Problem 68 Write a mathematical expression ... [FREE SOLUTION]

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Chapter 1: Problem 68

Write a mathematical expression for each and simplify. Half of \(-30\)

Short Answer

Expert verified

The simplified mathematical expression for half of -30 is \(-\frac{30}{2} = -15\).

Step by step solution

Write the expression

First, let's write the expression for finding half of -30, which can be represented as \(-\frac{30}{2}\).

Divide by 2

Now, we divide -30 by 2: \[ -\frac{30}{2} = -15 \] The result of half of -30 is -15.

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Key Concepts

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

Solving Equations

In algebra, solving equations is about finding the value or values that make the equation true. An equation is like a balance scale. Think of each side needing to be equal. When we see something like \( x + 3 = 5 \), we want to find what number x equals, so both sides balance.

Steps in solving equations often include:

Identify the problem: Find what's being asked. What is unknown?
Isolate the variable: Use inverse operations, like adding to both sides, dividing, etc., to "uncover" the variable.
Check your solution: Substitute your answer back into the original equation to make sure it works.

When dealing with more complex expressions, these steps might involve multiple actions, but the core idea remains the same: keep the balance.

Simplification

Simplification in algebra means making an expression easier to work with, generally by reducing it to its simplest form. This process can involve several operations.

Here's what we typically do when simplifying:

Combine like terms: If you have \(2x + 3x\), you combine them to get \(5x\).
Apply distributive property: Multiply each term inside a bracket by the term outside, e.g., \(2(x + 3) = 2x + 6\).
Perform operations: Calculate any numerical expressions present.

By following these steps, we make algebraic expressions more manageable and ready for solving or further manipulation.

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign, such as -1, -5, or -30. They can express situations like debts or temperatures below zero.

When dealing with negative numbers, there are some rules to remember:

Adding a negative is the same as subtracting: \(3 + (-2) = 3 - 2 = 1\).
Subtracting a negative is the same as adding: \(3 - (-2) = 3 + 2 = 5\).
Multiplying or dividing two negative numbers results in a positive number: \(-2 \times -3 = 6\).
Multiplying or dividing a negative and a positive number results in a negative number: \(-2 \times 3 = -6\).

Understand these rules to handle negative numbers accurately in algebraic expressions.

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91影视

Write a mathematical expression for each and simplify. Half of \(-30\)

Short Answer

Step by step solution

Write the expression

Divide by 2

Key Concepts

Solving Equations

Simplification

Negative Numbers

One App. One Place for Learning.

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