Problem 354 Simplify. $$ -\frac{4 x}{32 ... [FREE SOLUTION]

Chapter 1: Problem 354

Simplify. $$ -\frac{4 x}{32 y} $$

Short Answer

Expert verified

-\frac{x}{8y}

Step by step solution

Simplify the Fraction

Start by simplifying the fraction $-\frac{4x}{32y}$. We can do this by dividing both the numerator and the denominator by their greatest common divisor.

Identify the Greatest Common Divisor

The greatest common divisor (GCD) of 4 and 32 is 4. Thus, divide both the numerator and the denominator by 4.

Perform the Division

Divide the numerator $4x$ by 4: $\frac{4x}{4} = x$.\Divide the denominator $32y$ by 4: $\frac{32y}{4} = 8y$.

Simplify the Result

After dividing, the fraction $-\frac{4x}{32y}$ simplifies to $-\frac{x}{8y}$.

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Key Concepts

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

Greatest Common Divisor

The greatest common divisor, or GCD, is a key concept when simplifying fractions. It is the largest number that can exactly divide both the numerator and the denominator without leaving a remainder. Finding the GCD helps us reduce fractions to their simplest form.
For example, consider the numbers 4 and 32. The GCD of 4 and 32 is 4, because 4 is the largest number that can divide both evenly.
When simplifying the fraction $-\frac{4x}{32y}$, we use the GCD to make the numerator and denominator smaller, making the fraction easier to work with.

Numerator and Denominator Division

Once we have the GCD, the next step is to divide the numerator and the denominator by this value. This process reduces the fraction step-by-step.
For our example fraction, $-\frac{4x}{32y}$, we find the GCD to be 4.
We then divide both the numerator and the denominator by 4:

Numerator: \frac{4x}{4} = x\
Denominator: \frac{32y}{4} = 8y\

This division helps in breaking down the fraction. By making the numerator and the denominator as small as possible, we simplify the fraction further.

Fraction Simplification

Simplifying fractions is the process of making the fraction as simple as possible. When simplifying, we keep the value of the fraction the same but make it easier to understand and work with.
Let's revisit our example: $-\frac{4x}{32y}$.
We already divided the numerator and denominator by their GCD (4):
\frac{4x}{4} = x\ and \frac{32y}{4} = 8y\.
This means the simplified fraction is \-\frac{x}{8y}\.
This fraction is now in its simplest form and represents the same value as the original fraction. Simplifying helps us see relationships between fractions more clearly and makes calculation easier.

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91影视

Simplify. $$ -\frac{4 x}{32 y} $$

Short Answer

Step by step solution

Simplify the Fraction

Identify the Greatest Common Divisor

Perform the Division

Simplify the Result

Key Concepts

Greatest Common Divisor

Numerator and Denominator Division

Fraction Simplification

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