Fractions and Recurring Decimals

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.