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Fractions represent a part of a whole and are expressed as two numbers separated by a slash: the numerator and the denominator.

• Numerator (top number): Represents the number of parts you have.
• Denominator (bottom number): Represents how many parts make up a whole.

The fraction itself tells us how many parts of a whole we are considering. In the case of percentages, converting to a fraction involves placing the percentage number over 100, as a percentage is just a part of one hundred.
For instance, converting 29% to a fraction results in \( \frac{29}{100} \).
Understanding fractions is crucial as they are often used to describe portions of quantities and are fundamental in computations involving division of whole entities.
Importantly, fractions can sometimes be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). However, if the numerator is a prime number that does not divide evenly into the denominator, as with 29, the fraction remains in its simplest form.

Decimals are another method to express parts of a whole, similar to fractions. They rely on the base 10 number system, which is linked naturally to our counting system. A decimal point divides a number into its integer and fractional parts.
When expressing a percentage as a decimal, we essentially adjust the scale of the number by dividing it by 100.
This is because a percentage inherently implies "per hundred." So, 29% can be transformed into a decimal by calculating \( 29 \div 100 = 0.29 \).
This tells us that 29% is equivalent to 0.29 in decimal form.
The convenience of decimals over fractions often lies in the ease of calculations, especially with addition, subtraction, and comparing sizes. They are used extensively in everyday commerce and science for precise measurements and financial calculations.

Prime numbers are the building blocks of our number system. A prime number is a natural number greater than 1, having no divisors other than 1 and itself. This means they cannot be evenly divided by any number except for these two.
Consider number 29, used in our example.
It is a prime number because:

• It doesn't divide evenly by any number other than 1 and 29.
• This property makes it impossible to further simplify the fraction \( \frac{29}{100} \) because there are no common factors between the numerator and the denominator.

Prime numbers are fundamental in mathematics due to their indivisible nature, and they are especially crucial in areas like cryptography and number theory.
The understanding of prime numbers helps in recognizing when fractions are in their simplest form and what steps can or cannot be taken to simplify mathematical expressions further.