2. 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.

3. 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.

5. Examples:
 Write each shaded area as a fraction.

6. 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.

8. Examples:

9. Examples:

10. 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 are
related to school subjects?

11. 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.

12. Proper (Simple) Fractions

13. 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.

14. Types of fraction
 Mixed Numbers
 A number which consists of a whole number and a
proper fraction is called a mixed number.

15. Mixed Numbers
Suppose that we have two whole pizzas and
of a pizza. We can write that we have

16. Writing an Improper Fraction as a
Mixed 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

17. Example:

18. Writing a Mixed Number as an
Improper 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.

19. Example:

20. Equivalent Fractions
 Fractions which have the same value are called
equivalent fractions.

21. Example:
 Determine whether they are equivalent.

22. 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.

23. Example:
 Find three equivalent fractions for each fraction.

24. 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.

25. Example:
 Reduce each fraction to its lowest terms.