Properties of Real Numbers Reflexive Property Anything equals

Properties of Real Numbers Reflexive Property Anything equals itself A=A 15 = 15 b² = b²

Symmetric Property • If a = b, then switch it to b = a Reverse it!!!! • If 5 + 3 = 8, then 8 = 5 + 3 • If 4 quarters = 10 dimes, then 10 dimes = 4 quarters.

Transitive Property • If a = b and • b = c, • then a = c. • If 10 pennies = 1 dime, • and 1 dime = 2 nickels, then 10 pennies = 2 nickels

Substitution Property • Anything can be substituted for its equal somewhere else. • If n = 13, then 4 n = 4× 13 • If a = 33, then 2 a = 2 × 33

Additive Identity • For any number “a”, a + 0 = a Any number plus 0 is the same number you started with. • 5+0=5 • -17 + 0 = -17 • . 3124 + 0 =. 3124

Multiplicative Identity • For any number “a”, a × 1 = a Any number times 1 is the same number you started with. • 15 × 1 = 15 • -9 × 1 = -9 • . 483 × 1 =. 483

Additive Inverse • Any number and its opposite are additive inverses of each other. They add to zero. • • • -8 + 8 = 0 14 + -14 = 0 2/ + (-2/ ) = 0 3 3

Multiplicative Inverse • For every fraction a/b, where b ≠ 0, there is a fraction b/a, such that a/ b/ b × a = 1 • • • 3/ 4/ 4× 3= 1 -5/ × -2/ = 1 2 5 7 × 1 /7 = 1

Multiplicative Property of Zero • Any number times zero equals zero. 94 × 0 = 0 -1951 × 0 = 0 2, 345, 678, 901 × 0 = 0

Commutative Property • The order of numbers being added or multiplied does not change the final answer. • 5 + 4 = 9 and 4 + 5 = 9 , too • 9 + -19 = -10 and -19 + 9 = -10 • 8 x 7 = 56 and 7 x 8 = 56

Associative Property • The way you group 3 or more numbers when adding or multiplying them does not change the final answer. • 3+ (4 + 5) = (3 + 4) + 5 Note: numbers are in same order, just the parentheses moved… • ( 9 + 1) + 12 = 9 + ( 1 + 12) • (2 x 3) x 4 = 2 x (3 x 4) Note: numbers are in same order, just the parentheses moved… • (5 x -2) x 6 = 5 x (-2 x 6)

Distributive Property • The Distributive property is when you are multiplying one term times a group of terms being added or subtracted • 5(2 a + 4 b – 7 c) = 10 a + 20 b – 35 c • -2 ab(3 a² - 4 ab + 9 b²) = -6 a³b + 8 a²b² - 18 ab³