Fractions

Understanding FractionsIn mathematics, the word ‘fraction’ represents

a part that is broken off from a whole. A broken whole may be a part of a cake, a part of a stick, or a part of a group, etc.

A fraction is a part of a whole thing or a part of a group of things.

For example, the pizza on the left is a whole. There is one pizza, and it is cut into five equal slices, or parts. When we

say, ‘ of the pizza has been eaten,’ we mean that two of

the five equal slices of the pizza have been eaten.€

2

5

Examples:Write each shaded area as a fraction.

Terms of a FractionA fraction consists of two numerals with a

horizontal bar between them. The horizontal bar is called the fraction bar.

The number above the fraction bar is called the numerator and the the number below the fraction bar is called the denominator. The numerator and the denominator are called the terms of the fraction.

Examples:

Examples:

Examples:Write a fraction to describe each situation.

a. There are fifteen boys and thirteen girls in a class. Which part of the class are girls?

b. Five out of the eleven players on a football team have a yellow card.

c. A box of compact discs contains three Maths CDs, four Physics CDs, five Chemistry CDs, four audio CDs, and five video CDs. How many of the CDs arerelated to school subjects?

Types of fractionProper (Simple) FractionsIf the numerator of a fraction is smaller than

its denominator, it is called a proper (or simple) fraction.

Proper (Simple) Fractions

Types of fractionImproper FractionsIf the numerator of a fraction is greater than or

equal to its denominator, it is called an improper fraction.

Types of fractionMixed NumbersA number which consists of a whole number and

a proper fraction is called a mixed number.

Mixed Numbers

Suppose that we have two whole pizzas and

of a pizza. We can write that we have

Writing an Improper Fraction as a Mixed Number1. Divide the numerator by the denominator.2. Write the quotient as a whole number, and

the remainder (if it exists) as the numerator of the fraction part of the mixed number. The denominator remains the same. So we write

Example:

Writing a Mixed Number as an Improper Fraction1. Multiply the whole number by the

denominator of the fraction.2. Add this product to the numerator.3. Write the sum as the numerator of the

improper fraction over the denominator of the fraction.

Example:

Equivalent FractionsFractions which have the same value are

called equivalent fractions.

Example:Determine whether they are equivalent.

Enlarging a FractionThe value of a fraction does not change when

its numerator and denominator are both multiplied by the same non-zero number.

Example:Find three equivalent fractions for each

fraction.

Simplifying and Reducing a Fraction1. Find the prime factors of the numerator

and the denominator.2. Divide the numerator and the denominator

by the common prime factors.3. The result after division is the reduced

fraction.

Example:Reduce each fraction to its lowest terms.