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Chapter 4: Problem 46

Simplify. $$ \frac{325}{625} $$

Short Answer

Expert verified
\[ \frac{13}{25} \]

Step by step solution

01

- Identify the Greatest Common Divisor (GCD)

Find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 325 and 625 is 25.
02

- Divide Both the Numerator and the Denominator by the GCD

Divide the numerator (325) and the denominator (625) by their GCD (25): \[ \frac{325 \/ 25}{625 \/ 25} = \frac{13}{25} \]
03

- Write the Simplified Fraction

The simplified form of the fraction is: \[ \frac{13}{25} \]

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Key Concepts

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

headline of the respective core concept
In mathematics, simplifying a fraction involves breaking it down to its simplest form. You do this by finding the greatest common divisor (GCD) of the numerator and the denominator. Here's a more detailed look at the core concepts to help you fully understand the process.
headline of the respective core concept
The greatest common divisor (GCD) is the largest number that evenly divides both the numerator and the denominator of a fraction. Finding the GCD is crucial in simplifying fractions because it allows you to reduce both parts of the fraction evenly. For example, to simplify the fraction \( \frac{325}{625} \), you first need to find the GCD of 325 and 625.
To do this, list the factors of each:
  • Factors of 325: 1, 5, 13, 25, 65, 325
  • Factors of 625: 1, 5, 25, 125, 625
The largest number that appears in both lists is 25. Therefore, the GCD is 25. By dividing both the numerator and the denominator by the GCD, you can simplify the fraction.
headline of the respective core concept
The numerator is the number above the fraction line. It represents a part of a whole or a set. When you simplify a fraction, you divide the numerator by the greatest common divisor (GCD). In the example \( \frac{325}{625} \), the numerator is 325.
To simplify, divide 325 by the GCD, which is 25: \frac{325}{25} = 13. So, the simplified numerator is 13.
headline of the respective core concept
The denominator is the number below the fraction line. It shows the total number of parts the whole is divided into. When simplifying a fraction, you also divide the denominator by the greatest common divisor (GCD). In our example \( \frac{325}{625} \), the denominator is 625.
To simplify, divide 625 by the GCD, which is 25: \frac{625}{25} = 25. So, the simplified denominator is 25.

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Most popular questions from this chapter

Estimate by rounding as directed. $$ \begin{aligned} &198.67432-24.5007\\\ &\text { nearest ten } \end{aligned} $$

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