%2F(-8))%2B((-5)%2F(6))-times(3)%2F(4)%3D((7)%2F(-8))times(3)%2F(4)%2B((-5)%2F(6))times(3)%2F(4).jpeg "((7)/(-8))+((-5)/(6)) Times(3)/(4)=((7)/(-8))times(3)/(4)+((-5)/(6))times(3)/(4)")
Understanding the Distributive Property of Multiplication
The equation ((7)/(-8))+((-5)/(6)) times(3)/(4)=((7)/(-8))times(3)/(4)+((-5)/(6))times(3)/(4) demonstrates the distributive property of multiplication over addition. This property is a fundamental concept in algebra and is widely used in simplifying expressions and solving equations.
What is the Distributive Property?
In simple terms, the distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. It can be represented by the following formula:
a(b + c) = ab + ac
Where 'a', 'b', and 'c' are any numbers.
Applying the Distributive Property to the Equation
In our given equation, we have:
- a = (3)/(4) (the number we are multiplying by)
- b = (7)/(-8) (the first addend)
- c = (-5)/(6) (the second addend)
Applying the distributive property, we can rewrite the equation as:
((3)/(4)) * ((7)/(-8) + (-5)/(6)) = ((3)/(4)) * (7)/(-8) + ((3)/(4)) * (-5)/(6)
This clearly shows that multiplying the sum of ((7)/(-8)) and ((-5)/(6)) by (3)/(4) is equivalent to multiplying each of them individually by (3)/(4) and then adding the results.
The Importance of the Distributive Property
The distributive property is crucial in simplifying complex algebraic expressions. It allows us to break down multiplication problems into simpler ones, making them easier to solve. It also plays a critical role in solving equations, especially those involving parentheses.
Conclusion
The equation ((7)/(-8))+((-5)/(6)) times(3)/(4)=((7)/(-8))times(3)/(4)+((-5)/(6))times(3)/(4) effectively demonstrates the distributive property of multiplication. By understanding and applying this property, we can simplify complex expressions and tackle more challenging algebraic problems.