What is a fraction and how is it represented mathematically?

A fraction is a way to represent a part of a whole, expressed as a ratio of two integers, where the numerator indicates how many parts are taken and the denominator indicates how many equal parts the whole is divided into. Mathematically, it is represented as a/b, where a is the numerator and b is the denominator.

What is the formula to convert a decimal to a fraction?

To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 1, then multiply the numerator and denominator by 10 for every digit after the decimal point. For example, to convert 0.75 to a fraction: 0.75 = 75/100, which simplifies to 3/4.

How do you convert a percentage to a decimal?

To convert a percentage to a decimal, divide the percentage by 100. For example, to convert 25% to a decimal: 25 ÷ 100 = 0.25.

If 25% of a number is 50, what is the number?

Let the number be x. Then, 0.25x = 50. To find x, divide both sides by 0.25: x = 50 ÷ 0.25 = 200.

What is the relationship between fractions and percentages?

A fraction can be converted to a percentage by multiplying by 100. For example, to convert 1/4 to a percentage: (1 ÷ 4) × 100 = 25%.

Simplify the expression: (5/6) × (12/15).

To simplify, multiply the numerators and denominators: (5 × 12)/(6 × 15) = 60/90. Now, simplify by dividing both by 30: 60 ÷ 30 = 2 and 90 ÷ 30 = 3. Thus, the simplified form is 2/3.

Convert 0.125 to a fraction and simplify.

0.125 can be expressed as 125/1000. To simplify, divide both the numerator and denominator by 125: 125 ÷ 125 = 1 and 1000 ÷ 125 = 8. Thus, 0.125 = 1/8.

What is the formula for finding the percentage of a number?

To find the percentage of a number, multiply the number by the percentage (as a decimal). For example, to find 30% of 200: 0.30 × 200 = 60.

If 60% of a number is 180, what is the number?

Let the number be x. Then, 0.60x = 180. To find x, divide both sides by 0.60: x = 180 ÷ 0.60 = 300.

How do you find the common denominator of two fractions?

To find the common denominator, identify the least common multiple (LCM) of the two denominators. For example, for 1/3 and 1/4, the LCM of 3 and 4 is 12. Thus, the common denominator is 12.

If a product is discounted by 20% and the original price is 50, what is the sale price?

To find the sale price, first calculate the discount: 20% of 50 is 0.20 × 50 = 10. Then subtract the discount from the original price: 50 - 10 = 40. Thus, the sale price is 40.