91Ó°ÊÓ

Long division is a step-by-step procedure for dividing multi-digit numbers. It's a method that allows us to divide numbers to find both the quotient and the remainder. The key in long division is to solve the problem one digit at a time, starting from the leftmost digit of the number you're dividing.

To use long division to convert a fraction like \(\frac{28}{350}\) to a decimal, you'd first set up the division with 28 inside the division bracket, and 350 outside. You then determine how many times 350 fits into 28 or parts of 28, writing the partial quotient above the line, and proceed until you've either got a remainder of zero or you've reached a satisfactory degree of accuracy for the decimal.

The process of converting a fraction to a decimal involves dividing the numerator (top number) by the denominator (bottom number). This gives a decimal which can be rounded to a specific number of decimal places depending on the required precision.

For the fraction \(\frac{28}{350}\), you divide 28 by 350. You can use long division or a calculator to get this result. In this case, the quotient is 0.08. It's important for students to be comfortable with this process, as decimals are more commonly used and are easier to work with in many mathematical settings compared to fractions.

Once you have converted a fraction to a decimal, the next step is to convert it to a percentage. This is done by multiplying the decimal by 100. The concept here is that 'percent' means 'per hundred', so you're essentially finding how many parts out of one hundred the decimal represents.

In our example, the decimal conversion of \(\frac{28}{350}\) is 0.08. To find the percentage, you multiply 0.08 by 100, which equals 8%. This step translates the decimal into a percentage that is easy to understand and interpret in everyday situations, such as determining discounts or calculating statistics.

Elementary algebra is the branch of mathematics that deals with variables and constants, using symbols to represent numbers in equations and formulas. When converting fractions to percentages, algebraic thinking helps in understanding the relationships between ratios, decimals, and percentages.

For example, when we multiply by 100 to convert a decimal into a percentage, we are actually applying basic algebraic principles. In algebraic terms, if the decimal is 'd', the percentage 'P' is given by the equation \(P = d \times 100\). It's this kind of algebraic manipulation that is crucial for understanding and performing conversions between different mathematical representations.