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Solving equations is a foundational skill in algebra. It involves finding the value of an unknown variable that makes an equation true. In the problem, we are given that 47.25 is a certain percentage of a number, which we need to find. This unknown number can be denoted by a variable, commonly "x".
To solve the equation, set up an equality where the percentage expressed as a decimal is multiplied by "x", and equals the known number of 47.25. This sets up the equation as:

• \( 0.105x = 47.25 \)

To isolate "x", divide both sides of the equation by the decimal value. Through this division, we can find the value of "x" which will satisfy the equation:

• \( x = \frac{47.25}{0.105} \)

Finally, performing the calculation gives us an approximation of x, solving the problem.

Converting a percentage to a decimal is an essential step in solving percentage problems. Percentages are out of 100, so the conversion simply involves shifting the decimal point two places to the left.
For the given percentage of \(10 \frac{1}{2}\%\):

• First, convert the mixed number to a decimal by considering its fractional part, that is, \(\frac{1}{2}\) becomes 0.5.
• The whole percentage becomes 10.5% once they are combined.
• To convert, divide by 100 by moving the decimal two places left, becoming 0.105.

This conversion allows accurate computations when solving equations without directly dealing with percentages.

Fraction to decimal conversion is straightforward but important for handling fractions in equations or when dealing with mixed numbers. A fraction characterizes a part of a whole and its conversion can simplify calculations.
Here's how you can convert a fraction like \(\frac{1}{2}\) to a decimal, which is crucial for converting percentages like \(10\frac{1}{2}\%\):

• Perform the division: Divide the numerator (1) by the denominator (2), resulting in 0.5.

By converting fractions to decimals, calculations in algebra become easier to manage, especially when combined with whole numbers in expressions or equations. This technique strengthens understanding of different number forms used in math.