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Chapter 6: Problem 5

Write as a reduced ratio or rate. 6 days to 2 days

Short Answer

Expert verified
The ratio 6 days to 2 days is simplified to 3:1.

Step by step solution

01

Identify the Given Values

Determine the values given in the problem. Here, 6 days and 2 days are the given values.
02

Express as a Ratio

Write the given values as a ratio: \( \frac{6}{2} \).
03

Simplify the Ratio

Simplify the ratio by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2 in this case: \( \frac{6 梅 2}{2 梅 2} = \frac{3}{1} \).
04

Express the Simplified Ratio

Write the simplified ratio as 3:1.

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Key Concepts

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

Ratios and Proportions
To fully understand ratios and proportions, you need to grasp their basic definitions. A ratio is a comparison of two quantities showing the relative sizes of two or more values. For example, a ratio of 6 days to 2 days compares two different amounts of time.

Proportions, on the other hand, are equations that express the equality of two ratios. When two ratios are equal, they are said to be proportional. For example, if you have a ratio 3:1, it can be explained proportionally as 3 is to 1 as 6 is to 2.
Simplifying Ratios
Simplifying ratios means reducing them to their simplest form. The aim is to make the ratio easier to understand and work with. To simplify a ratio, follow these steps:

1. Identify the values to be compared. For instance, in our exercise, we have 6 days and 2 days.
2. Write the ratio as a fraction: \( \frac{6}{2} \).
3. Find the greatest common divisor (GCD) of the numbers in the ratio. The GCD is the highest number that divides both the numerator and the denominator evenly.
4. Divide both the numerator and the denominator by the GCD. In this case, the GCD is 2: \( \frac{6 梅 2}{2 梅 2} = \frac{3}{1} \).

Thus, the simplified ratio of 6 days to 2 days is 3:1.
Greatest Common Divisor
The greatest common divisor (GCD) is a key concept in simplifying ratios. It's the largest number that can evenly divide two or more numbers without leaving a remainder.

Here's how you can find the GCD:
1. List out the factors of each number. Factors of 6 are 1, 2, 3, and 6. Factors of 2 are 1 and 2.
2. Identify the highest factor that both numbers share. In our case, it's 2.
3. Use this GCD to divide both the numerator and the denominator of the ratio.

For the ratio \( \frac{6}{2} \), dividing both the numerator and denominator by 2 simplifies it to \( \frac{3}{1} \). Therefore, 2 is the GCD of 6 and 2, making our simplified ratio 3:1.

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Most popular questions from this chapter

Solve the proportion. $$\frac{4}{3}=\frac{n}{5}$$

Solve the proportion. Be sure to check your answers. $$\frac{3}{40}=\frac{w}{10}$$

In a recent year, the rate of breast cancer in women was 110 cases per \(100,000\) women. At that time, the state of California had approximately \(14,000,000\) women. How many women in California would be expected to have breast cancer?

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