A Real Number is any number that can be placed on a continuous number line, including natural numbers, integers, fractions, decimals, and irrational numbers like √2 and π, essentially every number that isn't an imaginary number.
Solved Problems
Problem 1: Give some examples of commutative properties.
Solution:
For addition
- 8 + 3 = 3 + 8 = 11
- 26 + 11 = 11 + 26 = 37
 For multiplication
- 12 × 5 = 5 × 12 = 60
- 2 × 5 = 5 × 2 = 10
Problem 2: Simplify 70 × (20 + 9) by distributive property.
Solution:
As per the distributive propertyÂ
⇒ 70 × (20 + 9) = 70 × 20 + 70 × 9
⇒ 70 × (20 + 9) = 1400 + 630
⇒ 70 × (20 + 9) = 2030
Problem 3: Verify the associative property for the following: (30 + 60) + 7 = 30 + (60 + 7)
Solution:
To verify the given expression, calculate the LHS and RHS separately,Â
LHS = (30 + 60) + 7Â
⇒ LHS = 90 + 7Â
⇒ LHS = 97Â
RHS = 30 + (60 + 7)
⇒ RHS= 30 + 67
⇒ RHS= 97
⇒ LHS = RHS [Hence, verified.]
Practice Problems
1. Use the commutative property of addition to simplify: 12 + (-8)
2. Apply the associative property of multiplication: (3 × 2) × 5
3. Use the distributive property to expand: 4(x + 3)
4. Identify the additive identity in the equation: y + __ = y
5. Find the multiplicative inverse of 6.
6. Use the commutative property of multiplication to rewrite: 3ab
7. Apply the associative property of addition: (15 + (-7)) + 2
8. Use the distributive property to factor: 6x + 12
9. Find the additive inverse of -3.5.
10. Determine if the following is an example of the closure property of multiplication for real numbers: √2 × √3
