Fractions, Percentages, Ratios, and Decimals

Fractions

Fractions represent parts of a whole number, such as half (1/2), thirds (1/3), quarters (1/4), fifths (1/5), sixths (1/6), seventh (1/7), eighths (1/8), ninths (1/9), tenths (1/10), eleventh (1/11), twelfths (1/12) etc. In mathematics, fractions are used to compare quantities, solve word problems, and perform arithmetic operations. They can also be expressed using common denominators (lesser common multiple) to simplify their representation.

Fractions have three main components: numerator (the top number), denominator (the bottom number), and fraction bar. For example, in the fraction 2/3, 2 is the numerator, 3 is the denominator, and the fraction bar separates them.

Fraction concepts include finding equivalent fractions, adding and subtracting fractions with unlike denominators, multiplying and dividing fractions, and converting fractions to decimals or percentages.

Percentages

Percentage is another mathematical concept that represents one part out of hundred. It is commonly used to express proportions of something to its total value. When you want to find what percentage of total it has, you divide one by the total number of parts, multiply it by 100%, and express it in terms of percentage.

For instance, if we say that 20% of the students like reading, it means that 20 out of every 100 students like reading (which is 20/100 * 100 = 20%).

In real life applications, percentages can be found in different forms such as discounts, interest rates, population growth, test scores, exam results, salaries, tips, taxes, sales figures and much more.

Ratios

A ratio compares two numbers or values. Ratio is often represented as "a : b", where 'a' is the first quantity, 'b' is the second quantity, and they share a common base unit. The ratio is typically written so that the smaller number is placed after the colon.

Ratios are useful when comparing two quantities to see how they relate to each other. For example, if there are 4 boys for every 5 girls, this could be expressed as a ratio of 4:5. This means that for every group of 4 boys, there will be 5 girls. This allows us to make comparisons between groups with different sizes.

Decimals

Decimals are numbers composed of digits followed by a decimal point, representing fractions. For instance, 3/4 can be expressed as 0.75. A decimal point separates the integer (whole number) from the fractional part (decimal part).

Decimal fractions can be classified into four types based on their non-terminating nature: terminating decimals, repeating decimals, simple recurring decimals, and complex recurring decimals. Terminating decimals have only a finite sequence of digits after the decimal point before becoming zeroes, while non-terminating decimals repeat an infinite sequence of digits.