Download LESSON 2 FRACTIONS

LESSON 2
FRACTIONS
Learning Outcomes

By the end of this lesson, students should
be able to:
◦ Understand types of fractions.
◦ Convert improper fractions into mixed
numbers.
◦ Write a fraction in lowest terms.
◦ Add, subtract, multiply and divide fractions.
◦ Convert decimals to fractions.
◦ Convert fractions to decimals.
Topics

Understanding the types of fractions.
◦ Improper fractions and mixed numbers.
◦ Writing a fraction in lowest terms.
◦ Adding, subtracting, multiplying and dividing
fractions.
◦ Converting decimals to fractions.
◦ Converting fractions to decimals.
Understanding the types of fractions

A fraction represents part of a whole.
Fractions are written in the form of one
number over another, with a line between
two numbers. The line, or bar between
the top number and the bottom number
means “divided by”. The top number is
called the numerator, and the bottom
number is called the denominator.
Types of fractions
Proper fraction:
 Numerator smaller than denominator e.g.
2/3, ¾, 8/15 and 9/10
 Improper fraction
 Numerator equal or greater than
denominator e.g. 5/5, 11/5, 3/2 and 9/4

 Mixed fraction
 Whole number and proper fraction e.g.
Contd…
2 5 1
1 , 4 , 27
3 6 2
Converting fractions
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Mixed numbers to improper fractions
A mixed number can be changed to an
improper fraction as follows:
Multiply the whole number by the
denominator of the fraction.
Add the numerator to that product. The
resulting sum becomes the new fraction’s
numerator.
Put that sum (the new numerator) over the
original fraction’s denominator.
Example
2 3  4  2 14
4 

3
3
3
Contd…
Improper fractions to mixed numbers
 To convert an improper fraction to a
mixed number, divide the numerator of
the improper fraction by the denominator,
and place the remainder (if any) over the
original denominator (the divisor).
 Example
 Convert 29/5 to mixed numbers

29
4
5
5
5
Contd…
Writing a fraction in lowest terms
 If both the numerator and denominator
of a fraction cannot be divided without
remainder by any number other than 1,
then the fraction is in lowest terms
 The lowest terms for 2/4 is ½

Contd…
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Adding and subtracting fractions
Fractions with the same denominator are
called like fractions. Such fractions have a
common denominator. Addition and
subtraction of fractions which have a common
denominator can be done by applying the
operation on both numerators.
Example
Add 3/5 and 1/5
3/5 + 1/5 = 4/5
 Fraction with different denominators, are
called unlike fractions. To add or subtract
unlike fractions, a common denominator
should be found or generated. Once a
common denominator exists, apply the
operation on both numerators.


Subtraction
 ½ - 2/3
Multiplying and dividing fractions
 Multiplying proper or improper fractions
Three steps are involved when multiplying
proper and improper fractions:
 Multiply the numerators.
 Multiply the denominators.
 Reduce to lowest terms if necessary.

Multiplying mixed numbers

To multiply mixed numbers, first convert
them into improper fractions. Then
proceed as with multiplication of proper
fractions.
Dividing proper or improper fractions
To divide proper or improper fractions,
the followings steps should be observed:
 Invert the divisor or divisors (turned
upside down). The divisor is the number
by which we are dividing. The inverse of a
number is referred to as its reciprocal.
 Proceed with multiplication.

Dividing mixed numbers
Steps to divide mixed numbers are as
follows:
 Convert all mixed numbers to improper
fractions.
 Invert the divisor or divisors and change
signs from division to multiplication.
 Proceed as in multiplication

Converting decimals to fractions
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Decimals can be converted to fractions. For
example, 0.32 is properly read as “thirty-two
hundredths”, which is the same as 32/100.
Rules to convert decimals to fractions:
Count the digits to the right of the decimal point.
Place that many zeros in the denominator of the
common fraction.
Remove the decimal point from the number in
the numerator position.
Place a 1 in front of the zeros in the denominator
position.
Convert to a mixed number and/or reduce to
lowest terms if necessary.
Converting fractions to
decimals

To convert a fraction to a decimal, divide
the numerator of the fraction by the
denominator
Lesson Summary

This lesson explains the types of fractions
and the calculations involving fractions.
Calculation using fractions will be easier if
you know how to simplify and convert
fractions to decimals, and vice versa