9 Algebra Rules & Properties to Solve Your Complex Homework Problems Fast!

Many students find algebra a monotonous & tiring concept to study. It requires dedicating proper time to understand the problem and provide a solution for it. That’s why most students seek algebra homework help from experts, as they have excellent skills to analyze the question and give a perfect result.

Becoming a professional is not that easy, but not impossible as well. With practice and dedication, anyone can become an expert. You have to remember all the rules & laws that you will require in your paper.

Hence, here are the 9 rules & properties of algebra that you should memorize to solve the complex questions of homework smoothly.

9 Rules & Properties of Algebra to Solve the Complex Problems!

1. Starting with the first rule – The Commutative Property of Addition, which means that both sides of the plus signs can exchange the places. Still, the outcome will remain same in both the situation.

The Rule is => a + b = b + a

Examples:

Real Numbers

4 + 6 = 6 + 4

Algebraic Expressions

4z + z = z + 4z

2. The second rule is Commutative Property of Multiplication, which means the same as in addition. Swapping the digits will lead to no change in outcome.

The Rule is => a × b = b × a

Examples:

Real Numbers

10 × 14 = 14 × 10

Algebraic Expressions

(6y - 4) × y = y × (6y - 4)

3. The third rule is Associative Property of Addition, which means it does not matter where you put the parenthesis () the outcome will always be the same.

The Rule is => (a + b) + c = a + (b + c)

Examples:

Real Numbers

(6 + 9) + 18 = 6 + (9 + 18)

Algebraic Expressions

(9a + 6 a) + a = 9a + (6 a + a)

4. The fourth rule is Associative Property of Multiplication, which means the same wherever you put the parenthesis, the answer will remain the same.

The Rule is => (a × b) × c = a × (b × c)

Examples:

Real Numbers

(28 ×12) × 40 = 28 × (12 × 40)

Algebraic Expressions

(10 b × 25 b) × b = 10 b × (25 b × b)

5. The Fifth Law is Distributive Properties of Addition Over Multiplication, which means adding all the digits first and then multiplying will result equivalent if multiply first and add later.

The Rule is => a × (b + c) = a × b + a × c

And (a + b) × c = a × c + b × c

Examples:

Real Numbers

12 × (12 + 18) = 12 × 12 + 12 × 18

(12 + 18) × 7 = 12 × 7 + 18 × 7

Algebraic Expressions

c × (c 24 + c) = c × c 24 + c × c

(24 c + c) × 23 c = 24 c × 23 c + c × 23c

6. The sixth law states that the reciprocal of a non-zero real number ‘z’ will present as 1/z and z × (1/z) = 1

Examples:

Real Numbers

Reciprocal of 9 is 1/9 and 9 × (1/9) = 1

7. The Seventh rule states that the additive inverse of ‘x’ will be -x.

The Rule is => a + (- a) = 0

Examples:

-(-3) = 3 and - 3 + (3) = 0

8. The eighth law states that the additive identity is 0.

and c + 0 = 0 + c = c

9. The ninth law of algebra states that the multiplicative identity is 1.

and y × 1 = 1 × y = y

Above are the various rules & properties of algebra that can help you become a master in solving all the problems. Hope, you will find the formulas helpful as suggested by the best algebra homework help experts.