Problem 56 Perform each operation. $$ \... [FREE SOLUTION]

Chapter 6: Problem 56

Perform each operation. $$ \frac{5}{8} \cdot 0.25 $$

Short Answer

Expert verified

The result is $ \frac{5}{32} $.

Step by step solution

Convert Decimal to Fraction

The first step is to convert the decimal number into a fraction. We have the decimal number 0.25. To convert it into a fraction, write 0.25 as $ \frac{25}{100} $, then simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 25. Thus, $ \frac{25}{100} = \frac{1}{4} $.

Multiply Fractions

Now we multiply the fractions. We have $ \frac{5}{8} $ and $ \frac{1}{4} $. Multiply the numerators together: $ 5 \times 1 = 5 $ and the denominators: $ 8 \times 4 = 32 $. The resulting fraction is $ \frac{5}{32} $.

Simplify the Result (if needed)

Check if the fraction $ \frac{5}{32} $ can be simplified. Since there are no common factors between 5 and 32, $ \frac{5}{32} $ is already in its simplest form.

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Key Concepts

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

Decimal to Fraction Conversion

Decimals can be easily transformed into fractions, allowing us to perform fraction operations more fluidly. Let's consider the decimal 0.25 as an example. We need to express it as a fraction. To do this:

Count the number of decimal places. In 0.25, there are two decimal places.
Write the decimal as a fraction with 1 followed by the same number of zeros as there are decimal places. Hence, 0.25 becomes $ \frac{25}{100} $.
Finally, simplify the fraction by identifying the greatest common divisor (GCD) between the numerator and denominator. For $ 25 $ and $ 100 $, the GCD is $ 25 $.

After dividing both by their GCD, we get $ \frac{1}{4} $. This process of conversion is crucial when we want to perform operations involving both decimals and fractions.

Multiply Fractions

Multiplying fractions is straightforward and involves two simple steps. Let's explore this by multiplying $ \frac{5}{8} $ and $ \frac{1}{4} $. Here鈥檚 how it works:

First, multiply the numerators of the fractions. That means taking $ 5 $ from $ \frac{5}{8} $ and multiplying it by $ 1 $ from $ \frac{1}{4} $, which results in $ 5 $.
Next, multiply the denominators. So, $ 8 $ from $ \frac{5}{8} $ times $ 4 $ from $ \frac{1}{4} $ equals $ 32 $.

Put together, the resulting fraction is $ \frac{5}{32} $. Multiplication of fractions does not require common denominators, making the process more rapid and efficient. Just remember to multiply both the numerators and the denominators.

Simplification of Fractions

Simplifying fractions is an important step in making sure our answers are as concise as possible. Given the fraction $ \frac{5}{32} $, let's see if it can be simplified:

To simplify, check for any common factors of the numerator and the denominator. Here, 5 and 32 have no common factors other than 1.
If common factors exist, divide both the numerator and the denominator by the greatest common factor.

Since $ 5 $ and $ 32 $ do not share any common factors besides 1, $ \frac{5}{32} $ remains in its simplest form. Simplification helps in providing the clearest possible solution and in some cases, can make further mathematical operations easier.

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91影视

Perform each operation. $$ \frac{5}{8} \cdot 0.25 $$

Short Answer

Step by step solution

Convert Decimal to Fraction

Multiply Fractions

Simplify the Result (if needed)

Key Concepts

Decimal to Fraction Conversion

Multiply Fractions

Simplification of Fractions

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