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Chapter 6: Problem 20

Write the ratio in lowest terms. 14 oz to 7 oz

Short Answer

Expert verified
2:1

Step by step solution

01

- Identify Given Values

The problem gives two quantities: 14 ounces and 7 ounces.
02

- Set Up the Ratio

Write the ratio of the two quantities as a fraction. This gives us \( \frac{14}{7} \).
03

- Simplify the Fraction

Divide the numerator and the denominator of the fraction by their greatest common divisor (GCD). The GCD of 14 and 7 is 7. So, \( \frac{14 \div 7}{7 \div 7} = \frac{2}{1} \).
04

- Write the Simplified Ratio

The simplified ratio is 2:1.

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Key Concepts

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

Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.
To simplify a ratio, finding the GCD is crucial.
Let's break down how to find the GCD.

  • List all the divisors of each number.
  • Identify the largest common divisor shared by the numbers.

For example, if we have the numbers 14 and 7, their divisors are:

  • Divisors of 14: 1, 2, 7, 14
  • Divisors of 7: 1, 7

The largest common divisor is 7. This is the GCD.
Once we know the GCD, we can simplify the fractions or ratios accordingly.
Fraction Simplification
Fraction simplification is the process of reducing a fraction to its lowest terms.
This means the numerator and denominator have no common divisors other than 1.
Here鈥檚 how to simplify fractions:
  • Divide both the numerator and denominator by their GCD.

Let's use the fraction from our exercise: \( \frac{14}{7} \).
We already know the GCD is 7. Now, we divide both by 7:

\[ \frac{14 \, \div \, 7}{7 \, \div \, 7} = \frac{2}{1} \]
This simplified fraction \( \frac{2}{1} \) represents the same ratio but in the simplest form.
Ratio
A ratio is a comparison of two quantities showing the relative sizes of the two values.
Ratios can be written in several ways, with a colon separating the numbers (e.g., 2:1), or as a fraction (e.g., \( \frac{2}{1} \)).
Understanding ratios helps in comparing quantities easily.
  • Write the given quantities as a fraction.
  • Simplify the fraction by dividing both the numerator and denominator by their GCD.

In our exercise, we started with the ratio of 14 ounces to 7 ounces.
Writing it as a fraction gives us \( \frac{14}{7} \).
After simplification, we found this ratio to be 2:1.
This tells us that for every 2 ounces in the first quantity, there is 1 ounce in the second.

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