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Chapter 6: Problem 22

Write the ratio in lowest terms. 21 days to 30 days

Short Answer

Expert verified
The ratio in lowest terms is 7:10.

Step by step solution

01

Identify the Given Values

First, note that the given values are 21 days and 30 days. These numbers will form the ratio 21:30.
02

Find the Greatest Common Divisor (GCD)

Next, find the GCD of 21 and 30. The factors of 21 are 1, 3, 7, and 21. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The greatest common divisor is 3.
03

Divide Both Terms by the GCD

Divide each term of the ratio by the GCD (which is 3). Calculate: \ \text{\( \frac{21}{3} = 7 \)} \ \text{\( \frac{30}{3} = 10 \)} This simplifies the ratio 21:30 to 7:10.

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Key Concepts

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

Greatest Common Divisor
To simplify a ratio, the key is to find the Greatest Common Divisor (GCD). This is the largest number that can evenly divide both terms of the ratio.

Here, we had the numbers 21 and 30. By listing their factors:
  • The factors of 21 are 1, 3, 7, and 21.
  • The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The largest number common to both lists is 3. So, the GCD of 21 and 30 is 3.

Finding the GCD helps make our work easier because we can simplify the ratio by dividing both terms by this number.
Simplifying Ratios
Once you have the GCD, simplifying the ratio becomes straightforward.

For our ratio of 21:30, we found the GCD to be 3. We simplify the ratio by dividing each term by the GCD:
  • 21 divided by 3 is 7.
  • 30 divided by 3 is 10.
Thus, the simplified ratio of 21:30 is 7:10.

This process ensures the ratio is presented in its lowest terms, making it simpler and more meaningful.
Prealgebra
Understanding ratios and how to simplify them is a fundamental pre-algebra concept. These skills are essential as they lay the groundwork for more advanced mathematical topics.

Learning to calculate the GCD and simplifying ratios helps strengthen your number sense and prepares you for algebra and beyond.

With pre-algebra concepts, remember:
  • You often break down complex problems into smaller, manageable steps.
  • Understanding the basics helps you solve more complicated problems in the future.
Stay patient and practice regularly to master these foundational concepts.

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Most popular questions from this chapter

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