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Chapter 5: Problem 75

Find the value of each expression. Give the result as a decimal. $$ \frac{1}{5}-2(7.8) $$

Short Answer

Expert verified
The value of the expression is \(-15.4\).

Step by step solution

01

Simplify the Expression inside the Parentheses

The expression given is \( \frac{1}{5} - 2(7.8) \). Start by simplifying the expression inside the parentheses by multiplying \(2\) by \(7.8\). \[ 2 \times 7.8 = 15.6 \]
02

Replace the Simplified Expression in the Equation

Now that we know \(2 \times 7.8 = 15.6\), substitute \(15.6\) back into the original expression. \[ \frac{1}{5} - 15.6 \]
03

Convert the Fraction to a Decimal

Convert the fraction \( \frac{1}{5} \) into a decimal. \( \frac{1}{5} = 0.2 \).
04

Perform the Subtraction

Now subtract \(15.6\) from the decimal form of \( \frac{1}{5} \), which is \(0.2\).\[ 0.2 - 15.6 = -15.4 \]

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Key Concepts

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

Decimal Subtraction
Subtracting decimals involves lining up the numbers based on their decimal points and performing the subtraction as you would with whole numbers. Imagine you have the numbers 0.2 and 15.6, which need to be subtracted.
  • Ensure the decimal points are aligned, placing extra zeros if necessary (although it isn't needed here).
  • Subtract from right to left, borrowing as needed from higher place values.
In the expression given, we needed to calculate \( 0.2 - 15.6 \). Since 0.2 is less than 15.6, the result of the subtraction is negative, calculated as -15.4. Understanding that subtracting a larger number from a smaller number results in a negative value is crucial. It helps in better grasping the concept of how negative results reflect the difference in values.
Fraction to Decimal Conversion
Converting fractions into decimals is often a necessary step for simplifying expressions, especially when they involve both decimals and fractions. To convert a fraction, divide the numerator (top number) by the denominator (bottom number). For instance, in the expression \(\frac{1}{5}\), you perform the division:
  • Divide 1 by 5.
  • The decimal equivalent is 0.2.
Fractions like \(\frac{1}{5}\) are simple enough that they often come up in calculations. Knowing common fractions and their decimal equivalents can speed up your work. For example, \(\frac{1}{4} = 0.25\) and \(\frac{1}{2} = 0.5\). Practicing these conversions helps in both understanding and quickly recalling them during problem-solving.
Expression Simplification
Simplifying expressions is about breaking down a problem into more manageable parts. The expression in the problem, \( \frac{1}{5} - 2(7.8) \), involves several components: multiplication, fractions, and subtraction.
  • First, resolve any multiplication or division within parentheses: \(2 \times 7.8 = 15.6\).
  • Replace the product back into the original expression.
  • Convert any fractions into decimals to ease the calculation: \(\frac{1}{5} = 0.2\).
  • Finally, perform the subtraction: \(0.2 - 15.6 = -15.4\).
Breaking down expressions into smaller, easily comprehensible steps simplifies solving them. This method not only helps prevent mistakes but also builds a deeper understanding. It's always beneficial to verify each step, ensuring that each piece of the puzzle is correct before moving on to the next.

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Most popular questions from this chapter

The 10 tallest buildings in the world, completed as of the end of 2016 , are listed in the following table. Use this table to answer. If necessary, round results to one decimal place. $$ \begin{array}{|l|c|} \hline \text { Building } & \text { Height in Feet } \\ \hline \text { Burj Khalifa, Dubai } & 2717 \\ \hline \text { Shanghai Tower, Shanghai } & 2073 \\ \hline \text { Makkah Royal Clock Tower, Mecca } & 1972 \\ \hline \text { Ping An Finance Center } & 1965 \\ \hline \text { Lotte World Tower } & 1819 \\ \hline \text { One World Trade Center, New York City } & 1776 \\ \hline \text { Guangzhou CTF Finance Center, Guangzhou } & 1739 \\ \hline \text { Taipei 101, Taipei } & 1667 \\ \hline \text { Shanghai World Financial Center, Shanghai } & 1614 \\ \hline \text { International Commerce Center, Hong Kong } & 1588 \\ \hline \end{array} $$ Find the mean height of the six tallest buildings.

Divide. \(\frac{13.1}{10}\)

The area of a rectangle is 38.7 square feet. If its width is 4.5 feet, find its length.

The following pulse rates were recorded for a group of 15 students: $$ 78,80,66,68,71,64,82,71,70,65,70,75,77,86,72 $$ Find the median.

Divide. \(\frac{17.7}{10}\)
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