Problem 67 Multiply or divide as indicated.... [FREE SOLUTION]

Chapter 2: Problem 67

Multiply or divide as indicated. See Examples 1 through 14. $$ \frac{-12}{-4} $$

Short Answer

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Step by step solution

Understand the problem

We need to perform division. The problem is to divide $-12$ by $-4$. When both the numerator and the denominator have the same sign, the result will be positive.

Basic division

Divide 12 by 4 as you normally would, ignoring the signs for this step. 12 divided by 4 equals 3.

Determine the Sign

Both numbers, $-12$ and $-4$, are negative. Dividing two negative numbers results in a positive number. Therefore, the result is positive 3.

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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 with a minus sign ($-$) in front of them. They represent values less than zero. Often encountered in everyday life, like temperatures below freezing, depth below sea level, or owing money.
Understanding negative numbers is crucial for solving math problems involving subtraction or division.
When dealing with negative numbers, the sign indicates the direction on the number line:

Positive numbers move to the right of zero.
Negative numbers move to the left of zero.

This principle is vital in division, as the signs dictate the outcome. Keep in mind that two like signs (both positive or both negative) make the result positive, while two unlike signs (one positive and one negative) make the result negative.

Basic Division

Division is the process of splitting a number (dividend) into equal parts by another number (divisor). It's one of the four fundamental arithmetic operations.
The result of division is called the quotient. Basic division can be understood using simple numbers before integrating complex negative values.
For example, dividing 12 by 4 works as repeatedly subtracting 4 from 12, which gives 3 as the number of times 4 fits into 12. In fractional form, this division is shown as $ \frac{12}{4} = 3 $.
When performing division, ignore the signs at first to find the absolute value of the quotient. Once you've determined this basic division, apply the sign rules to finish.

Sign Rules

Sign rules help determine the sign of the result in division. These rules are straightforward and easy to remember:

If both numbers (dividend and divisor) have the same sign (both positive or both negative), the result is positive.
If the numbers have different signs (one positive and one negative), the result is negative.

For instance, dividing $-12$ by $-4$ follows these rules:- Both numbers are negative, so the result is positive.- Ignoring the negative signs, divide the absolute values to get 3. Since the signs were the same, the final answer is positive 3, or simply 3.These rules are a powerful tool for quickly deciding the outcome's sign, making any division involving negative numbers hassle-free.

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91影视

Multiply or divide as indicated. See Examples 1 through 14. $$ \frac{-12}{-4} $$

Short Answer

Step by step solution

Understand the problem

Basic division

Determine the Sign

Key Concepts

Negative Numbers

Basic Division

Sign Rules

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