 FOIL METHOD

#### FOIL Method:

A.     The FOIL method stands for – First, Outside, Inside, Last.  This method can be used to multiply any 2 digit numbers together.  However, there are many cases where other strategies should be used since the FOIL method is somewhat time-consuming.

B.     The FOIL method comes from algebra:

(10a + b) (10c + d) = 100ac + 10(bc + ad) + bd

C.     Using numbers instead of variables we can get the following steps:

1.      Multiply the ones digits together (or the last digits).  ‘L’

2.      Multiply the inside numbers and the outside numbers and add them together.  ‘O’ + ‘I’.

3.      Multiply the tens digits together (or the first digits).  ‘F’

4.      Putting these steps together we get an answer in the form : ‘F’ (‘O’+’I’) ‘L’ or FOIL.

5.      Keep track of any numbers you need to carry to add to any of these steps.

Ex   12 x 34 =_________.

a)      2 x 4 = 8.  Write down 8.

b)      2 x 3 + 1 x 4 = 6 + 4 = 10.  Write down 0 and carry *1.

c)      1 x 3 = 3 + *1 = 4.  Write down 4.

Ex   45 x 24 =_________.

a)   5 x 4 = 20.  Write 0, carry *2.

b)   5 x 2 + 4 x 4 = 10 + 16 = 26 + *2 = 28.  Write 8, carry *2.

c)   4 x 2 = 8 + *2 = 10.  Write 10.

D.     Sometimes the FOIL method can be adapted to multiply 3 digit numbers as well.

Ex   114 x 42 =_________.

a)   To multiply by 114 using the FOIL method, think of ‘F’ as being 11 in this case.

b)      4 x 2 = 8.  Write 8.

c)       4 x 4 + 11 x 2 = 16 + 22 = 38.  Write 8, carry *3.

d)      11 x 4 = 44 + *3 = 47.  Write 47. 