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Chapter 4: Problem 549

Mixed Practice, In the following exercises, solve. $$\frac{8}{15}=-d$$

Short Answer

Expert verified
d = -\frac{8}{15}

Step by step solution

01

Understand the Equation

The given equation is \ \( \frac{8}{15} = -d \ \). The goal is to solve for \( d \).
02

Isolate the Variable

To isolate \( d \), we need to get rid of the negative sign. Multiply both sides of the equation by \ -1 \ to make \( d\) positive. So,\ -1 \times \frac{8}{15} = -1 \times -d \. This simplifies to \ - \frac{8}{15} = d \.
03

Simplify the Right Side

Simplify \( - \frac{8}{15} \). Since there are no further simplifications needed, we have \( d = - \frac{8}{15} \).

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Key Concepts

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

Prealgebra Concepts
Prealgebra is a crucial foundation for understanding algebra and advanced math. It involves basic arithmetic like addition, subtraction, multiplication, and division, as well as introductory algebraic concepts. In this equation \(\frac{8}{15} = -d\), we see the use of fractions and negative signs, both of which are integral to prealgebra. Here, we learn to manage these components while solving for a variable. Understanding these basics ensures you can tackle more complex equations in the future.
Isolating Variables
Isolating variables is one of the key techniques in algebra and prealgebra. It means rearranging an equation so that the variable you're solving for is alone on one side of the equation. In the problem \(\frac{8}{15} = -d\), we want to make \(d\) positive and by itself. We do this by multiplying both sides of the equation by -1. This transforms the equation into a more manageable form: -1 times \(\frac{8}{15}\) equals \(d\). This process makes it clear and straightforward to find the value of \(d\).
Multiplication in Solving Equations
Multiplication is a fundamental operation in algebra, especially when isolating variables. When we multiplied both sides of \(\frac{8}{15} = -d\) by -1, we used multiplication to change the sign of \(d\), making it positive. The key rule is to perform the same operation on both sides of the equation to maintain equality. By multiplying by -1 on both sides, we get \(- \frac{8}{15} = d\). Multiplication, whether dealing with integers, fractions, or negative numbers, is an indispensable tool in solving equations.

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Most popular questions from this chapter

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\left(-\frac{5}{6}\right)\) when (a) \(x=\frac{1}{3} \quad\) (b) \(x=-\frac{1}{6}\)

In the following exercises, simplify. $$ \frac{2}{d}+\frac{9}{d} $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. 2\(x^{2} y^{3}\) when \(x=-\frac{2}{3}\) and \(y=-\frac{1}{2}\)

In the following exercises, simplify. $$ \frac{-6}{\frac{6}{11}} $$

In the following exercises, add. $$\frac{15}{32}+\frac{9}{32}$$
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