CHAPTER 1: FRACTIONS. ADD, SUBTRACT. © John Wiley and Sons © John Wiley and Sons 2013 Essential Mathematics for Economics and Business, 4 th Edition

© John Wiley and Sons 2013 Fractions Examples on the following slides: Addition and subtraction involving fractions: © John Wiley and Sons 2013

© John Wiley and Sons 2013 Fractions A fraction is written as follows: Where a and b may be numbers or symbols The top line is called the ‘numerator’ The bottom line is called the ‘denominator’

© John Wiley and Sons 2013 Addition or subtraction of fractions Worked Example 1.3: Simplify the following expression giving your answer as a single fraction

© John Wiley and Sons 2013 Add/Subtract Fractions: See text page 5 Terminology: a common denominator: In this case the common denominator is 7  3  5, which is the product of the denominators from all three individual fractions A common denominator is a number or expression that is divisible exactly by the denominator of each individual fraction

© John Wiley and Sons 2013 Worked example 1.3 Addition and subtraction of fractions: Then for each fraction in turn…. 1. Divide its denominator into the common denominator 2. Then multiply the result by its numerator (top line) 3. Bring down the sign between this and the next fraction 4. Repeat steps 1, 2 and 3 with the next fraction Start by writing down the common denominator Method

© John Wiley and Sons 2013 First fraction The result is 3  5 Then multiply the result by its numerator (top line). i.e. 3  5 is multiplied by 1 Enter this answer as shown opposite Bring down the sign ( + in this case) and continue 7 1 Numerator Denominator  Divide its denominator (7) into the common denominator (7  3  5) Common denominator

© John Wiley and Sons 2013 Second fraction then multiply the result by its numerator (top line) i.e. 7  5 is multiplied by 2. Enter this result as shown opposite. Bring down the sign ( - in this case) and continue Numerator Denominator  Divide its denominator into the common denominator Method…

© John Wiley and Sons 2013 Third fraction Then multiply the result by its numerator (top line) i.e. 7  3 is multiplied by 4 Numerator Denominator Common denominator Divide its denominator into the common denominator

© John Wiley and Sons 2013 Simplify

© John Wiley and Sons 2013 Add/Subtract Fractions involving x Example: Simplify the following expression, giving your answer as a single fraction In this case the common denominator is 7  3  5..the product of all individual denominators First take a common denominator.

© John Wiley and Sons 2013 To add or subtract fractions: example 1. Divide its denominator into the common denominator 2. Then multiply the result by its numerator 3. Bring down the sign between this and the next fraction 4. continue on to the next fraction continued-  For each ìndividual fraction in following expression…. Method…

© John Wiley and Sons 2013 First fraction The result is 3  5 Then multiply the result by its numerator (top line). i.e. 3  5 is multiplied by x Bring down the sign between this and the next fraction ( + in this case) and continue 7 x Numerator Denominator  Divide its denominator (7) into the common denominator (7  3  5)

© John Wiley and Sons 2013 Second fraction then multiply the result by its numerator (top line) i.e. 7  5 is multiplied by 2x Bring down the sign between this and the next fraction ( - in this case) and continue Numerator Denominator  Divide its denominator into the common denominator

© John Wiley and Sons 2013 Third fraction Then multiply the result by its numerator (top line) i.e. 7  3 is multiplied by 4 x Numerator Denominator Divide its denominator into the common denominator

© John Wiley and Sons 2013 Simplify

© John Wiley and Sons 2013 Add/Subtract Fractions Example: Write the following expression as a single fraction Take a common denominator In this case the common denominator is 7  3  5  x NOTE: this is NOT the product of all denominators

© John Wiley and Sons 2013 Add/Subtract Fractions 1. divide its denominator into the common denominator 2. then multiply the result by its numerator 3. insert sign between this and the next fraction 4. continue on to the next fraction For each fraction

© John Wiley and Sons 2013 First fraction the result is 3  5 then multiply the result by its numerator (top line). i.e. 3  5 is multiplied by 1 bring down the + sign and continue. 7x7x 1 Numerator Denominator common denominator  divide its denominator(7 x ) into the common denominator:7  3  5 x x

© John Wiley and Sons 2013 Second fraction Then multiply the result by its numerator (top line) i.e. 7  5 is multiplied by 2 Bring down the sign( - in this case) and continue to the next fraction Numerator Denominator Common denominator  Divide its denominator into the common denominator

© John Wiley and Sons 2013 Third fraction divide its denominator into the common denominator then multiply the result by its numerator (top line) i.e. 7  3 is multiplied by 4 Numerator Denominator Common denominator

© John Wiley and Sons 2013 Simplify

© John Wiley and Sons 2013 Add/Subtract Fractions Example: Simplify the following expression into a single fraction Take the common denominator. In this case the common denominator is 7  3  5  x

© John Wiley and Sons 2013 Add/Subtract Fractions 1. divide its denominator into the common denominator 2. then multiply the result by its numerator 3. insert sign between this and the next fraction 4. Continue on to the next fraction For each separate fraction in question,

© John Wiley and Sons 2013 First fraction the result is 3  5 then multiply the result by its numerator (top line). i.e. 3  5 is multiplied by 1 insert sign between this and the next fraction ( + in this case) 7x7x 1 Numerator Denominator  divide its denominator (7) into the common denominator (7  3  5  x )

© John Wiley and Sons 2013 Second fraction then multiply the result by its numerator (top line) i.e. 7  5 × x is multiplied by 2x2x Write in the result and bring down the sign and continue Numerator Denominator  divide its denominator into the common denominator

© John Wiley and Sons 2013 Third fraction divide its denominator into the common denominator then multiply the result by its numerator (top line) i.e. 7  3  x is multiplied by 4 Numerator Denominator Common denominator

© John Wiley and Sons 2013 Simplify