Problem 269 - Intermediate Algebra

Question

In the following exercises, divide. Round money monetary answers to the nearest cent. $$ \$ 117.25 \div 48 $$

Step-by-Step Solution

Answer

Approx $2.44

Step 1: Set Up the Division Problem

Prepare the division problem: Divide 117.25 by 48, which can be written as \ \[ 117.25 \div 48 \].

Step 2: Perform the Division

Carry out the division using long division or a calculator. When using a calculator, the result of dividing 117.25 by 48 is approximately 2.442708333.

Step 3: Round to the Nearest Cent

Since monetary values are rounded to the nearest cent (two decimal places), round 2.442708333 to 2.44.

Key Concepts

Long Division

Long division might look complicated, but with practice, it can be quite straightforward. It's a method used for dividing larger numbers by breaking them down into simpler steps. Here's a quick guide to understand it better:

• First, set up the division problem. For instance, to divide 117.25 by 48, you place 117.25 inside the division symbol (called the dividend) and 48 outside (the divisor).
• Next, determine how many times the divisor can go into the initial part of the dividend. Start from the left and move right. For this example, 48 can't go into 1, 11, or 117 evenly, but it goes into 117 twice.
• Multiply the divisor by the current quotient (2 in this case) and subtract the result from the relevant part of the dividend.
• Next, bring down the next digit and repeat the process.

It might take some trials and errors, but it's worth the effort!

Rounding to Nearest Cent

Rounding to the nearest cent means adjusting your number so that it shows only two decimal places.
This rule is especially important for monetary values to ensure accuracy. Here’s how:

• After performing the division, you might get a number with many decimal places, like 2.442708333.
• Look at the third decimal place. If it's 5 or greater, round up the second decimal place by one. If it's less than 5, keep the second decimal place as it is.
• In our example, 2.442708333 is rounded to 2.44 since the third decimal place is 2 (which is less than 5).

Remember, this is crucial for ensuring your financial calculations are precise.

Calculator Usage

Using a calculator can make division problems much simpler and faster. Here's how to make the best use of it:

• Enter the dividend (the number being divided) first. For our example, type 117.25.
• Press the division symbol (often shown as ÷).
• Input the divisor (the number you’re dividing by). For this, type 48.
• Hit the equals sign (=) to get the result, which should be approximately 2.442708333.

Calculators are handy but always double-check your steps to ensure correctness. They can sometimes show more decimal places than needed; remember to round your answer appropriately if working with money.