B. 5+3 =8 8 x 6 = 48 Answer:

10. xponents “22” 2 • Used to multiply the same number repeatedly. • Exponent tells how many times a base number is multiplied to itself. • 5 = 5x5x5 =125 • An example of an equation using exponents is: 5 x 2 Choose the proper way to solve the equation: • A.2 = 4 4x5 = 20 • B. 5 x 2 = 10 10 = 100 Answer: 2 3 2

11. ultiplication “x” • Use the table on the right to help you. • Multiplication is just a faster way to add. • Choose the proper way to solve the equation: • 2 + 5 x 3 • A.5 x 3 = 15 15 + 2 = 17 • B.2 + 5= 7 7 x 3 = 21 Answer:

12. ivision “÷” • Division is splitting a larger number into smaller parts. • Remember to check your division with multiplication. • An example of an equation with division in it is: Choose the correct way to solve the equation: 12 4 + 2 • A.4 + 2 = 6 12 6 = 2 • B. 12 4 = 3 3 + 2 = 5 Answer:

13. ddition “+” • It is tempting to want to solve addition first in an equation. • Remember: only solve addition first if it is in parenthesis. • An example of an equation with addition in it is: Choose the proper way to solve the equation (113 + 19) + 81 =? A. 113 + 19 = 132 132 + 81 = 213 B. 19 + 81 = 100 100 + 113 = 213 Answer:

14. ubtraction ”-” • Subtraction is when you take away an equal or smaller amount from a number. • You can check your subtraction with addition. • An example of an equation with subtraction in it is: 74 – (12 - 4) The proper way to solve this equation is: A. 74 – 12 = 62 62 – 4 = 58 B. 12 – 4 = 8 74 – 8 = 66 Answer:

15. Review The Order of Operations is: P.E.M.D.A.S.F.L.T.R arenthesis xponents ultiplication ivision ddition ubtraction FLTR

16. Practice 6x4÷2+3=? • 24÷2+3 • 12+3 Answer:

17. Practice 15÷(6x2-9)=? • 15÷(12-9) • 15÷(3) Answer:

18. Practice (32+5)÷7=? • (9+5)÷7 • 14÷7 Answer:

19. Practice 7+(6x52+3)=? • 7+(6x25+3) • 7+(150+3) • 7+(153) Answer:

20. Practice • (18+2)÷5 • 20÷5 Answer: (3x6+2)÷5=?

21. Tips to Remember: An easy way to remember PEMDASFLTR is: leasexcuse y ear unt ally From Leaving the Room