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Chapter 5: Problem 25

Divide. $$6 \div 50$$

Short Answer

Expert verified
\( \frac{3}{25} \)

Step by step solution

01

- Understand the Division

The exercise requires dividing 6 by 50. This can be written as the fraction \( \frac{6}{50} \).
02

- Simplify the Fraction

To simplify the fraction \( \frac{6}{50} \), find the greatest common divisor (GCD) of 6 and 50. The GCD of 6 and 50 is 2.
03

- Divide the Numerator and Denominator by the GCD

Divide both the numerator (6) and the denominator (50) by their GCD (2): \( \frac{6 \div 2}{50 \div 2} = \frac{3}{25} \).

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Key Concepts

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

division
Division involves splitting a quantity into equal parts. In this exercise, we are dividing the number 6 by 50. This can be represented as the fraction \(\frac{6}{50}\).
A fraction can be thought of as a division problem. It shows how many times the denominator fits into the numerator.
For example, \(6 \div 50 \) means how many times 50 fits into 6.
Writing it as a fraction, as we did earlier, helps us see the problem more clearly.
greatest common divisor (GCD)
The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder.
We need the GCD to simplify fractions because it tells us how much we can divide the numerator and denominator evenly.
You can find the GCD by listing the factors of each number and choosing the largest one they have in common.
For 6, the factors are: 1, 2, 3, 6.
For 50, the factors are: 1, 2, 5, 10, 25, 50.
The common factors are 1 and 2, and the largest is 2. Hence, the GCD of 6 and 50 is 2.
simplifying fractions
Simplifying fractions means making them as simple as possible.
To do this, we divide both the numerator and denominator by their GCD.
In our example, the fraction is \( \frac{6}{50} \) and the GCD is 2.
We simplify by dividing both 6 and 50 by 2:
  • \(6 \div 2 = 3\)
  • \(50 \div 2 = 25\)
So, \(\frac{6}{50}\ =\frac{3}{25}\).
This is the simplified form of the fraction.
numerator and denominator
A fraction consists of two parts: the numerator and the denominator:
  • The numerator is the top number and indicates how many parts we have. In this example, the numerator is 6.
  • The denominator is the bottom number and shows into how many parts the total is divided. Here, the denominator is 50.
When simplifying the fraction \(\frac{6}{50}\), we focus on reducing these numbers by dividing both by their GCD (which, as we found, is 2).
This gives us the simplified fraction \(\frac{3}{25}\).

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