Problem 28 - Prealgebra

Question

Multiply. $$0.06(625)$$

Step-by-Step Solution

Answer

0.06 multiplied by 625 is 37.5.

Step 1: Convert to Fraction

First, convert the decimal number 0.06 into a fraction. Recall that 0.06 is equal to 6 hundredths, which can be written as \( \frac{6}{100} \).

Step 2: Simplify the Fraction

Next, simplify the fraction \( \frac{6}{100} \). Both 6 and 100 are divisible by 2, so divide them by 2 to get \( \frac{3}{50} \).

Step 3: Set Up the Multiplication

Now multiply the simplified fraction by 625. The multiplication problem is now \( \frac{3}{50} \times 625 \).

Step 4: Multiply the Numerator by 625

Multiply the numerator of the fraction, which is 3, by 625. \( 3 \times 625 = 1875 \).

Step 5: Divide the Result by the Denominator

Divide the result from Step 4 by the denominator of the fraction, which is 50. Calculate \( \frac{1875}{50} \), which simplifies to \( 37.5 \).

Step 6: Check the Answer

Finally, review each step to ensure correctness. The calculations align, confirming that 0.06 multiplied by 625 equals 37.5.

Key Concepts

Fractions

Fractions represent parts of a whole number.They consist of a numerator (top number) and a denominator (bottom number). For example, in the fraction \( \frac{6}{100} \), 6 is the numerator and 100 is the denominator.The numerator signifies the number of parts you have, while the denominator shows the total number of equal parts in the whole.Understanding fractions is crucial when addressing problems that involve parts of a whole, such as performing multiplications or divisions with fractions.This knowledge is especially useful when converting decimals to fractions as it offers a more visual representation of the value.Additionally, it enriches our ability to handle various mathematical operations, providing flexibility in calculations.

Simplifying Fractions

Simplifying fractions means making them as simple as possible.This involves reducing the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).

• For instance, consider the fraction \( \frac{6}{100} \).
• Both 6 and 100 can be divided by 2, their GCD, to simplify the fraction to \( \frac{3}{50} \).

Simplified fractions make calculations easier and results clearer. By reducing fractions, we often deal with smaller numbers and simpler expressions, making subsequent operations more straightforward.In financial and scientific calculations, working with simplified fractions enhances accuracy and understanding.

Decimal to Fraction Conversion

Converting decimals to fractions is a valuable skill in mathematics.It involves expressing the decimal number as a fraction with a numerator and a denominator.

• To convert, count the decimal places. For example, 0.06 has two decimal places.
• This makes it equivalent to 6 hundredths, written as \( \frac{6}{100} \).

Once you write the decimal as a fraction, the next step usually involves simplifying the fraction.This simplifies not just the appearance but can also make future calculations easier and more logical.Conversion is particularly useful when you have to perform operations like multiplication or division with decimals, as working directly with fractions often simplifies the process.Moreover, in many mathematical proofs and real-world applications, fractions offer a clearer insight compared to decimals.