Revision Guide: Fractions

A fraction represents a part of a whole, expressed as a/b where 'a' is the numerator and 'b' is the denominator.

Cut one object into two equal parts results in each part being 1/2, or half of the whole.

Dividing items equally among people illustrates fractions; e.g., 1 roti shared by 2 equals 1/2 roti each.

For 1/5 and 1/9, 1/5 is greater since sharing with fewer means larger parts.

Fractions like 1/2, 1/3, etc., are called unit fractions; they show one part of equal divisions.

Fractions can represent parts of a whole, such as dividing a pizza into 4 equal slices results in 1/4 slices.

Whole numbers can be written as fractions. For example, '3' is equivalent to '3/1'.

To add fractions with the same denominator, sum the numerators, keep the denominator common.

Like addition, subtracting fractions requires a common denominator; subtract the numerators.

To multiply fractions, multiply the numerators together and the denominators together (a/b) × (c/d) = ac/bd.

Dividing fractions involves multiplying by the reciprocal of the second fraction; a/b ÷ c/d = a/b × d/c.

An improper fraction has a numerator larger than its denominator, e.g., 5/4.

A mixed number combines a whole number with a fraction, e.g., 1 1/2.

Divide the numerator by the denominator to convert an improper fraction to a mixed number.

A ratio expresses a relationship between two quantities, related to fractions, e.g., 1:2 is equivalent to 1/2.

Assuming larger denominators mean larger values is incorrect. E.g., 1/9 < 1/5.

Fractions have historical roots; ancient texts show early use of fractions in civilizational mathematics.

In word problems, visualizing the scenario helps in identifying and using the correct fractions.

To compare and order fractions, convert them to a common denominator or decimal format.

Visual aids like pie charts can help illustrate how fractions represent parts of a whole in tangible ways.