Problem 43 - Prealgebra

Question

Simplify each of the following as much as possible, and write all answers as decimals. $$6\left(\frac{3}{5}\right)(0.02)$$

Step-by-Step Solution

Answer

The simplified decimal is 0.072.

Step 1: Simplify the Fraction

Start by simplifying the fraction \( \frac{3}{5} \). As it's already in its lowest terms, convert it to a decimal to make multiplication easier later. \( \frac{3}{5} = 0.6 \).

Step 2: Convert to Decimals

Now, write all components of the expression as decimals. We already have \( \frac{3}{5} = 0.6 \) and \( 0.02 \) is already a decimal. The entire expression now is \( 6 \times 0.6 \times 0.02 \).

Step 3: Perform the Multiplication

Multiply the converted decimals and the integer in sequence. First, calculate \( 6 \times 0.6 = 3.6 \). Then multiply the result by the next decimal: \( 3.6 \times 0.02 \).

Step 4: Calculate Final Result

Multiply \( 3.6 \) by \( 0.02 \) to get the final simplified decimal value. \( 3.6 \times 0.02 = 0.072 \).

Key Concepts

Decimal Conversion

When we talk about decimal conversion, we're focusing on transforming numbers into a decimal format to make calculations smoother. This often involves converting fractions or other numerical forms into decimals. Instead of working with fractions like \( \frac{3}{5} \), we convert it directly into its decimal form, in this case, \( 0.6 \). This makes subsequent operations, such as multiplication, much simpler and more straightforward.

• Recognizing equivalent decimals helps you quickly switch between different formats.
• Decimal conversion is key for operations in both everyday math and in more complex applications.

Fraction to Decimal

Changing a fraction into a decimal is easier than it sounds. It involves a division process. For the fraction \( \frac{3}{5} \), it simply means dividing 3 by 5. Upon performing this division, you receive the decimal number \( 0.6 \).

• This method allows a fraction to be quickly changed to a decimal.
• Fraction to decimal conversion is essential for precise calculations.

To make sure you're on the right track, use a calculator to divide the numerator (top of the fraction) by the denominator (bottom of the fraction). By doing this, the decimal form you get can be easily used in further arithmetic operations.

Simplifying Fractions

Simplifying fractions is the technique of reducing them to their smallest values. It helps make operations less cumbersome. With \( \frac{3}{5} \), despite it being already simplest, understanding this process is vital.If you start with a more complex fraction, always look at the numerator and denominator. Try to find the greatest common divisor (GCD) and divide both by this number. With simplified fractions, or when directly converting to decimals, calculations like multiplication become far more manageable.

• Check if the fraction is reducible.
• If it isn’t, you are ready to convert it directly.