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Chapter 4: Problem 283

In the following exercises, find the difference. $$\frac{9}{13}-\frac{4}{13}$$

Short Answer

Expert verified
\(\frac{5}{13}\)

Step by step solution

01

- Identify the fractions

First, identify the fractions involved in the subtraction problem: ewline The given fractions are \(\frac{9}{13}\) and \(\frac{4}{13}\).
02

- Ensure common denominator

Check if the fractions have a common denominator: ewline Both fractions have the same denominator (13), so no adjustments are needed. This allows for simple subtraction.
03

- Subtract the numerators

Subtract the numerators of the two fractions while keeping the denominator the same:ewline \(\frac{9}{13} - \frac{4}{13} = \frac{9 - 4}{13}\)
04

- Simplify the result

Simplify the result of the subtraction: ewline \(\frac{9 - 4}{13} = \frac{5}{13}\). This is the final simplified form.

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Key Concepts

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

common denominator
Understanding the concept of a common denominator is crucial when dealing with fractions, especially in subtraction. A common denominator is a shared multiple of the denominators of two or more fractions. This ensures that the fractions are parts of the same whole and can be easily added or subtracted.
To find a common denominator, follow these steps:
  • Identify the denominators of the fractions you want to subtract.
  • If the denominators are different, find the least common multiple (LCM) of these denominators. The LCM is the smallest number that both denominators divide into evenly.
For example, in our exercise, both fractions \(\frac{9}{13}\) and \(\frac{4}{13}\) already have the same denominator (13). This makes our work easier as we can directly subtract the numerators without any adjustments needed.
subtracting fractions
Subtracting fractions involves a few clear steps that simplify the process. Let's go through them:
  • Ensure the fractions have a common denominator, as we discussed earlier.
  • Once the denominators are the same, subtract the numerators (the top numbers of the fractions) and keep the denominator unchanged.
In our given problem: \(\frac{9}{13} - \frac{4}{13}\), we can see that the denominator is already common. Therefore, we subtract the numerators directly:
\(\frac{9-4}{13} = \frac{5}{13}\)
This step-by-step approach simplifies the subtraction and prevents errors.
simplifying fractions
The final step in subtracting fractions is simplifying the result. Simplifying a fraction means reducing it to its simplest form where the numerator and the denominator have no common factors other than 1. Here's how to do it:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by their GCD.
  • The result is the simplified fraction.
In our solution, \(\frac{5}{13}\), we notice that 5 and 13 have no common factors other than 1, so it cannot be simplified further. Thus, \(\frac{5}{13}\) is already in its simplest form.
Remember, simplifying fractions ensures that your answer is as clear and concise as possible.

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Most popular questions from this chapter

In the following exercises, translate and solve. The quotient of \(p\) and \(-4\) is \(-8 .\)

In the following exercises, evaluate. $$ y-\frac{4}{5} $$ $$ (a)y=-\frac{4}{5} $$ $$ (b)y=\frac{1}{4} $$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\left(-\frac{5}{6}\right)\) when (a) \(x=\frac{1}{3} \quad\) (b) \(x=-\frac{1}{6}\)

In the following exercises, simplify. $$\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}$$

In the following exercises, perform the indicated operation. $$ 8 \frac{6}{11}-2 \frac{9}{11} $$
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