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Chapter 5: Problem 34

Solve. $$ \frac{x}{6}=\frac{1}{6} $$

Short Answer

Expert verified
x = 1

Step by step solution

01

Identify the equation

The problem presents the equation: \[ \frac{x}{6} = \frac{1}{6} \] Both sides of the equation are fractions.
02

Set up the equation

Recognize that in order for the fractions to be equal, their numerators must be equal because their denominators are already equal (6).
03

Equate the numerators

Set the numerator of the left-hand fraction equal to the numerator of the right-hand fraction: \[ x = 1 \]
04

Solve for x

Since the equality \( x = 1 \) is straightforward, the solution to the equation is: \[ x = 1 \]

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities in formulae and equations. In this exercise, we are dealing with an algebraic equation involving fractions.
To solve for a variable (like x in this case), we follow specific steps to isolate and identify its value.
By understanding the relationship between different parts of an equation, algebra helps us solve real-world problems.
The focus here is recognizing that, even with fractions, the same principles apply as with whole numbers.
Fractions
Fractions represent parts of a whole. They consist of a numerator (top number) and a denominator (bottom number).
In our problem, the fractions are \(\frac{x}{6}\) and \(\frac{1}{6}\). Both share the same denominator, making it easier to compare and solve.
When two fractions have the same denominator, their values depend solely on their numerators.
Therefore, to solve an equation involving such fractions, we focus on equating their numerators. This simplification can make the solution more straightforward, as we saw in the exercise.
Equal Numerators
When working with fractions, having equal numerators and denominators can simplify solving the equation.
In the equation \(\frac{x}{6} = \frac{1}{6}\), the denominators are already equal (6).
Thus, for the two fractions to be equal, their numerators must also be equal.
By setting the numerators equal to each other 鈥� \({x = 1}\) 鈥� and solving for x, we find that x equals 1.
This principle of equal numerators works because the equality holds true only if the parts (numerators) being divided by the same whole (denominator) are identical.

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Most popular questions from this chapter

Mariah bought \(\frac{3}{4} \mathrm{lb}\) of cheese at the city market and gave \(\frac{1}{2} \mathrm{lb}\) of it to Lindsay. How much cheese did Mariah have left? \([3.3 \mathrm{~d}]\)

Solve. Round the answer to the nearest thousandth. $$ \frac{12.0078}{56.0115}=\frac{789.23}{y} $$

Find each unit price Then, in each exercise, determine which size is the better buy based on unit price alone. $$ \begin{array}{|c|c|c|} \hline \text { Size } & \text { Price } & \text { Unit Price } \\ \hline 45 \text { oz } & \$ 5.90 & \\ 75 \text { oz } & \$ 8.59 & \\ \hline \end{array} $$

Multiply. Simplify, if possible. $$ 3 \frac{4}{5} \cdot 2 \frac{1}{4} $$

Solve. $$ \frac{15}{y}=\frac{3}{4} $$
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