Basic operations on whole numbers

ORDER OF OPERATIONS (PEMDAS/ BODMAS)

Can you answer this?

7 – 1 x 0 + 3 ÷ 3 = ?

In arithmetic, there are two types of components: the numbers themselves and the operators (also called operations) that tell you what to do with those numbers. The basic operators in arithmetic are addition (sum), subtraction (difference), multiplication (product) and division (quotient).

So, in the sum 7 x 3 + 5 there are three numbers; 7, 3 and 5 and two operators, a multiplication (x) and an addition (+). The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here.

exponents (index) and roots
multiplication and division
addition and subtraction

The definitive order of operations is summed up in the acronym BODMAS, which stands for Brackets, Order, Divide, Multiply, Add, Subtract. It would be easier if BODMAS was recognised worldwide, but unfortunately it

In the USA it’s normally called PEMDAS (Parenthesis, Exponent, Multiply, Divide, Add, Subtract). Canadians sit in the middle with BEMDAS (Brackets, Exponent, Multiply, Divide, Add, Subtract).

Regardless of the exact terminology, the sequence remains the same:

Step 1: Brackets

The highest level order is defined by anything contained in brackets. These sums are always calculated first. But what if there is more than one set of brackets? The rule then is to start at the innermost set and work outwards. Performing each bracketed calculation should leave you with a single number, allowing that set of brackets to be removed.

Step 2: Order or Exponent

The terms Order or Exponent all relate to operations containing powers or indices such as squaring or square rooting. These calculations are all performed second.

Steps 3 and 4: Divide and Multiply

The third and fourth steps, division and multiplication, have equal weight and so form a third level order of operations that are carried out at the same time. Importantly, when two or more operations of the same order appear one-after-another, the operations should be carried out from left to right.

So, if faced with a sum like:

18 ÷ 6 × 4 ÷ 8

You just work from left to right. Eighteen over six is three, times four is twelve, divided by eight is 1.5.

Steps 5 and 6: Add and Subtract

Again, these carry equal weight. Therefore the addition and subtractions form the fourth and final level order of operations The third and fourth steps, division and multiplication, have equal weight and so form a third level order of operations that are carried out at the same time, again working from left to right.

Can you answer this NOW?

7 – 1 x 0 + 3² ÷ 3 = ?

Here’s the solution:

7 – 0 + 9 ÷ 3 = 7 – 0 + 3 = 10

CLASS ACTIVITY

Evaluate the values of the following:

7 x 5 + 2 – 7 ÷ 1
15 ÷ 3 + 5 x 2
7 – 5 + 8 ÷ 2 x 2
12 (2 + 1) ÷ 2 + 2

ADDITION AND SUBTRACTION BY PLACE VALUE

A digit is any symbol used to write a whole number. A digit is one of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. All numbers are made up of one or more digits. A group of three digits is called a period. A small space separate the periods. At each space, say the name of the period. A place-value chart shows the value of the digits in a number.

USE OF NUMBER LINE

A number line is a graduated straight line which is used to represent numbers which can be positive or negative. The numbers increase as we progress to the right and decrease as we move to the left as shown in the figure below.

The arrows at the end of both sides of the straight line show the numbers progress along the number line. 0 is called the origin because positive and negative numbers ORIGINate from that point.

ADDITION AND SUBTRACTION ON THE NUMBER LINE

Addition: to add using the number line, we move to the right (forward) of the number line counting each step till the addition is complete. The number at the end is the result of the addition.

Subtraction: to subtract using the number line, we move to the left (backwards) of the number line counting each step till the subtraction is complete. The number at the end is the result of the subtraction.

Try out the exercises on this worksheet using the first representation as an example: