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Chapter 5: Problem 159

In the following exercises, divide. $$12 \div 0.08$$

Short Answer

Expert verified
150

Step by step solution

01

- Convert the Division

Convert the division into a fraction. The division of 12 by 0.08 can be written as a fraction: \[ 12 \, \div \, 0.08 = \frac{12}{0.08} \]
02

- Eliminate the Decimal

To simplify the fraction \( \frac{12}{0.08} \), eliminate the decimal in the denominator. Multiply both the numerator and the denominator by 100: \[ \frac{12}{0.08} \times \frac{100}{100} = \frac{12 \times 100}{0.08 \times 100} = \frac{1200}{8} \]
03

- Simplify the Fraction

Simplify the fraction \( \frac{1200}{8} \) by performing the division: \[ \frac{1200}{8} = 150 \]

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Key Concepts

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

fraction conversion
Let's start by turning a division problem into a fraction. When you see a problem like \(12 \div \ 0.08\), you can write it as a fraction to make it easier to manage. This is because division and fractions are just two sides of the same coin. So, \(12 \div \ 0.08\) becomes \(\frac{12}{0.08}\).
This conversion helps us visualize the problem in a familiar format, making the next steps simpler.
Think of the division sign as a cue to set up your fraction.
eliminating decimals
Next, we'll handle the decimals. Fractions are easier to deal with when they don't have decimals. To eliminate the decimal in the fraction \(\frac{12}{0.08}\), we can multiply both the top (numerator) and the bottom (denominator) by the same number. In this case, multiplying by 100 works well because it shifts the decimal two places to the right.
So, we compute: \(0.08 \times 100 = 8 \) and \(12 \times 100 = 1200\). Now, our fraction is \(\frac{1200}{8}\).
Multiplying by 100 helps to 'clear' the decimal from the denominator.
simplifying fractions
Simplifying a fraction means making it as simple as possible. For our fraction \(\frac{1200}{8}\), you perform the division indicated. Calculate: \(\frac{1200}{8} = 150\).
This means our simple fraction is now 150.
Remember, simplifying fractions often involves dividing both the numerator and the denominator by their greatest common divisor. In some cases, you might need additional steps like cross-multiplying to simplify.
basic arithmetic operations
This problem involves basic arithmetic operations like multiplication and division. Here鈥檚 a quick recap:
  • Multiplication helps clear decimals by shifting them to the right.
  • Division helps reduce fractions to the simplest form.
In our example, we multiplied by 100 to clear the decimal, then divided 1200 by 8 to simplify the fraction. These operations are fundamental and used in various math problems.
Feeling comfortable with basic operations is key to tackling more complex math problems.

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Most popular questions from this chapter

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