NOTATION AND WHOLE NUMBERS

Value and Place Value 

1. Digits are symbols used to write numerals; 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the digits used in our number system.
2. The number 2 345 689 has 7 digits.
   In words it is: two million, three hundred and forty-five thousands, six hundred and eighty-nine. 
3. The "place value" of each digit in 2 345 689 is as follows:

   The 2 is in the millions place.

   The 3 is in the hundred thousands place.

   The 4 is in the ten thousands place.

   The 5 is in the thousands place.

   The 6 is in the hundreds place.

   The 8 is in the tens place.

   The 9 is in the ones place.

4. The "value" of each digit in 2 345 689 is as follows:
   
   The 2 stands for 2 000 000 or 2 millions.

   The 3 stands for     300 000 or 3 hundred thousands.

   The 4 stands for      40 000 or 4 ten thousands.

   The 5 stands for       5 000 or 5 thousands.

   The 6 stands for          600 or 6 hundreds.

   The 8 stands for             80 or 8 tens.

   The 9 stands for               9 or 9 ones.
    
    

Symbols

< is greater than

> is greater than

= is equal to 

~ approximately equal to

Sequences

A number sequence is a set of numbers in which each number follows the last one according to some rule or pattern.
 
Examples: 

1. 422, 424, 426, 428 …. are even numbers.
   
   Rule: Start with 422 and add 2 each time.
   
2. 3 206, 3 203, 3 200, 3 197, 3 194 …
   
   Rule: Start with 3 206 and subtract 3 each time.
    

Factors

A factor is a number that is multiplied by another number to give a product.

In 2x5 = 10, 2 and 5 are the factors. When we multiply 2 by 5, we get a product of 10.
 

Multiples

A multiple of a number is the product of that number and a whole number. 0, 8, 16, 24, 32, 40 and so on are multiples of 8. 

Rounding

Rounding off a number to a specified place value means naming the multiple of a place value to which the number is closest.

Example: Round off 42 083 to the nearest ten.

42 083 is greater than 42 080 and less than 42 090. It is closer to 42 080. When a number is halfway between such as 42 085, it is rounded off to 42 090.

The Four Operations of Whole Numbers

Do what is in the bracket first.

Example: (36 + 18) x 2
= 54 x 2
= 108

When a mathematical expression without brackets involves mulitplication and division only, we work from left to right.

Example: 80 ÷ 2 x 3 
= 40 x 3
= 120

When a mathematical expression without brackets involves addition and subtraction only, we work from left to right.
 
Example: 105 – 95 + 16
= 10 + 16
= 26

When a mathematical expression involves several numbers and operations, we work in this way: 

1. Do the operation in the brackets first.
2. Do the multiplication and division from left to right.
3. Then do addition and subtraction from left to right.

Example: 12 + 14 ÷ (11 – 4) x 6 – 16

= 12 + 14 ÷7 x 6 – 16

= 12 + 2 x 6 – 16 

= 12 + 12 – 16

= 24 – 16

= 8

 

Problem Solving Guide

Carefully read the problem.

Identify the important data, information and key words.

Make a plan.

Work it out.

Check the working and statements.

Example:

Andy has twice as much money as Bob. Bob has $8.50 and Charles has three times as much as Andy and Bob have altogether. How much money do they have altogether?
 
 

2 x $8.50
= $17.00

Andy has $17.00 ………………………………………….. (a)

($8.50 + $17.00) x 3
= $76.50

Charles has $76.50 ………………………………………… (b)

$8.50 + 417.00 + $76.50
= $102.00

They have $102.00 altogether ……………………………... (c)