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Chapter 6: Problem 3

Write the ratio 4: 1 in two other ways.

Short Answer

Expert verified
The ratio 4:1 can also be written as \frac{4}{1}\ and 4/1.

Step by step solution

01

- Write the Ratio as a Fraction

Convert the given ratio 4:1 into fraction form. This can be done by writing \(\frac{4}{1}\).
02

- Simplify the Fraction if Necessary

In this case, \(\frac{4}{1}\) is already in simplest form.
03

- Express the Ratio Using Different Notations

The same ratio can be written using different notations: \(\frac{4}{1}\) can also be written as 4/1 or 4 to 1. Hence, the two other ways of writing the ratio 4:1 are: \frac{4}{1}\ and 4/1.

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Key Concepts

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

fraction form
Ratios can often be more easily understood when expressed in fraction form. The given ratio of 4:1 can be converted into a fraction by placing the first number (4) as the numerator and the second number (1) as the denominator. This results in the fraction \(\frac{4}{1}\).

Using fraction form helps in visually representing the ratio and makes it easier to perform mathematical operations.
For example, if we had a ratio of 8:2, representing it as \(\frac{8}{2}\) shows that the ratio can be simplified.
Simplifying fractions often provides a clearer view of the relationship between the two numbers.
simplifying fractions
Simplifying fractions involves reducing the fraction to its lowest terms. This means dividing both the numerator and the denominator by their greatest common divisor (GCD).

For instance, with the ratio 8:2, we can convert it to \(\frac{8}{2}\). Both 8 and 2 can be divided by their GCD, which is 2. Therefore,

\[\frac{8}{2} = \frac{8 \div 2}{2 \div 2} = \frac{4}{1}\].

So, simplifying the fraction provides a clearer representation, showing that 8:2 can be expressed more simply as 4:1. This step is crucial for ensuring clarity and understanding in mathematics.
notations in mathematics
Mathematics uses various notations to express the same concept. For ratios, the same relationship can be written in multiple forms. The ratio 4:1 can be expressed as \(\frac{4}{1}\), 4/1, or written out as '4 to 1'.

This flexibility in notation allows us to represent the relationship in a format that best suits the context.

For example:
  • 4:1 (colon form)
  • \(\frac{4}{1}\) (fraction form)
  • 4/1 (slash form)
  • 4 to 1 (written form)


Understanding and utilizing these notations can enhance your mathematical communication and interpretation skills.

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