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Chapter 4: Problem 91

Simplify the expression. $$\frac{14 x y z}{7 z}$$

Short Answer

Expert verified
The simplified expression is 2xy.

Step by step solution

01

Identify common factors

Look at the numerator and the denominator to identify any common factors. The numerator is 14xyz, and the denominator is 7z. Notice that both contain the factor 'z'.
02

Factor out common terms

Factor out the common term 'z' from both the numerator and the denominator. This gives \( \frac{14xyz}{7z} = \frac{14xy \times z}{7 \times z} \).
03

Cancel the common terms

The term 'z' in the numerator and denominator are the same, so they can be canceled out. This simplifies to \( \frac{14xy}{7} \).
04

Simplify the fraction

Now, simplify \( \frac{14xy}{7} \) by dividing both the numerator and denominator by 7. This gives \( \frac{14xy}{7} = 2xy \).

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Key Concepts

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

common factors
When you're asked to simplify an expression, one of the first things you should look for are common factors. A common factor is a number or variable that appears in both the numerator and the denominator. By identifying common factors, you can start the process of simplification more easily. In our example, the expression is \( \frac{14xyz}{7z} \). Both the numerator (14xyz) and the denominator (7z) share the factor 'z'. This shared 'z' is a common factor that we can use to simplify the expression.
factoring
Once you've identified the common factors, the next step is factoring them out. Factoring involves writing the expression in a way that clearly shows the common factors. In our example, we factor out 'z' from both the numerator and the denominator: \( \frac{14xyz}{7z} = \frac{14xy \times z}{7 \times z} \). This step is crucial because it sets you up for the next part鈥揷anceling terms.
canceling terms
After factoring out the common terms, the same terms in both the numerator and the denominator can be canceled. Canceling just means that you remove these identical terms from both parts of the fraction. This step drastically simplifies the expression. Continuing with our example, the factor 'z' appears in both the numerator and the denominator, so we can cancel them and simplify to \( \frac{14xy}{7} \).
simplification
The final step in our process is simplification. Simplification is the act of making an expression as simple as possible. Here, you'll take what's left after you've canceled common terms and simplify further if needed. For our example, \( \frac{14xy}{7} \) can be simplified by dividing both the numerator and the denominator by 7. This gives us \( \frac{14xy}{7} = 2xy \). Now, the expression is in its simplest form, which is easy to work with in further calculations.

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