Understanding Fractions In 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 onepizza, and it is cut into five equal slices, or parts. When wesay, ‘ of the pizza has been eaten,’ we mean that two ofthe five equal slices of the pizza have been eaten.
Examples: Write each shaded area as a fraction.
Terms of a Fraction A 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:Write a fraction to describe each situation.a. There are fifteen boys and thirteen girls in a class. Whichpart of the class are girls?b. Five out of the eleven players on a football team have ayellow card.c. A box of compact discs contains three Maths CDs, fourPhysics CDs, five Chemistry CDs, four audio CDs, and fivevideo CDs. How many of the CDs arerelated to school subjects?
Types of fraction Proper (Simple) Fractions If the numerator of a fraction is smaller than its denominator, it is called a proper (or simple) fraction.
Types of fraction Improper Fractions If the numerator of a fraction is greater than or equal to its denominator, it is called an improper fraction.
Types of fraction Mixed Numbers A number which consists of a whole number and a proper fraction is called a mixed number.
Mixed NumbersSuppose that we have two whole pizzas andof a pizza. We can write that we have
Writing an Improper Fraction as aMixed Number 1. 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
Writing a Mixed Number as anImproper Fraction 1. 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.
Equivalent Fractions Fractions which have the same value are called equivalent fractions.
Example: Determine whether they are equivalent.
Enlarging a Fraction The 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 Fraction 1. 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.