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Chapter 8: Problem 4

Find the ratio of 8 to 13. A. 13: 8 B. 8: 21 C. 13: 21 D. 8: 13

Short Answer

Expert verified
The ratio of 8 to 13 is 8:13, which corresponds to option D.

Step by step solution

01

Identify the Numerator and Denominator

To find the ratio of two numbers, we need to determine which number we are comparing to which. The exercise asks for the ratio of 8 to 13, meaning 8 is the numerator and 13 is the denominator.
02

Write the Ratio

Write the ratio of 8 to 13 in standard ratio format. Ratios are often written using a colon, so the correct format would be 8:13.
03

Match the Answer

Look through the provided answer options to find the one that matches the ratio 8:13. The correct choice will be option D, which is 8:13.

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Key Concepts

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

Understanding the Numerator
In any fraction or ratio, the numerator is the top number. It represents how many parts of the whole are being considered. In the context of a ratio, the numerator indicates the first quantity in the comparison. For example, when we have the ratio of 8 to 13, the number 8 is the numerator.
This number tells us the portion of the total that the ratio is addressing first.
  • The numerator is always found before the colon in a ratio written as such (e.g., 8:13).
  • When interpreting problems, identify the order of terms to properly place the numerator.
When dealing with numerical relationships, always verify the positioning of each number in the scenario to ensure clarity. Remember, the numerator is crucial in setting the initial context of any given comparison.
The Role of the Denominator
Just like in fractions, the denominator in a ratio is found as the bottom number. It tells us the total parts or the reference point for the numerator's portion. Within the ratio "8 to 13," the number 13 serves as the denominator. It frames the larger set or quantity against which the numerator is compared.
Understanding the denominator is essential because it sets the scale of the comparison.
  • The denominator follows the colon in ratio expressions (e.g., 8:13).
  • Choosing the correct denominator ensures the ratio accurately reflects the intended comparison.
In mathematical operations or story problems, identifying the denominator correctly allows for meaningful comparisons and conversions between parts and their wholes.
Writing Ratios in Ratio Format
Ratios are a useful way to compare quantities, and they are typically written in a specific format. The standard "ratio format" employs a colon to separate the two numbers being compared, such as in 8:13.
Writing ratios properly helps communicate comparisons clearly and concisely.
  • The order of numbers is important; it affects the meaning of the ratio.
  • Ratios can be simplified like fractions, by dividing both numbers by their greatest common divisor.
The "ratio format" 8:13 specifically denotes 8 parts of one quantity to every 13 parts of another. Be aware that in list choices, understanding format conventions will assist in selecting the accurate ratio representation, as seen with option D, which shows 8:13. Proper formatting aids clear and consistent communication in mathematics and practical scenarios.

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