Question

Prep Exercise 6 When dividing two num bers that have the same sign, the result is ___. Prep Exercise 7 When dividing two numbers that have different signs, the result is ___. divide. $$-\frac{42}{7}$$

Short answer

Answer: The result of dividing -42 by 7 is -6.

Step-by-step solution

Divide the numbers without considering the signs

First, we will perform division without considering the signs of the numbers and find the result. Divide 42 by 7: $$\frac{42}{7} = 6$$

Determine the sign of the result

Since the numerator is negative and the denominator is positive, the division result will be negative (as per Prep Exercise 7).

Write down the final result

Considering the result of the division and the sign, we have the final result: $$-\frac{42}{7} = -6$$

Key concepts

Integer Division Rules

When working with integer division, there are specific rules to follow to obtain the correct answer. Firstly, division is essentially finding out how many times one number can fit into another. This remains true for integers, which can be positive or negative whole numbers.

• Identify the numbers involved: These numbers include the numerator (the number being divided) and the denominator (the number you are dividing by).
• Perform division: Ignore any signs initially and focus solely on the numerical values. For example, dividing 42 by 7 yields 6 because 42 divided by 7 is 6.

By understanding these basic integer division rules, students can easily work through problems like dividing -42 by 7, focusing initially just on the numbers as if they were positive.

Sign Rules in Division

When performing division, understanding the sign rules is crucial to determining whether the result will be positive or negative.
The core sign rules are:

• Positive divided by positive results in a positive number.
• Negative divided by negative also results in a positive number.
• Positive divided by negative results in a negative number.
• Negative divided by positive results in a negative number.

Thinking of signs as directions or indicators can help. If both signs match (positive and positive or negative and negative), the result is positive. If the signs differ, the result is negative. Therefore, when dividing -42 by 7, we separate the signs and find that a negative divided by a positive gives us -6.

Positive and Negative Division Results

The result of dividing two numbers depends greatly on the signs of those numbers. In integer division, the overall sign of the answer can be understood with basic sign rules. Positive results arise when both integers share the same sign. Negative results occur when the integers have different signs.

• If both numbers are positive or both are negative, the result is positive, as seen with exercises where negative and negative or positive and positive pairs are divided.
• If one number is positive and the other is negative, the result is negative, illustrating exercises like -42 divided by 7.

Being aware of these outcomes helps remove confusion when solving integer division problems, ensuring clarity in determining the signs and final results of division operations.