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Chapter 5: Problem 91

Perform the indicated operations. Round the answer to the nearest hundredth when necessary. $$6.5 \div\left(-\frac{3}{5}\right)$$

Short Answer

Expert verified
The住resultis.-$$10:.}, }

Step by step solution

01

Rewrite the Division

Rewrite the division of a number by a fraction as the multiplication of the number by the reciprocal of the fraction. In this case, rewrite $$6.5 \frac{\frac{5}{ 3}}{ -\frac{}{\frac{3}{5}}}\(}\)
02

Multiply the Numbers

Now perform the multiplication: $$6(5) \frac{-1}{}$.$$3.$$)
03

Calculate the Result

Perform the multiplication to get the result.}

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Key Concepts

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

Division of Fractions
To divide a number by a fraction, you need to multiply the number by the reciprocal of the fraction. This makes the division process easier. For example, to solve the problem \(6.5 \div\left( -\frac{3}{5} \right)\), you should first find the reciprocal of \(-\frac{3}{5}\). Once you have the reciprocal, you turn the division into a multiplication. This transformation is essential for simplifying the complex process of dividing by a fraction. It is important to understand this step well, as it is the foundation for solving the problem correctly.
Multiplication of Fractions
Once you have rewritten the division problem as a multiplication one, the next step is to multiply the given numbers. Using our example, after converting \(6.5 \div\left( -\frac{3}{5} \right)\) to \(6.5 \times\left( -\frac{5}{3} \right)\), you simply need to multiply 6.5 by \(-\frac{5}{3}\). Multiplying fractions involves multiplying the numerators together and the denominators together. Since 6.5 can be written as \(\frac{65}{10}\), the arithmetic becomes straightforward. Performing the multiplication step makes the fractions easy to manage and leads you closer to your final answer.
Reciprocal of a Fraction
The reciprocal of a fraction is obtained by swapping its numerator and denominator. If you have a fraction \(\frac{a}{b}\), its reciprocal would be \(\frac{b}{a}\). For the fraction \(-\frac{3}{5}\), the reciprocal would become \(-\frac{5}{3}\). Finding the reciprocal is crucial when transforming division problems into multiplication problems. This step simplifies complex operations. Always remember, the reciprocal of a negative fraction is also negative.
Rounding Decimals
After performing the necessary arithmetic, sometimes it's required to round the result to a certain decimal place. In our example, after calculating \(6.5 \times\left( -\frac{5}{3} \right)\), you get an answer that might not be a whole number. By rounding to the nearest hundredth, you ensure the result fits neatly, making it easier to comprehend. To round decimals, look at the digit in the thousandth place. If it's 5 or more, round up the digit in the hundredth place by one. If it's less than 5, keep the digit in the hundredth place as it is. This rounding process ensures your answer is concise and clear.

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Most popular questions from this chapter

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The Athletic Department at Broward College bought 20 pizzas for \(\$ 10.95\) each, 10 Greek salads for \(\$ 3.95\) each, and 60 soft drinks for \(\$ 0.60\) each. What was the total bill including a sales tax of \(\$ 17.67 ?\)

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