Problem 273 - Intermediate Algebra

Question

In the following exercises, divide. Round money monetary answers to the nearest cent. $$ 5.2 \div 2.5 $$

Step-by-Step Solution

Answer

2.08

Step 1: Set Up the Division

Write out the division problem as \( \frac{5.2}{2.5} \).

Step 2: Convert to Whole Numbers

To make the division easier, multiply both the numerator and the denominator by 10: \( \frac{5.2 \times 10}{2.5 \times 10} = \frac{52}{25} \).

Step 3: Perform the Division

Divide 52 by 25 to get \( 52 \div 25 = 2.08 \).

Step 4: Round the Answer

Since the answer needs to be rounded to the nearest cent, we check the hundredths place to confirm it's already rounded correctly: \( 2.08 \).

Key Concepts

arithmetic

Division is a fundamental arithmetic operation. It involves splitting a number (the dividend) into equal parts, determined by another number (the divisor). In our exercise, we need to divide 5.2 by 2.5.

The key steps include:

• Writing the division problem in fraction form, like this: \( \frac{5.2}{2.5} \).
• Converting it to a simpler form to make the division easier.

Multiplying both the numerator and the denominator by 10 helps to get rid of the decimal point.

So, \( \frac{5.2 \times 10}{2.5 \times 10} = \frac{52}{25} \). Now, you can perform the division more easily.

rounding

Rounding is the process of adjusting a number to make it simpler, while keeping it close to its original value. This is especially useful in dealing with money. For this example, the instructions specify rounding to the nearest cent.

When you divide 52 by 25, you get 2.08. To round to the nearest cent, you check the hundredths place, which is the second digit to the right of the decimal point.

• If it is 5 or higher, you round up.
• If it is 4 or lower, you round down.

In our case, 2.08 is already rounded correctly because the hundredths place is an 8. So, it remains 2.08.

fractions in division

Working with fractions can seem tricky, but it's essential in division. By converting a division problem with decimals into a fraction, you can simplify the operation.

For example, the division problem \(5.2 \div 2.5\) can be written as \( \frac{5.2}{2.5} \). By multiplying both the numerator and the denominator by 10, you eliminate the decimals: \( \frac{52}{25} \).

This trick helps make the division simpler, eliminating the complexity of dealing with decimal points directly. It also makes it easier to perform long division, giving you a clearer, more manageable calculation process.