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Chapter 6: Problem 23

Write the ratio in lowest terms. \(\$ 60\) to \(\$ 50\)

Short Answer

Expert verified
6:5

Step by step solution

01

Write the Ratio

The given amount is \(\$ 60\) to \(\$ 50\). This translates to the ratio \(60:50\).
02

Simplify the Ratio

To simplify the ratio, divide both numbers by their greatest common divisor (GCD). The GCD of 60 and 50 is 10. Thus, divide each term by 10: \[\frac{60}{10}:\frac{50}{10}\].
03

Write the Simplified Ratio

After simplifying the terms, we get: \[6:5\]. Therefore, the ratio of \(\$ 60\) to \(\$ 50\) in lowest terms is \[6:5\].

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Key Concepts

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

Understanding Greatest Common Divisor (GCD)
Before simplifying ratios, it's important to understand the concept of the greatest common divisor (GCD). The GCD is the largest number that can exactly divide two or more numbers without leaving a remainder. For instance, to find the GCD of 60 and 50, start by listing down the factors of each:
  • Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  • Factors of 50: 1, 2, 5, 10, 25, 50

The highest common factor in both lists is 10, so the GCD of 60 and 50 is 10. Understanding the GCD helps in breaking down and simplifying ratios effectively.
What is a Ratio?
A ratio is a way to compare two quantities by showing how many times one value contains or is contained within the other. It is written in the form 'a to b' or 'a:b'. In our example, the ratio of \(60 to \)50 is written as 60:50. Ratios are useful in many fields, like cooking, engineering, and finance, for comparison and proportion purposes.
To visualize this, if you have 60 apples and 50 oranges, the ratio of apples to oranges can be represented as 60:50.
Simplifying Ratios to Their Lowest Terms
Simplifying a ratio means reducing it to its smallest form where both numbers in the ratio have no common divisors other than 1. This process is similar to simplifying fractions. To simplify the ratio 60:50, you need to divide both numbers by their GCD, which we found to be 10. Here鈥檚 the step-by-step breakdown:
  • Step 1: Write the ratio: 60:50
  • Step 2: Divide both numbers by their GCD of 10: \[ \frac{60}{10}:\frac{50}{10} \]
  • Step 3: Simplified ratio: 6:5

Now, the ratio 60:50 in its lowest terms is 6:5. The ratio of 6:5 means that for every 6 units of the first quantity, there are 5 units of the second quantity.

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Most popular questions from this chapter

If you flip a coin many times, the coin should come up heads about 1 time out of every 2 times it is flipped. If a coin is flipped 630 times, about how many heads do you expect to come up?

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