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Chapter 5: Problem 156

In the following exercises, divide. $$-1.15 \div(-0.05)$$

Short Answer

Expert verified
The result of \(-1.15\div -0.05\) is 23.

Step by step solution

01

Identify the Operation

Determine the mathematical operation required in this exercise. Here, you need to divide \(-1.15\) by \(-0.05\).
02

Identify Signs

Since both the dividend \(-1.15\) and the divisor \(-0.05\) are negative, the result will be positive because a negative divided by a negative is positive.
03

Perform the Division

Divide the absolute values: \[ \frac{1.15}{0.05} = 23 \].
04

Apply the Sign

Since we are dividing two negative numbers, the result is positive. Therefore, \(-1.15 \div -0.05 = 23\).

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero and are represented with a minus sign. They can be found to the left of zero on a number line.
Using negative numbers in operations follows different rules compared to positive numbers.
One important rule for multiplying and dividing is:
  • A negative number divided by another negative number results in a positive number. For example, in the exercise \(-1.15 \div(-0.05) = 23\), since both numbers are negative, the result is positive.
Understanding how to handle negative numbers is crucial for solving such problems correctly.
Absolute Value
The absolute value of a number is the distance of that number from zero on a number line, regardless of its direction. It鈥檚 always positive because distance cannot be negative.
If you see numbers with a negative sign, like \-1.15\ or \-0.05\, their absolute values are \1.15\ and \0.05\, respectively.
In the division exercise, dividing the absolute values helps to simplify the problem:
  • Divide the absolute value of \-1.15\ by \-0.05\: \[ \frac{1.15}{0.05} = 23\]. This focuses only on their sizes, without considering the signs.
After this, you can determine the final sign of the result by the original signs of the numbers.
Division Operation
Division is one of the four fundamental arithmetic operations. It鈥檚 the process of determining how many times one number is contained within another. For example, dividing \1.15\ by \-0.05\ tells us how many \0.05\ units fit into \1.15\.
Here's how to approach a division operation:
  • Identify the dividend (the number being divided) and the divisor (the number you are dividing by).
  • Compute the division. In our exercise: \(-1.15 \div -0.05)\, we divide the absolute values first to simplify: \[ \frac{1.15}{0.05} = 23\].
Apply the rule of signs at the end: since dividing two negative numbers results in a positive number, \-1.15 \div \-0.05 \) is \ 23.

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