Problem 271 - Intermediate Algebra

Question

In the following exercises, divide. Round money monetary answers to the nearest cent. $$ 1.44 \div(-0.3) $$

Step-by-Step Solution

Answer

The quotient is .

Step 1 - Identify the numbers

The numbers to be divided are 1.44 and -0.3. Note that division by a negative number will result in a negative quotient.

Step 2 - Perform the division

Divide 1.44 by 0.3. Ignore the negative sign initially: Upon calculating, we get:

Step 3 - Apply the sign

Include the negative sign in the quotient since we are dividing by a negative number. Hence, becomes

Step 4 - Final answer

The quotient obtained is: Round to the nearest cent as required for monetary values, though in this case it isn't necessary.

Key Concepts

Integer Division

When we talk about integer division, we are referring to the division of whole numbers. In this exercise, however, we are dividing decimals, which adds another layer of complexity.

Integers are whole numbers that can be positive, negative, or zero. For example: -5, 0, and 7 are all integers. When we perform integer division, we focus on finding out how many times one integer can be divided by another without considering the remainder.

But remember, when you divide two integers and the result is not an integer, you typically get a decimal. For example, dividing the integer 5 by the integer 2 gives you 2.5.

In our exercise, even though the numbers involved are not integers, the logic remains similar. First, you identify the absolute values of the numbers (ignore the negative sign temporarily) and perform the division. Then, you can add the sign back after the calculation.

This method can also be helpful in understanding the division of decimal numbers in a more intuitive way.

Negative Numbers

Negative numbers play a crucial role in this exercise. In our problem, we are dividing 1.44 by -0.3. Negative numbers are values less than zero and are denoted with a minus ('-') sign. It is important to understand how negative numbers affect the result of mathematical operations such as division.

Here are key points to remember:

• When you divide a positive number by a negative number, the result (quotient) is negative.
• When you divide two negative numbers, the result is positive.
• When you divide a negative number by a positive number, the result is negative.

In our exercise, we initially performed the division of 1.44 by 0.3, ignoring the negative sign. After finding the result, we included the negative sign in our final answer to indicate the division by a negative number.

Rounding Decimals

Rounding decimals is an essential skill, especially when dealing with monetary values. The general rule for rounding is to look at the digit immediately after the place value you are rounding to.

Here's a simple breakdown:

• If the digit is less than 5, you leave the rounding digit as it is.
• If the digit is 5 or more, you increase the rounding digit by one.

For monetary values, we usually round to the nearest cent (two decimal places). This ensures that our financial calculations are precise and practical.

In our exercise, the quotient obtained is straightforward and does not require rounding. However, if it did, you would follow the rounding rules to ensure accuracy. For example, rounding 2.678 to two decimal places would give you 2.68 because the third decimal digit (8) is more than 5.

By understanding these principles, you can handle any division problem involving decimals and ensure your final answer is both accurate and appropriate for the context.