Problem 10 - Prealgebra

Question

Find the percent of each number mentally. $$50 \% \text { of } 28$$

Step-by-Step Solution

Answer

50% of 28 is 14.

Step 1: Understanding 50%

To find 50% of a number, we need to remember that 50% is equivalent to one half. So we're finding half of the given number.

Step 2: Calculate Half of 28

To find one half of 28, simply divide 28 by 2.

Step 3: Perform the Division

Calculate \( 28 \div 2 \). This equals 14.

Key Concepts

Mental Math

Mental math is a valuable skill that allows you to perform calculations quickly and easily in your head without the need for a calculator or pen and paper. It involves methods and strategies that enable you to simplify calculations and solve problems effortlessly.

In the context of percentages, using mental math means being able to recognize common percentages like 50%, 25%, 10%, etc., and knowing how to quickly find these percentages of numbers using simple mental tricks. For example, finding 50% of a number is easy if you realize that you're just finding half of that number.

Being proficient at mental math can improve your confidence with numbers. It also allows for quick estimation, which is especially useful in daily activities like shopping or splitting bills.

Division

Division is one of the four basic operations in mathematics. It is essentially the process of dividing a number (the dividend) by another number (the divisor) to find how many times the divisor fits into the dividend. The result is known as the quotient.

When finding percentages like in the example problem, division plays a crucial role. Since 50% is equivalent to 1/2, calculating 50% of any number involves dividing that number by 2. In our example, to find 50% of 28, you perform the division:

\(28 \div 2 = 14\)

A good understanding of division helps not only in calculations but also in real-life scenarios like splitting a pizza evenly or understanding rates and ratios.

Fractions

Fractions are a way to represent a part of a whole. They consist of two numbers, the numerator (top number) and the denominator (bottom number), written as \(\frac{numerator}{denominator}\).

In the context of percentages, converting percentages to fractions can sometimes make calculations easier. For instance, knowing that 50% is equivalent to \(\frac{1}{2}\) helps streamline the calculation process, as it turns a percentage problem into a simple division problem.

Understanding fractions are fundamental, as they provide a basis for working with percentages, understanding ratios, and solving problems in various fields like cooking, construction, science, and finance.

By recognizing that percentages are essentially fractions out of 100, you can easily manipulate and calculate percentages using fractional techniques.