Fractions

Basics of Fractions

  • A fraction represents a part of a whole and is composed of a numerator (top number) and a denominator (bottom number).
  • The numerator indicates how many parts are being considered, while the denominator reveals how many equal parts the whole has been divided into.
  • A fraction is essentially a division operation. For example, the fraction 3/4 is equivalent to 3 divided by 4.

Simplest Form

  • A fraction is in its simplest form when the numerator and the denominator share no common factors other than 1.
  • To reduce a fraction to its simplest form, divide both the numerator and the denominator by their greatest common factor (GCF).

Equivalent Fractions

  • Equivalent fractions are different fractions that represent the same value. They can be created by multiplying or dividing the numerator and the denominator by the same number.
  • For instance, 2/4, 3/6, and 4/8 are all equivalent fractions, as they all represent the value of 1/2.

Adding and Subtracting Fractions

  • If fractions have the same denominator, simply add or subtract the numerators to add or subtract the fractions.
  • If denominators are different, one needs to find equivalent fractions with a common denominator (the least common multiple of the denominators) before adding or subtracting.

Multiplying and Dividing Fractions

  • To multiply fractions, multiply the numerators together for the new numerator and multiply the denominators together for the new denominator.
  • To divide fractions, flip the second fraction (reciprocal) and then follow the rules of multiplication.

Converting Between Fractions, Decimals, and Percentages

  • A percentage is a fraction with a denominator of 100.
  • A decimal is another way of representing a fraction, where the denominator is a power of 10.
  • Converting between these forms involves understanding these relationships and performing the relevant mathematical operations.

Mixed Numbers and Improper Fractions

  • A mixed number has both a whole number part and a fractional part (e.g. 1 2/3).
  • An improper fraction has a numerator larger than or equal to its denominator (e.g. 5/4 or 7/7).
  • Conversion between these two forms often comes up in mathematical problems and calculations.