Fractions and representation

Fractions: Basics and Representation

Fraction Components

• A fraction is represented as b/c.
• b is the numerator.
• c is the denominator.

Fraction as Portions of a Whole

• Fractions represent parts of a whole.
• Example: A pie cut into six equal slices; eating one slice means you've consumed 1/6 of the pie.

Visual Representation of Fractions

• Example: If there are eight slices and three are shaded, the fraction representing the shaded portion is 3/8.
• To represent 2/5, divide a shape into five equal parts and shade two of them.

Fractions as Division

• Fractions also represent division relationships.
• The relationship can be checked using multiplication.
• If a/b = n, then b * n = a.
• Example 1: 20/5 = 4, and 5 * 4 = 20.
• Example 2: 63/63 = 1, and 63 * 1 = 63.

Using a Calculator

• 20/5 is calculated as 20 divided by 5, resulting in 4.
• 63/63 is calculated as 63 divided by 63, resulting in 1.

Zero in Fractions

Zero as the Numerator

• If the numerator is zero, such as 0/12, the fraction equals zero.
• 0/12 = 0, because 12 * 0 = 0.

Zero as the Denominator

• If the denominator is zero, such as 12/0, the fraction is undefined.
• Testing zero as a solution: If 12/0 = 0, then 0 * 0 should equal 12, which is false.
• Testing 12 as a solution: If 12/0 = 12, then 0 * 12 should equal 12, which is also false.

Undefined Expressions

• A fraction with zero in the denominator has no numerical solution; it's an undefined expression.
• There is no number that, when multiplied by zero, yields a non-zero numerator.

Calculator Behavior

• 0/12 (zero divided by 12) yields zero.
• 12/0 (12 divided by zero) results in an error because division by zero is undefined.