Problem 44 - Prealgebra

Question

Simplify each of the following as much as possible, and write all answers as decimals. $$8\left(\frac{4}{5}\right)(0.03)$$

Step-by-Step Solution

Answer

The simplified result is 0.192.

Step 1: Convert Fraction to Decimal

First, convert the fraction \( \frac{4}{5} \) into a decimal. Divide 4 by 5 to get 0.8.

Step 2: Multiply Decimals

Next, multiply the decimal equivalent of \( \frac{4}{5} \), which is 0.8, by 0.03. \( 0.8 \times 0.03 = 0.024 \).

Step 3: Final Multiplication with Integer

Finally, multiply the result, 0.024, by 8 to obtain the final answer. \( 8 \times 0.024 = 0.192 \).

Key Concepts

Decimal Conversion

Converting fractions into decimals is an essential math skill that helps simplify complex expressions. If you have a fraction like \( \frac{4}{5} \), turning it into a decimal involves simple division. Here, you divide the numerator (4) by the denominator (5). Doing this manually, you'll see that 4 divided by 5 equals 0.8. This conversion is handy because working with decimals often allows more straightforward operations, especially in calculations involving other decimals. So, whenever you have a fraction, think about converting it to a decimal for easier handling in equations.

Multiplication of Decimals

Once you've converted any fractions to decimals, you may need to multiply these decimals together. Let's consider multiplying 0.8 by 0.03. The key here is to multiply the numbers as if they were whole, ignoring the decimal points initially. Multiply 8 and 3 to get 24. Now, count the number of decimal places: there are two in 0.03 and one in 0.8, making a total of three. Place the decimal point in your answer, 24, three places from the right to get 0.024. The multiplication of decimals can seem tricky at first, but remembering to adjust for the decimal places at the end makes it manageable.

Fraction Simplification

While converting to decimals is helpful, understanding how to simplify fractions is equally vital. Simplifying a fraction means finding an equivalent fraction where the numerator and denominator have no common factors other than 1. This is sometimes necessary before converting to a decimal when working with complex expressions. If given a more complicated fraction, you should always look to simplify it first. However, in cases like \( \frac{4}{5} \), where the fraction is already in its simplest form, you can proceed directly to decimal conversion. Knowing when and how to simplify can save time and effort in solving math problems.