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Chapter 2: Problem 17

Evaluate each expression. $$-300 \div 6$$

Short Answer

Expert verified
The result is -50.

Step by step solution

01

Identify the Operation

The problem given is asking for the division of two numbers. It is a simple division operation.
02

Set Up the Division Expression

Write the division expression as \(-300 \div 6\). This means dividing -300 by 6.
03

Calculate the Division

Divide 300 by 6 to determine the quotient: \(\frac{300}{6} = 50\). But since we are dividing a negative number by a positive number, the result will be negative. Thus, \(-300 \div 6 = -50\).

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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 that are less than zero. They are represented with a minus sign (-). In basic arithmetic, understanding how negative numbers work in operations like division is crucial. For instance, when you divide a negative number by a positive number, the result or quotient will also be negative. This is because you're essentially distributing the negative sign across the division operation. An easy way to remember this is to know that a positive divided by a negative gives a negative result and vice versa.
Division Operation
The division operation is one of the four basic arithmetic operations, alongside addition, subtraction, and multiplication. Division is essentially about splitting a number into equal parts or groups. In the expression \(-300 \div 6\), you're asked to divide -300 by 6.

This operation involves seeing how many times 6 can be subtracted from -300, until you reach zero, but since -300 is already negative, it modifies the procedure to deal with signs too. Understanding division is key to mastering arithmetic.
Quotient
The quotient is the result of the division operation. It tells you how many times one number fits into another. In our example, \(-300 \div 6 = -50\), -50 is the quotient.

This answer represents that 6 can fit into 300, 50 times, but because our dividend (-300) is negative, our quotient too, becomes negative. The idea that multiplying the quotient back by the divisor returns us to the original number is a useful way to verify our answer. Thus, \(-50 \times 6 = -300\) shows our math is correct.
Basic Arithmetic
Basic arithmetic involves the simple operations of addition, subtraction, multiplication, and division. Each of these operations has its own rules and applications. Understanding these rules is crucial for solving math problems correctly.

In division, especially when involving negative numbers, the rules include knowing how the signs interact and how to manipulate them. It's about breaking larger math challenges into simple steps you can manage. Practicing problems with different operations enriches your comprehension and strengthens your math skills.

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