Problem 274 - Intermediate Algebra

Question

In the following exercises, divide. Round money monetary answers to the nearest cent. $$ 14 \div 0.35 $$

Step-by-Step Solution

Answer

40

Step 1: Understand the problem

The exercise asks to divide 14 by 0.35 and round the answer to the nearest cent if it represents a monetary value.

Step 2: Set up the division

The expression given is 14 divided by 0.35. This can be written as \( \frac{14}{0.35} \).

Step 3: Adjust the divisor to a whole number

To make the division easier, multiply both the numerator (14) and the denominator (0.35) by 100 to eliminate the decimal in the denominator. \[ \frac{14 \times 100}{0.35 \times 100} = \frac{1400}{35} \]

Step 4: Perform the division

Now, divide 1400 by 35. \[ \frac{1400}{35} = 40 \]

Step 5: Round to the nearest cent (if needed)

In this case, the quotient is already an integer, and no rounding is necessary.

Key Concepts

rounding to the nearest cent

Rounding to the nearest cent is essential when dealing with monetary values to ensure accuracy and fairness. Currencies like the dollar have two decimal places.
This means when dividing or multiplying, you need to round off your answer to two decimal places. Here's how you do it:

• Look at the number in the third decimal place (thousandths place).
• If it is 5 or more, increase the second decimal place by one.
• If it is less than 5, leave the second decimal place as it is.
  
  In the given example, the result was exactly 40, which doesn’t require rounding. But if it had been, say, 40.123, you would round it to 40.12.

arithmetic operations

Understanding basic arithmetic operations like addition, subtraction, multiplication, and division is crucial.
Division, in particular, can often involve both whole numbers and decimals, as seen in this exercise. Here’s a short breakdown of these operations:

• **Addition** combines two or more numbers.
• **Subtraction** finds the difference between two numbers.
• **Multiplication** is repeated addition of a number.
• **Division** determines how many times one number is contained within another.
  In our example, dividing 14 by 0.35 required changing the division into a simpler form by eliminating the decimal in the divisor, which resulted in division with whole numbers.
  This makes the process more intuitive and easier to calculate accurately. Understanding and mastering these operations can significantly improve your math skills.