Fractions and Recurring Decimals

Fractions: A fraction represents a part of a whole. It is written as a/b where ‘a’ is the numerator (representing the part) and ‘b’ is the denominator (representing the whole).
To simplify a fraction: Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number.
To add or subtract fractions: Make sure the denominators are the same (common denominator), then add or subtract the numerators and place the answer over the common denominator. Simplify if necessary.
To multiply fractions: Multiply the numerators together for the new numerator, and the denominators together for the new denominator. Simplify if necessary.
To divide fractions: Flip the second fraction (reciprocal), then follow the steps for multiplying fractions.
Recurring Decimals: These are decimals that have digits that repeat in a pattern. They are often indicated by placing a bar or dot over the digit(s) that repeat.
To convert a recurring decimal to a fraction: Let x be the repeating decimal. Write another equation that moves the decimal point to just after the repeating part. Subtract the two equations to solve for x.
Recurring decimals can often be represented as fractions. For example, 0.666… (0.6 recurring) can be represented as 2/3.
To convert a fraction to a decimal: Divide the numerator by the denominator using long division.
Terminating decimals: These are decimals that end, and can also be represented as fractions. For instance, 0.5 is the decimal equivalent of 1/2.
To determine if a fraction will be a terminating decimal: A fraction in lowest terms will be a terminating decimal if and only if all the prime factors of its denominator are either 2 or 5 (the prime factors of 10). If the fraction’s denominator has any prime factors other than these, it will be a repeating decimal.

Remember, practice is key to mastering the art of solving fractions and recurring decimals. Work on a variety of problems and ensure you understand the underlying concept rather than just memorising the procedures.