Problem 40 - Beginning and Intermediate Algebra

Question

Find each quotient. \(\frac{-35}{-5}\)

Step-by-Step Solution

Answer

The quotient is 7.

Step 1: Write down the problem

Consider the division problem \(\frac{-35}{-5}\).

Step 2: Simplify the signs

Dividing a negative number by a negative number will give a positive result. So, \(\frac{-35}{-5} = \frac{35}{5}\).

Step 3: Perform the division

Next, divide 35 by 5. \(35 \div 5 = 7\).

Step 4: Write the final answer

Thus, the quotient of \(\frac{-35}{-5}\) is 7.

Key Concepts

Quotient

The term 'quotient' is used in mathematics to refer to the result of a division problem. For instance, if you have a division problem like \(\frac{-35}{-5}\), you are looking to find its quotient. In simpler terms, dividing \(-35\) by \(-5\) will yield a number, and that number is called the quotient. When working on division problems, identifying what the quotient represents can help you understand the overall process.
For example, in our problem, once we perform the division \(\frac{35}{5}\) after simplifying signs, we get the quotient as 7.

Simplifying Signs

One of the keys to solving division problems, especially involving negative numbers, is simplifying signs. When you divide two numbers that are both negative, the result is positive. Here's why:

• Negative divided by Negative = Positive
• Negative divided by Positive = Negative
• Positive divided by Negative = Negative
• Positive divided by Positive = Positive

In our problem \(\frac{-35}{-5}\), we're dividing -35 by -5. Since both numbers are negative, we know the quotient will be positive. Thus, we can simplify the expression to \(\frac{35}{5}\). Understanding these rules makes it easier to handle division problems involving negative numbers.

Division Process

Now, let's discuss the actual division process. Once you've simplified the signs, you just need to perform the division like any standard division problem. Here's a step-by-step breakdown:

• Identify the numbers to be divided. In this case, it's 35 and 5.
• Divide the number in the numerator by the number in the denominator. So, divide 35 by 5.
• Perform the division: 35 divided by 5 equals 7.

So, the final answer, or the quotient, of dividing -35 by -5 is 7. Simplifying the signs first makes the division straightforward and easy to handle.