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Chapter 4: Problem 3

Identify the numerator and denominator. Then simplify the fraction. \(\frac{2100}{7000}\)

Short Answer

Expert verified
\( \frac{3}{10} \)

Step by step solution

01

Identify the Numerator

The numerator is the top number in a fraction. In the fraction \(\frac{2100}{7000}\), the numerator is 2100.
02

Identify the Denominator

The denominator is the bottom number in a fraction. In the fraction \(\frac{2100}{7000}\), the denominator is 7000.
03

Find the Greatest Common Divisor (GCD)

To simplify the fraction, first find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 2100 and 7000 is 700.
04

Divide Numerator and Denominator by GCD

Divide both the numerator and the denominator by the GCD to simplify the fraction. \(\frac{2100 \/ 700}{7000 \/ 700} = \frac{3}{10} \).

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Key Concepts

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

Numerator and Denominator
Every fraction consists of two parts: the numerator and the denominator. The numerator is the top number, and it represents how many parts we have. For example, in the fraction \(\frac{2100}{7000}\), the numerator is 2100. The denominator is the bottom number, and it shows how many parts make a whole. In our example fraction, the denominator is 7000. Understand that the fraction signifies a division: \(\frac{numerator}{denominator}\). So, \(\frac{2100}{7000}\) essentially means 2100 divided by 7000. Recognizing these two components is crucial for any fraction operation, including simplification.
Greatest Common Divisor (GCD)
The greatest common divisor, or GCD, is the largest number that can evenly divide both the numerator and the denominator of a fraction. Finding the GCD is essential to simplify fractions. For example, to simplify \(\frac{2100}{7000}\), we need to determine their GCD. Use the Euclidean algorithm or factor both numbers to find it. In this case, the GCD of 2100 and 7000 is 700. This means 700 is the largest number that can divide both 2100 and 7000 without leaving a remainder. Identifying the GCD helps reduce the fraction to its simplest form.
Fraction Simplification
Simplifying a fraction involves reducing it to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). Take the fraction \(\frac{2100}{7000}\) as an example. Here, the GCD is 700. We simplify the fraction by dividing both the numerator and the denominator by 700: \(\frac{2100 \:/ 700}{7000 \:/ 700} = \frac{3}{10}\). After this step, the fraction \(\frac{2100}{7000}\) is simplified to \(\frac{3}{10}\). Simplifying fractions makes them easier to understand and work with.

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Most popular questions from this chapter

How many eighths are in \(2 \frac{3}{8} ?\)

a. What fraction of the alphabet is made up of vowels? (Include the letter \(y\) as a vowel, not a consonant.) b. What fraction of the alphabet is made up of consonants?

Label the fraction as proper or improper. $$\frac{2}{3}$$

Plot the fraction on the number line. $$-\frac{4}{3}$$

Convert the mixed number to an improper fraction. $$6 \frac{1}{3}$$
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