Fractions  Fractions are a way of showing a portion of material compared with the whole thing.  E.g. ½ Pizza, half time, 1/3 off.

Simplifying Fractions  Sometimes when you do a calculation involving fractions you get an answer that must be simplified.  To do this you divide top and bottom numbers by the SAME number and repeat using various numbers (2, 3, 5, etc.) until you cannot divide any further !!!

Simplifying Fractions  Remember that you must treat top and bottom numbers identically !!!  Example: Simplify

Divide top and bottom by 5 giving We can divide by 5 again, giving So, Simplifies to give So are all the same fraction They are called equivalent fractions 5 20

Now you try the following:

Sometimes a fraction is “top heavy” like: In these cases, divide the top by the bottom leaving a remainder. The main number is integer (whole numbers) the remainder is still a fraction. Now simplify the remaining fraction part as before. 3 r 2

Now you try the following:

Adding Fractions + = + =

Why Not ??????????? +=

Fractions can only be added or subtracted if the denominators are the same. + += 3 / / 5 = 4 / 5 Common denominators

1/41/4 1/31/3 + 1/41/4 1/31/3 += ? 1/41/4 1/31/3 + = 3 / / 12 = 7 / 12

Addition of Fractions Addition of fractions is a little complicated, BUT providing you follow the procedure you should not have too much difficulty. First multiply the bottom numbers 5 × 3 Now cross multiply as follows (2 × 3) + (5 × 1) Work out = = Is it possible to simplify?

Now you try the following:

Subtraction of Fractions This is virtually identical to the addition of fractions. The only difference is that the addition sign is replaced by subtraction. BUT remember to do the cross- multiplying in the right order (as shown, down before up).

Multiply the bottom line. 5 × 4 Now cross multiply (3 × 4)–(5 × 1) Work it out = = Finally check if the fraction can be simplified!! In this case, NO

Now you try the following:

Multiplication of Fractions This is best done by example: We do straight line multiplying = = Simplifying HOW?

Now you try the following:

Division of Fractions This is similar to multiplication but involves one more step first!! Change the ÷ to a × and turn the second fraction upside down. Now multiply as before = Simplifying

Now you try the following:

Converting fractions to decimals Simple….. Just divide the top number by the bottom!!! 3 ÷ ?

Now you should try questions from either the green textbook or the white workbook.

Divide top and bottom by 5 giving We can divide by 5 again, giving 5 20 Simplifying Fractions are all the same fraction They are called equivalent fractions Sometimes a fraction is “top heavy” like In these cases, divide the top by the bottom leaving a remainder. The main number is integer (whole numbers) the remainder is still a fraction. Now simplify the remaining fraction part as before. :

Addition of Fractions Addition of fractions is a little complicated,BUT providing you follow the procedure you should not have too much difficulty. First multiply the bottom numbers 5 × 3 Now cross multiply as follows (2 × 3)+(5 × 1) Work out = = Is it possible to simplify? Multiply the bottom line. Now cross multiply (3 × 4) – (5 × 1) = 5 × 4 Subtraction of Fractions

Multiplication of Fractions We do straight line multiplying Division of Fractions This is similar to multiplication but involves one more step first!! Change the ÷ to a × and turn the second fraction upside down. Now multiply as before