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Chapter 1: Problem 673

Write as the ratio of two integers. (a) -12 (b) 9.279

Short Answer

Expert verified
-12 as a ratio is \(\frac{-12}{1}\). 9.279 as a ratio is \(\frac{9279}{1000}\).

Step by step solution

01

Understanding the problem

We need to express the given numbers as ratios of two integers. Essentially, we want to write each number in the form \(\frac{a}{b}\), where \(a\) and \(b\) are integers.
02

Converting -12 to a ratio of two integers

-12 can be directly written as a ratio of two integers. Since -12 is already an integer, it can be expressed as \(\frac{-12}{1}\).
03

Converting 9.279 to a ratio of two integers

To express 9.279 as a ratio of two integers:1. Count the number of decimal places. 9.279 has three decimal places.2. Remove the decimal by multiplying the number by 1000 (since there are three decimal places), turning 9.279 into 9279.3. To compensate for the multiplication, we use 1000 as the denominator.4. The ratio is thus \(\frac{9279}{1000}\). Since 9279 and 1000 have no common factors, this fraction is already in its simplest form.

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Key Concepts

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

ratios
A ratio is a comparison between two quantities. It indicates how many times one number contains another. Ratios can be expressed in different forms such as fractions, with a colon, or even with words. For example, a ratio of 2 to 3 can be written as 2:3 or \(\frac{2}{3}\). Understanding ratios can help in solving problems related to proportions, and they are widely used in real-world applications like recipes and maps.
In the context of the given problem, converting numbers to the ratio of two integers involves representing them in the form \(\frac{a}{b}\). This is essentially the same as expressing them as fractions, since fractions are just another way of showing a ratio.
integers
Integers are whole numbers that can be positive, negative, or zero. They do not have any fractional or decimal parts. Examples include -12, 0, and 42.
In the original exercise, we are given -12, which is an integer. To express -12 as the ratio of two integers, we can simply write it as \(\frac{-12}{1}\). Since -12 is already an integer, converting it to the ratio of two integers is straightforward.
For any integer\( 'n'\), it can always be written as \(\frac{n}{1}\). Understanding this simple truth helps in dealing effortlessly with converting integers to fractions or ratios.
fractions
A fraction represents a part of a whole and consists of a numerator (the top number) and a denominator (the bottom number). The fraction \( \frac{a}{b}\) indicates that 'a' parts of size \( \frac{1}{b}\) make up the whole.
In the exercise, converting 9.279 to a ratio involves turning it into a fraction by removing the decimal. Here's how:
  • Count the decimal places. For 9.279, there are 3 decimal places.
  • Multiply the number by 1000 (since there are three decimal places). 9.279 becomes 9279.
  • Use 1000 as the denominator to balance the multiplication. This gives us the fraction \( \frac{9279}{1000} \).
Since 9279 and 1000 do not have any common factors, \( \frac{9279}{1000} \) is already in its simplest form.
This example shows the importance of understanding fractions and performing operations like simplification.

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Most popular questions from this chapter

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Helen bought a 24-pound turkey for her family's Thanksgiving dinner and wants to know what time to put the turkey in to the oven. She wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey: (a) First, by multiplying \(24 \cdot 20\) to find the total number of minutes and then multiplying the answer by \(\frac{1}{60}\) to convert minutes into hours. (b) Next, by multiplying \(24\left(20 \cdot \frac{1}{60}\right)\). (C) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \((24 \cdot 20) \frac{1}{60}, \quad\) and \(\quad(b),\) where you multiplied \(24\left(20 \cdot \frac{1}{60}\right),\) should be equal?
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