Download presentation

Presentation is loading. Please wait.

Published byMatthew Page Modified over 9 years ago

1
Properties of Real Numbers The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

2
Commutative Property of Addition a + b = b + a Example:7 + 3 = 3 + 7 Two real numbers can be added in either order to achieve the same sum.

3
Commutative Property of Multiplication a x b = b x a Example:3 x 7 = 7 x 3 Two real numbers can be multiplied in either order to achieve the same product.

4
Associative Property of Multiplication (a x b) x c = a x (b x c) Example: (6 x 4) x 5 = 6 x (4 x 5) When three real numbers are multiplied, it makes no difference which are multiplied first. Notice how multiplying the 4 and 5 first makes completing the problem easier.

5
Associative Property of Addition (a + b) + c = a + (b + c) Example: (29 + 13) + 7 = 29 + (13 + 7) When three real numbers are added, it makes no difference which are added first. Notice how adding the 13 + 7 first makes completing the problem easier mentally.

6
Additive Identity Property a + 0 = a Example: 9 + 0 = 9 The sum of zero and a real number equals the number itself. Memory note: When you add zero to a number, that number will always keep its identity.

7
Multiplicative Identity Property a x 1 = a Example: 8 x 1 = 8 The product of one and a number equals the number itself. Memory note: When you multiply any number by one, that number will keep its identity.

8
Additive Inverse Property a + (-a) = 0 Example: 3 + (-3) = 0 The sum of a real number and its opposite is zero.

9
Multiplicative Inverse

10
Property of Zero (Multiplication) When any number is multiplied with zero, the answer is zero. 98,756,432 X 0 = 0

11
Property of Opposites a + (-a) = 0 If you added opposite #’s and ended with 0

12
Distributive Property a(b + c) = ab + ac ora(b – c) = ab – ac Example: 2(3 + 4) = (2 x 3) + (2 x 4) or 2(3 - 4) = (2 x 3) - (2 x 4) Distributive Property is the sum or difference of two expanded products.

13
Properties of Equality Addition property of equality If a = b, then a + c = b + c. Adding the same number to both sides of an equation does not change the equality of the equation. Subtraction property of equality If a = b, then a – c = b – c. Subtracting the same number from both sides of an equation does not change the equality of the equation. Multiplication property of equality If a = b and c ≠ 0, then a c = b c. Multiplying both sides of the equation by the same number, other than 0, does not change the equality of the equation. Division property of equality If a = b and c ≠ 0, then a ÷ c = b ÷ c. Dividing both sides of the equation by the same number, other than 0, does not change the equality of the equation.

14
Transitive Property If a = b and b = c, then a = c If one quantity equals a second quantity and the second quantity equals a third quantity, then the first equals the third. If 1000 mm = 100 cm and 100 cm = 1 m, Then 1000 mm = 1m

15
Symmetric Property If a + b = c then c = a + b If one quantity equals a second quantity, then the second quantity equals the first. If 10 = 4 + 6, then 4 + 6 = 10

16
Reflexive Property a = a a + b = a + b Any quantity is equal to itself. 7 = 7 2 + 3 = 2 + 3

17
Justify Steps in Solving Equations http://www.phschool.com/atschool/academy123/englis h/academy123_content/wl-book-demo/ph-374s.html http://www.phschool.com/atschool/academy123/englis h/academy123_content/wl-book-demo/ph-374s.html

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google