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Chapter 5: Problem 92

Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$\left(\frac{1}{12}\right)(6.24) \div(-2.1)$$

Short Answer

Expert verified
-0.25

Step by step solution

01

Multiply the fractions

First, multiply the fraction \(\frac{1}{12}\) by 6.24: \(\frac{1}{12} \times 6.24\). To do this, perform the multiplication: \(\frac{1 \times 6.24}{12} = \frac{6.24}{12} = 0.52\)
02

Divide the result

Now, divide the result from Step 1 (0.52) by \(-2.1\): \(\frac{0.52}{-2.1}\). Perform the division: \(\frac{0.52}{-2.1} \approx -0.2476\)
03

Round the result

Round the result to the nearest hundredth. The value \(-0.2476\) rounded to the nearest hundredth is \(-0.25\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplying fractions
Multiplying fractions might seem a bit tricky at first, but with practice, it becomes second nature. In this exercise, it starts with the task \(\frac{1}{12} \times 6.24\).

To multiply a fraction by a decimal (6.24 in this case), we follow these steps:
  • First, convert the decimal to a fraction. 6.24 can be written as \(\frac{624}{100}\).

  • Next, multiply the two fractions: \(\frac{1}{12} \times \frac{624}{100}\).

  • Perform the multiplication across the numerators and denominators: \(\frac{1 \times 624}{12 \times 100} = \frac{624}{1200}\).

  • Simplify the fraction: \(\frac{624}{1200} = \frac{52}{100} = 0.52\).
This simple approach shows how to break down the problem into manageable steps, resulting in a straightforward multiplication process.
dividing fractions
Dividing fractions involves a small trick called 'reciprocal multiplication.' In the exercise, after finding the product 0.52, we divide it by \( -2.1 \).

Here are the steps:
  • First, understand that dividing by a number is the same as multiplying by its reciprocal. So, dividing by \(-2.1\) is the same as multiplying by \(-\frac{1}{2.1}\).

  • Next, recognize that 2.1 is equal to \(\frac{21}{10}\). So the reciprocal of \(-2.1\) is \(-\frac{10}{21}\).

  • Now, multiply 0.52 by \(-\frac{10}{21}\).
The multiplication process involves:

\(0.52 \times -\frac{10}{21} = -\frac{0.52 \times 10}{21} = -\frac{5.2}{21} \approx -0.2476\)

This process simplifies the division of fractions into something much more manageable!
rounding decimals
Rounding decimals is an essential skill in mathematics to make numbers easier to work with. In the last step of our exercise, we round \(-0.2476\) to the nearest hundredth.

Here's the process:
  • Identify the place value you need to round to (in this case, the nearest hundredth, which is the second digit after the decimal).

  • Look at the next digit to the right (the thousandths place) to decide if you need to round up or down. Here, we examine the digit 7 from \(-0.2476\).

  • If the next digit is 5 or greater, round the last digit up. If it's less than 5, leave the last digit as is. Since 7 is greater than 5, we round up.
This makes the rounded result \(-0.25\).

Understanding these place values and rules for rounding ensures that you can handle any decimal rounding in your math problems!

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