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Chapter 5: Problem 209

Convert each fraction to a decimal. \(-\frac{310}{25}\)

Short Answer

Expert verified
-12.4

Step by step solution

01

- Understand the problem

The problem requires converting the fraction \( -\frac{310}{25} \) into a decimal.
02

- Divide the numerator by the denominator

To convert the fraction to a decimal, divide the numerator (310) by the denominator (25). Since the fraction is negative, remember to add the negative sign to the result of the division: \( 310 \div 25 = 12.4 \).
03

- Apply the negative sign

The original fraction was negative, so include the negative sign in the decimal result: \( -12.4 \).

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Key Concepts

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

Division
To convert a fraction to a decimal, the main operation needed is division. Division is a way to see how many times one number is contained within another. For our fraction \(-\frac{310}{25}\), we need to divide 310 by 25. Imagine you have 310 apples and you want to pack them in boxes that can hold 25 apples each. Division helps you figure out how many full boxes you will have. So, you perform the division: \(310 梅 25 = 12.4\). Since the fraction is negative, make sure the decimal is negative as well. The final answer is \(-12.4\). Division can be tricky sometimes, but breaking it into smaller, simpler steps can really help.
Fractions
A fraction represents a part of a whole. It is written as \(\frac{a}{b}\), where \(a\) is called the numerator, and \(b\) is the denominator. In our exercise, the fraction given is \(-\frac{310}{25}\). Here, 310 is the numerator that tells us how many parts we have, and 25 is the denominator that tells us into how many sections the whole is divided. When we convert a fraction to a decimal, we are essentially performing division. Fractions can also be negative if either the numerator or the denominator (but not both) is negative, as in our example where the fraction is \(-\frac{310}{25}\).
Negative Numbers
Negative numbers are numbers less than zero, and they appear with a minus sign \(-\) in front. In our exercise, \(-\frac{310}{25}\) is a negative fraction because it has a negative sign. When converting a negative fraction to a decimal, you first ignore the negative sign and simply divide the numbers. For \(310 梅 25 = 12.4\), we then reintroduce the negative sign: \(-12.4\). Always remember that a negative divided by a positive, or vice versa, yields a negative result. Understanding negatives is key in mathematics, especially when dealing with real-world scenarios like debts, temperatures below zero, or elevations below sea level.

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