-x-(-2.5)-distributive-property.jpeg "(3-8y) X (-2.5) Distributive Property")
Using the Distributive Property with Multiplication
The distributive property is a powerful tool in mathematics that allows us to simplify expressions involving multiplication. It states that multiplying a sum (or difference) by a number is the same as multiplying each term of the sum (or difference) by that number and then adding (or subtracting) the results.
Let's look at an example using the expression (3-8y) x (-2.5):
Breaking it Down
- Identify the terms: In this expression, we have two terms: 3 and -8y.
- Apply the distributive property: Multiply each term by -2.5:
- (3) x (-2.5) = -7.5
- (-8y) x (-2.5) = 20y
- Combine the results: Since we had subtraction in the original expression, we keep it in the final answer: -7.5 + 20y
The Final Answer
Therefore, (3-8y) x (-2.5) = -7.5 + 20y using the distributive property.
Why Does it Work?
The distributive property works because multiplication is essentially repeated addition. When we multiply (3-8y) by -2.5, we are adding -2.5 to itself (3-8y) times.
Think of it this way:
- (3-8y) x (-2.5) is the same as:
- -2.5 + (-2.5) + (-2.5) + ... (3-8y) times
Applying the distributive property allows us to simplify this repetitive addition into a more manageable form.
Importance
Understanding and using the distributive property is fundamental in simplifying algebraic expressions, solving equations, and understanding more advanced mathematical concepts. It's a powerful tool that helps us work with numbers more efficiently.