Problem 281 - Intermediate Algebra

Question

In the following exercises, convert each fraction to a decimal. $$ -\frac{310}{25} $$

Step-by-Step Solution

Answer

-12.4

Step 1: Understand the fraction

The fraction to convert to a decimal is \(-\frac{310}{25}\).

Step 2: Divide the numerator by the denominator

Perform the division \(-310 ÷ 25\).

Step 3: Simplify the division

Divide 310 by 25: \(310 ÷ 25 = 12.4\).

Step 4: Apply the negative sign

The result of the division is 12.4. Since the original fraction is negative, the final result is -12.4.

Key Concepts

fractions

Fractions are a way to represent a part of a whole. They consist of two parts: the numerator and the denominator.
The numerator (top number) tells us how many parts we have. The denominator (bottom number) tells us how many equal parts the whole is divided into. For example, in the fraction \(-\frac{310}{25}\), 310 is the numerator and 25 is the denominator.
In this problem, our job is to convert this fraction to a decimal. Remember that fractions can sometimes also be negative, which signifies that the value is less than zero.

decimal conversion

Decimal conversion involves converting a fraction or a percentage into its decimal form. For instance, converting \(\frac{1}{4}\) to its decimal form gives us 0.25.
To convert a fraction like \(-\frac{310}{25}\) to a decimal, you need to divide the numerator by the denominator. Here’s how you can do it:

• Take the numerator (310) and divide it by the denominator (25).
• This will give you 310 ÷ 25 = 12.4.
• Since our original fraction was negative, our final answer will also be negative: -12.4.

This is now in decimal form and is straightforward by performing simple division.

negative numbers

Negative numbers are numbers less than zero. They are represented with a minus sign (-).
In the context of converting fractions to decimals, if your fraction is negative (like \(-\frac{310}{25}\)), the resulting decimal will also be negative.
Always remember, the negative sign does not affect the division process itself. It is simply added to the result of the division.
For example, if we get a decimal result of 12.4 from \(\frac{310}{25}\), we apply the negative sign to get -12.4 because the original fraction was negative.

division

Division is one of the four basic arithmetic operations, the others being addition, subtraction, and multiplication. It essentially means splitting a number into equal parts. For example, dividing 310 by 25.
Here’s how to do it step by step for this problem:

• The fraction to be converted is \(-\frac{310}{25}\).
• Divide 310 by 25. This means finding out how many times 25 fits into 310.
• The result of 310 ÷ 25 is 12.4.
• Apply the negative sign from the original fraction to the result, giving us -12.4.

Division can sometimes leave us with decimals, like in this example, making it important to execute it carefully.