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Chapter 1: Problem 390

Simplify. $$ \frac{5}{\frac{3}{10}} $$

Short Answer

Expert verified
The simplified form is \( \frac{50}{3} \).

Step by step solution

01

- Understand the Expression

The given expression to simplify is \( \frac{5}{\frac{3}{10}} \). This is a fraction divided by another fraction.
02

- Rewrite the Division

Rewrite the division of fractions as a multiplication by the reciprocal. The expression \( \frac{a}{\frac{b}{c}} \) can be rewritten as \( a \times \frac{c}{b} \). So, \( \frac{5}{\frac{3}{10}} \) becomes \( 5 \times \frac{10}{3} \).
03

- Multiply the Fractions

Now multiply the fractions. \( 5 \times \frac{10}{3} = \frac{5 \times 10}{3} = \frac{50}{3} \).

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Key Concepts

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

Dividing Fractions
Dividing fractions might seem complex at first, but it becomes simple once you understand the steps involved. When you divide by a fraction, you are essentially multiplying by its reciprocal. Let's use an example to make this clearer. Suppose you have the fraction division problem \(\frac{5}{\frac{3}{10}}\). The trick here is to convert this division into a multiplication problem. This leads us to the concept of the 'reciprocal'.
Reciprocal
A reciprocal of a fraction is simply swapping its numerator and denominator. For instance, the reciprocal of \(\frac{3}{10}\) is \(\frac{10}{3}\). This is crucial when dividing fractions, as it lets us turn a division problem into a multiplication one. In our example, we change \(\frac{5}{\frac{3}{10}}\) to \(5 \times \frac{10}{3}\). By using the reciprocal, we simplify the complex division into a straightforward multiplication.
Multiplying Fractions
Once we've converted our division problem into multiplication using the reciprocal, it's time to multiply the fractions. To multiply, you simply multiply the numerators together and the denominators together. Applying this to our example, we get: \(\frac{5 \times 10}{3} = \frac{50}{3}\). This way, the complex-looking division of fractions boils down to the simpler multiplication of fractions. Remember, practice makes perfect, so keep applying these steps, and soon it will be second nature!

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Most popular questions from this chapter

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $$\$ 80\(. Her dental insurance required her to pay \)20 \%\( of the cost as a copay. Calculate Carrie's copay: (a) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings. (b) Next, by multiplying \)[5(0.20)](80)\( (c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \)5[(0.20)(80)]\( and \)(b),\( where you multiplied \)[5(0.20)](80),$$ should be equal?

Convert the units. Lynn's cruise lasted 6 days and 18 hours. Convert the time to hours.

Convert the units. Faye is 4 feet 10 inches tall. Convert her height to inches.

Simplify using the distributive property. $$ 5(2 n+9)+12(n-3) $$

Convert the units. Crista will serve 20 cups of juice at her son's party. Convert the volume to gallons.
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