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Chapter 6: Problem 23

Find 1.1 of the sum of 8.6 and 4.2 .

Short Answer

Expert verified
1.1 times the sum of 8.6 and 4.2 is 14.08.

Step by step solution

01

Addition

Begin by adding the two numbers, 8.6 and 4.2. To add these numbers, align the decimals and add each column starting from the right.\[\begin{array}{c} \; 8.6 \ +\;4.2 \ \hline 12.8 \end{array}\]Thus, the sum of 8.6 and 4.2 is 12.8.
02

Multiplication by 1.1

Next, multiply the sum obtained in Step 1 by 1.1 to find 1.1 times the sum.\[1.1 \times 12.8\]To calculate this, perform the multiplication: 1.1 times 12.8 can be simplified by multiplying as follows: \[1.1 \times 12.8 = 14.08.\]Thus, 1.1 of the sum is 14.08.

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Key Concepts

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

Addition
Addition is one of the fundamental arithmetic operations. It involves combining two or more numbers into a total sum. For example, adding 8.6 and 4.2 involves putting these two numbers together. The key to successful addition, especially with decimals, is careful alignment. When you align numbers properly, you ensure that each digit is in the right column, making the calculation accurate. Begin by placing the decimal points directly above one another. This is crucial for accuracy:
  • Align the decimal points of the numbers.
  • Add each column starting from the rightmost digit.
For our numbers, 8.6 added to 4.2 results in 12.8. Each digit retains its place value, thanks to this alignment.
Decimal Alignment
Aligning decimals is a vital step when working with decimal numbers in arithmetic operations. Before you perform addition or subtraction with decimals, align their decimal points. This might seem like a simple step, but it plays a significant role in arriving at the correct answer. The process involves lining up numbers vertically based on their decimal points:
  • Make sure the digits before and after the decimal point correspond.
  • Add zeros if necessary to ensure each column can be properly calculated.
If decimals are not aligned, digits can be misplaced, leading to incorrect results. In operations with decimals, it鈥檚 also helpful to re-check the alignment before finalizing your answer.
Multiplication
Multiplication is another essential arithmetic operation. It involves repeated addition of a number. In this context, calculating 1.1 times the sum of 8.6 and 4.2 demonstrates this idea. After obtaining the sum 12.8, you multiply it by 1.1. To multiply decimal numbers:
  • Ignore the decimals and perform the multiplication as if they are whole numbers.
  • Count the total number of decimal places involved in the original numbers.
  • Place the decimal in the product so that it has this many decimal places in total.
In our example, 1.1 times 12.8 originally translates to multiplying 110 by 128. You adjust the decimal afterwards, resulting in 14.08, respecting the original decimal places.

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Most popular questions from this chapter

Write each decimal using digits. Nine and twelve-hundredths.

Perform each operation. $$ \frac{7}{2} \cdot\left(\frac{5}{4}+0.30\right) $$

Perform the following operations. \(0.5 \frac{1}{4}+(0.3)^{2}\)

Convert each decimal to a proper fraction or a mixed number. 58.63

Perform each operation and simplify. $$ 10.000 \cdot 0.14 $$
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