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Chapter 4: Problem 548

Mixed Practice, In the following exercises, solve. $$\frac{11}{20}=-f$$

Short Answer

Expert verified
-\frac{11}{20}

Step by step solution

01

Identify the Equation

The given equation is \(\frac{11}{20} = -f\). The goal is to solve for the variable \(f\).
02

Isolate the Variable

Isolate \(f\) by multiplying both sides of the equation by \(-1\). This will cancel the negative sign on \(f\).
03

Solve for the Variable

After multiplying both sides by \(-1\), the equation becomes \(f = -\frac{11}{20}\). Therefore, \(f = -\frac{11}{20}\).

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Key Concepts

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

Isolate the Variable
When solving equations, a crucial step is to isolate the variable. This means we aim to get the variable by itself on one side of the equation.
In our equation, \( \frac{11}{20} = -f \), the variable we need to isolate is \( f \).
To do this, we need to remove any coefficients or constants attached to the variable. Remember, whatever operation we perform on one side of the equation, we must perform on the other to keep it balanced.
  • Identify the variable and the terms attached to it. Here, \( f \) has a negative sign.
  • Use inverse operations to cancel out these terms. Since \( f \) is negative, we multiply both sides of the equation by -1.
  • Check your new equation to confirm that the variable is isolated.
Once we've isolated \( f \), we move on to the next concept to solve the equation.
Multiplication Property of Equality
The multiplication property of equality tells us that we can multiply both sides of an equation by the same number without changing the equality.
This property is useful when we need to isolate a variable that is being multiplied or divided by a coefficient.
In the equation, \( \frac{11}{20} = -f \), we want to get rid of the negative sign attached to \( f \).
  • To apply this property, multiply both sides by \( -1 \).
  • When multiplied, the equation changes from \( \frac{11}{20} = -f \) to \( -\frac{11}{20} = f \).
  • Thus, \( f \) is isolated and we simplify the equation to \( f = -\frac{11}{20} \).
This step ensures that the isolation of the variable is mathematically consistent, preserving the balance of the equation.
Fractions
Fractions often create confusion, but they just represent parts of a whole number.
In our problem, \( \frac{11}{20} \) is a fraction where 11 is the numerator and 20 is the denominator.
Handling equations with fractions follows the same principles as with whole numbers, though it might require a step or two more for simplification.
  • Identify the fraction and understand its parts. Here, \( \frac{11}{20} \) represents 11 parts out of 20.
  • When performing operations like multiplication or division, treat the fraction as a whole entity. For example, multiplying \( \frac{11}{20} \) by \( -1 \) results in \( -\frac{11}{20} \).
  • Simplifying fractions can often make the problem easier, though in this particular exercise, no further simplification is necessary since \( 11 \) and \( 20 \) share no common factors besides 1.
By understanding fractions and how to manipulate them, you can handle even more complex equations with ease.

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Most popular questions from this chapter

In the following exercises, simplify. $$ \frac{5}{20} $$

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In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{5}{12}-w\) when (a) \(w=\frac{1}{4} \quad\) (b) \(w=-\frac{1}{4}\)

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