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Chapter 3: Problem 14

\(-4 \div-3=\) ?

Short Answer

Expert verified
\(\frac{4}{3}\)

Step by step solution

01

Identifying Signs

When dividing two negative numbers, the result is positive. Therefore, the division of the two negatives, \(-4\) and \(-3\), will yield a positive result.
02

Dividing Absolute Values

Ignore the negative signs and divide the absolute values. Calculate \(\frac{4}{3}\) to find the value of the division.
03

Expressing the Result

Since dividing two negative numbers gives a positive result, the answer is positive \(\frac{4}{3}\).

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Key Concepts

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

Dividing Negative Numbers
When dealing with division involving negative numbers, it's essential to understand how signs affect the outcome. Just like multiplying, when you divide two negative numbers, the result is positive. This is a key rule in arithmetic to remember, and it helps simplify problems involving negatives. Let's see how this works.
  • Negative divided by negative results in positive.
  • This is because each negative cancels out, flipping the sign of the result.
The rule applies consistently, and understanding this concept provides a solid foundation for working with integers in various mathematical operations.
Absolute Values
When you encounter negative numbers in division, one helpful technique is to ignore the negative signs temporarily and focus on dividing their absolute values. Absolute value essentially means the 'magnitude' of a number, ignoring its sign.
  • The absolute value of \(-4\) is 4.
  • The absolute value of \(-3\) is 3.
By dividing these absolute values, \( \frac{4}{3} \), you simplify the operation. This step is crucial because it simplifies the division process, allowing you to focus solely on the numerical division without the distraction of negative signs.
Positive Results from Division
Once you've calculated the result of dividing the absolute values, it's time to address the final sign of the result. As previously noted, dividing two negative numbers yields a positive result. Therefore, the solution to the division problem becomes straightforward when you remember this rule.
  • After dividing the absolute values, check the signs.
  • The negative signs cancel out, leaving a positive division result.
Thus, \( -4 \div -3 = \frac{4}{3} \), and importantly, this result is positive. Understanding this pattern will help greatly with future problems involving negative division.

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Most popular questions from this chapter

\(\frac{3}{4}(-1)=\) ?

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