Problem 60 Apply the appropriate property t... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 60

Apply the appropriate property to simplify the expression. $$-3(25-m)$$

Short Answer

Expert verified

-75 + 3m

Step by step solution

Identify the Property

Identify the property that can be used to simplify the expression. Here, use the distributive property, which states that for any numbers a, b, and c, $ a(b + c) = ab + ac $.

Apply the Distributive Property

Use the distributive property to distribute -3 to both terms inside the parentheses: $ -3 \times 25 \text{ and } -3 \times -m $.

Perform the Multiplications

Perform the multiplications: $ -3 \times 25 = -75 $ and $ -3 \times -m = 3m $.

Combine the Results

Combine the results to get the simplified expression: $ -75 + 3m $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions

Simplifying expressions means rewriting them in an easier or more manageable form. This often involves removing parentheses and combining like terms.
In the case of the expression $ -3(25 - m) $, we use the distributive property to simplify it.
Here's a simple breakdown:

First, identify the terms inside the parentheses, which are $25$ and $-m$.
Then distribute the $-3$ to each term inside the parentheses.
Finally, combine the results to get your simplified expression.

This step-by-step approach helps in breaking down complex expressions into simpler ones.

Multiplication

Multiplication involves repeated addition of the same number. When simplifying expressions, multiplication is often used to apply the distributive property.
When we have the expression $ -3(25 - m) $, we need to multiply $-3 $ by each term inside the parentheses.
Here's how:

Multiply $-3$ by $25$: $-3 \times 25 = -75$
Multiply $-3$ by $-m$: $-3 \times -m = 3m$

These multiplications help distribute the $-3$ through the parentheses, which is a key part of simplifying the expression.

Negative Numbers

Negative numbers are numbers less than zero. They can be tricky, especially when performing operations like multiplication.
When working with negative numbers:

Remember that multiplying two negative numbers results in a positive number: $-3 \times -m = 3m$.
Multiplying a negative number and a positive number gives a negative result: $-3 \times 25 = -75 $.

Understanding how negative numbers work with multiplication helps in getting the signs right in your simplified expressions.

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91影视

Apply the appropriate property to simplify the expression. $$-3(25-m)$$

Short Answer

Step by step solution

Identify the Property

Apply the Distributive Property

Perform the Multiplications

Combine the Results

Key Concepts

Simplifying Expressions

Multiplication

Negative Numbers

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