Directed numbers continued
Clement Radcliffe, Contributor

Students of Pentab High School at 16 North Street, Kingston. - Ian Allen Photo

As we continue our review of Directed Numbers, you are invited to look at the answers to the problems given for the Homework last week.

Evaluate the following:

• ­ 2 x ­ 5 = 10
• ­ 22 ­ 14 + 6 = -30
• 12/25 x 5/9 ÷ 5/18 = 12/25 x 5/9 x 18/5 = 24/25
• ­ 18 ÷ 3 = -6
• 5a x ­ 4b = -20ab
• 
  

  11/12 + 5/6 ­ 2/3	(1 x 11) + (2 x 5) - (4 x 2)	= 11 + 10 - 8 =13/12
  	12	12
  (Please note that the LCM of 12, 6 and 3 is 12.)

Application of the Four Arithmetic Operations to Vulgar Fractions

In applying the four basic operations to vulgar fractions, students are required to observe the correct law with respect to the order of operation as follows:

B - Brackets
O - Of (Multiply)
M - Multiplu
D - Divide
A - Add
S - Subtract

BOMDAS identifies the order in which the operations should be carried out and most always be obeyed.

Let's practice the use of BOMDAS.

Practice 1

8 x (2 1/3 + 1/2) We first do the brackets (although we are required to add):
(2 1/3 + 1/2)
ie. (2 1/3 + 1/2) = 7/3 + 1/2. Using the L.C.M. of 2 and 3, that is 6, we get

To complete the problem, we now multiply: 8 x 17/6 = 68/3 = 22 2/3

Practice 2

Calculate the value of:

The line represents brackets and so the numerator may be evaluated first.
4 1/3 - 1 5/6 = 13/3 - 11/6 =

Evaluating the denominator:

1 3/7 x 2 2/3 = 10/7 x 8/3 = 80/21

Dividing

= 15/6 ÷ 80/21 = 15/6 x 21/80 = 21/32

Practice 3

Calculate the value of: 1 1/2 + 5 x 2 ÷ 1 2/3

We do the multiplication first:

1 1/2 + 10 ÷ 1 2/3

We then do the division:

1 1/2 + [10 x 3/5]
= 1 1/2 + 6
= 7 1/2

Points to note

• In solving a problem such as this, you may first evaluate either the numerator or the denominator.
• Finding the L.C.M CORRECTLY is a very important steo in the solution.
• As the question requires the exact value, you are not allowed to express the fraction in decimal form. If this is done, then your answer would be different from 21/32
  
  You may prove this on your own.
• Your working must be clearly shown in logical sequence.
  
  I close this week with the following:

1. Calculate the value of 2 1/3 - 1 1/2, expressing your answer as a fraction.

3. [2 1.3 - 1 5/8] ÷ 1 1/3

4. 16/25 x 5/7 ÷ 8/25

Finally, let me recommend that you keep all of these lessons together in a scrap book so that you can always refer to them. If you require previous copies you should be able to access these from the Gleaner Company.

* Clement Radcliffe is principal of Glenmuir High School in Clarendon.