Problem 442 Subtract. $$ \frac{11 z}{13}... [FREE SOLUTION]

Chapter 1: Problem 442

Subtract. $$ \frac{11 z}{13}-\frac{8}{13} $$

Short Answer

Expert verified

$\frac{11z - 8}{13}$

Step by step solution

Identify the Common Denominator

Notice that both fractions have the same denominator of 13. Because the denominators are the same, subtraction can be performed directly by subtracting the numerators.

Subtract the Numerators

Subtract the numerators of the fractions: \[ 11z - 8 \]

Write the Final Fraction

Combine the results from step 2 over the common denominator of 13. This gives: \[ \frac{11z - 8}{13} \]

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Key Concepts

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

common denominator

In fraction subtraction, the first critical step is to identify a **common denominator**. When comparing or performing operations on fractions, having the same denominator simplifies the process.

A common denominator is a shared multiple of the denominators of two or more fractions. In our exercise, both fractions鈥擻(\frac{11z}{13}\) and $\frac{8}{13}$鈥攁lready share a common denominator of 13. This allows us to go straight to the next step without needing to find or convert denominators to a common base.

subtracting numerators

Once you have a common denominator, you can proceed to **subtracting the numerators**. This is a straightforward operation since both fractions have the same denominator.

Using our example fractions $\frac{11z}{13}$ and $\frac{8}{13}$, we subtract the numerators directly:

Numerator of the first fraction: $11z$

Numerator of the second fraction: $8$

Subtract the second numerator from the first: \[ 11z - 8 \]. This result gives the numerator of the new fraction.

simplifying fractions

After subtracting the numerators, the last step involves **simplifying fractions** if necessary. Simplification means reducing the fraction to its simplest form where both the numerator and the denominator share no common factors other than 1.

In our example, $\frac{11z - 8}{13}$ is already in its simplest form as 11z - 8 and 13 do not share any common factors.

Checking for simplification:

Ensure the numerator and denominator have no common divisors other than 1.

If any common divisors exist, divide both by that number.

Simplified fractions are easier to read and work with, making the solution more elegant and understandable.

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91影视

Subtract. $$ \frac{11 z}{13}-\frac{8}{13} $$

Short Answer

Step by step solution

Identify the Common Denominator

Subtract the Numerators

Write the Final Fraction

Key Concepts

common denominator

subtracting numerators

simplifying fractions

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