Let's examine the division of a whole number by a fraction. We'll use the question: "What is 18 divided by 14/4?" To solve for this, we will dissect the problem into manageable elements. We've got whole number 18 (also identified as the dividend), and the divisor which is a fraction. This can also be divided into its numerator (14) and its denominator (4).
To calculate this, we must execute a series of steps. The first step is multiplying the whole number by the denominator of the fraction. For this example, you multiply 18 by 4 which equals to 72. Afterwards, you convert the numerator of the fraction into the denominator of the result. This gives you the fraction form of the answer, which is 72/14.
To further simplify, divide 72 by 14 to get the decimal form of the answer. The approximate result, up to three decimal places, is 5.14. Hence, 18 divided by 14/4 is 5.14 in decimal form and 36/7 in its simplest fractional form.
If you want to challenge and hone your division skills further, you can attempt the following practice problems:
1. What divided by 6 equals 78?
2. What is 9 divided by 10/5?
3. What is 9/6 divided by 8/4?
4. 69 divided by what equals 46?
5. What is 3/2 divided by 4?
These problems will surely stimulate and sharpen your mathematical acumen.
\[
\begin{align*}
\text{Whole number and dividend: } & 18 \\
\text{Numerator of the divisor: } & 14 \\
\text{Denominator of the divisor: } & 4 \\
\text{Step 1:} & 18 \times 4 = 72 \\
\text{Step 2:} & \frac{18 \times 4}{14} = \frac{72}{14} \\
\text{Decimal form:} & \frac{72}{14} = \frac{36}{7} = 5.14 \\
\end{align*}
\]
\[
\text{So, 18 divided by 14/4 in decimal form equals 5.14 and in fractional form, equals 36/7.}
\]