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Chapter 5: Problem 160

In the following exercises, divide. $$5 \div 0.04$$

Short Answer

Expert verified
125

Step by step solution

01

Convert Division into Fraction

Begin by converting the division expression into a fraction. The expression \(5 \div 0.04\) can be written as \( \frac{5}{0.04} \).
02

Eliminate the Decimal in the Denominator

To eliminate the decimal in the denominator, multiply both the numerator and the denominator by 100 (since 0.04 is equivalent to 4/100, multiplying by 100 shifts the decimal two places to the right). This gives \( \frac{5 \times 100}{0.04 \times 100} = \frac{500}{4} \).
03

Simplify the Fraction

Now, simplify the fraction \( \frac{500}{4} \). Dividing the numerator by the denominator results in \( 500 \div 4 = 125 \).

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Key Concepts

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

fraction conversion
When working with division involving decimals, turning the division into a fraction can make things a lot more manageable. In the example of dividing 5 by 0.04, the first step is to express this division as a fraction so: \(5 \div 0.04\) can be written as \(\frac{5}{0.04}\).\ Fractions can simplify complex division because they allow us to handle both the numerator and denominator in a clear, structured way. It鈥檚 like changing a language to one we are more familiar with! This format helps us apply well-known rules and properties of fractions.
decimal elimination
Next, let's tackle the decimal in our fraction. Decimals in the denominator can complicate things, so we eliminate them by converting the fraction into a simpler form with whole numbers.\
In our example, \(\frac{5}{0.04}\), we need to multiply both the numerator (5) and the denominator (0.04) by 100.\
Why 100? Because multiplying by 100 shifts the decimal point two places to the right, turning 0.04 into 4.\ This transforms our fraction into \(\frac{5 \times 100}{0.04 \times 100} = \frac{500}{4}\).\ Now, we have successfully changed our fraction to an equivalent one without any decimals!
simplifying fractions
Lastly, simplifying our fraction pulls everything together. Simplification helps us express the fraction in its simplest form by dividing both the numerator (500) and the denominator (4) by their greatest common divisor (GCD).\
In \(\frac{500}{4}\), 4 is the GCD that fits perfectly into both the numerator and denominator.\
Dividing 500 by 4 gives us 125.\
  • This results in \(500 \div 4 = 125\).
  • Thus, our simplified fraction is simply 125.
Simplifying fractions not only makes them easier to understand but also helps in achieving the final, most straightforward answer.\ This is particularly useful in various mathematical applications, ensuring clarity and precision.

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