Working with Whole Numbers

Key Concepts

• Numbers up to 10,000
• Word Form
• Standard and Expanded Form
• Pattern Rule
• Place Value
• Comparing Numbers
• Comparing Numbers using Symbols
• Ordering Numbers in Ascending and Descending
• Adding and Subtracting Multi-digit Numbers using Standard Algorithm

Introduction: 

In this chapter, we will learn to write numbers in three forms and count them by ones, tens, hundreds, or thousands, Working with Whole Numbers. 

We will also learn to find the value of each digit in a number, compare numbers, order numbers and about number patterns. 

Definition:  

Whole numbers: The numbers that start with ‘0’ are called whole numbers. Whole numbers are denoted by the symbol ‘W’. 

Example: 

The above numbers are starting with zero. Hence, they are called whole numbers. 

1.1: Numbers Up to 1,00,000 

1.1.1: Write the numbers in word form. 

Word form involves expressing numbers using words rather than numerals. 

E.g.: Express the following numbers in word form: 

1. 44,084 

Sol.: 

Ten thousand	Thousands	Hundreds	Tens	Ones
4	4	0	8	4

        Forty-four thousand eighty-four. 

2. 14,216 

Sol.: 

Ten thousand	Thousands	Hundreds	Tens	Ones
1	4	2	1	6

Fourteen thousand two hundred sixteen 

1.1.2: Express the numbers in standard form and expanded form. 

Standard form: Numbers written in standard form are written using only numbers. There are no words. 

E.g.: Twenty-four thousand, six hundred fifty express it in standard form. 

Sol.: 24,650  

Expanded form: It is a way to write numbers by showing the value of each digit. 

E.g.: Write the expanded form of 1462. 

Sol.: 14529 = 10,000 + 4000 + 600 + 20 + 9 

Example: 

1.1.3: Completing the pattern by finding the role. 

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. 

Example:  

Find the missing numbers by following the pattern rule. 

Sol.: 14 – 2 = 12 

        12 – 2 = 10 

        10 – 2 = 8 

           8 – 2 = 6 

           6 – 2 = 4 

So, the missing numbers are 10 and 4. 

E.g.: Read the number pattern. Find the next number. 

10 20 30 40 50 60 _ _ _ 

Sol.: Count up by 10’s from 10 to 80. 

10, 20, 30, 40, 50, 60, 70, 80, 90 

1.1.4: Finding the place value of a number. 

Place value can be defined as the value represented by a digit of a number based on its position in the number. 

Place Value Chart: 

E.g.: Identify the place value of 7 in 175268. 

Sol.:  

Hundred Thousand	Ten Thousand	Thousands	Hundreds	Tens	Ones
1	7	5	2	6	8

Place value of 7 = 70000 because it is in the ten thousand’s place. 

E.g.: Find the value of each digit in a number, 14629, using a place value chart  

Sol.:  

Ten Thousand	Thousands	Hundreds	Tens	Ones
0	0             0             0             0	0   0             0   0             0   0	0             0	0   0             0   0             0   0             0   0             0
1	4	6	2	9

Place value of 1 = 10,000 -> Ten thousands place 

Place value of 4 = 4000 -> Thousands place 

Place value of 6 = 600 -> Hundreds place 

Place value of 2 = 20 -> Tens place 

Place value of 9 = 9 -> Ones place   

14,629 

1.2: Comparing Numbers to 100,000 

To compare means to examine the difference between numbers to decide whether the numbers are greater than, smaller than or equal to each other.  

1.2.1: Compare 5-digit numbers using greater than and less than symbols. 

Greater than: The ‘greater than’ symbol used in Mathematics is placed between two values where the first number is greater than the second number. It is denoted by ‘>’. 

E.g.: Which number is greater: 30,000 or 42,000? 

Sol.: 42,000 > 30,000. Here, 

Compare the numbers of ten thousand in two numbers. 

4 ten thousand is greater than 3 ten thousand. 

Less than: The ‘less than’ symbol used in Mathematics is placed between two numbers where the first number is less than the second number. It is denoted by ‘<’. 

E.g.: Which number is less: 25,250 or 12,430? 

Sol.: 12430 < 25,250 

E.g.:  Compare 12345 and 67894 

Sol.: 12345 < 67894 

1.2.2: Ordering the numbers from the least to the greatest. 

If the numbers are arranged from the least to the greatest, the arrangement is called the ascending order. In this form, the numbers are in increasing order. 

E.g.: Arrange the numbers from least to greatest 54,630, 60,000, 24,240, 10,000. 

Sol.: The arrangement of numbers are as follows: 

10,000, 24,240, 54,630, 60,000 

Example: Arrange the numbers into ascending order. 

Sol.: 13254, 15420, 17584, 21568, 25481 

1.2.3: Ordering the numbers from the greatest to the least. 

If the numbers are arranged from the greatest to the least, the arrangement is called the descending order. In this form, the numbers are in decreasing order. 

E.g.: Arrange the numbers from the greatest to the least 25000, 10000, 50000, 15000. 

Sol.: 50,000, 25,000, 15,000, 10,000 

Example: 

Arrange the numbers into descending order. 

Sol.: 13254, 15420, 17584, 21568, 25481 

1.3: Adding and subtracting multi-digit numbers 

1.3.1: Adding and subtracting whole numbers using the standard algorithm. 

Standard algorithms for addition and subtraction are based on decomposing numbers written in base. This reduces the addition or subtraction of two multi-digit whole numbers to a collection of single-digit computations of place value units. 

Example: Addition and subtraction using the standard algorithm. 

1.3.2: Adding and subtracting multi-digit numbers. 

Addition can be defined as the taking of two or more numbers and adding them together. On the other hand, the concept of subtraction is just the opposite of addition as it involves taking away numbers from a group. 

E.g.: (a) Find the sum of 56,355 and 45,604. 

Sol.:  

        (b) Find the difference between 59,762 and 24,630. 

Sol.:  

Exercise:

1. Express the number 92,056 in word form.
2. Express the number 84,250 in expanded from.
3. Write the standard form of seventy-six thousand two hundred thirty.
4. 6, 12, 18, 24, ___   ____, find the missing numbers in the pattern.
5. In 51,254, find the place value of ‘2’.
6. Which number is greater: 74250 or 63240?
7. Which number is smaller: 32240 or 64250?
8. Arrange the following numbers form the least to the greatest. 23467, 12,250, 50240, 10,000.
9. Arrange the following numbers from the greatest to the least. 60,000, 96,000, 84,000, 98,000.
10. Find the sum of 96,240 and 24,250.
11. Find the difference of 84,720 to 12,250.
12. Write the standard form of twenty-four thousand five hundred.
13. Express the number 62,450 in word form.
14. Write the number 36,180 in expanded form.

Concept Map:

What have we learned:

In this chapter, we learned:

• The proficiency with whole numbers.
• How to read and write the numbers in numerals and in words.
• About comparing numbers using ‘greater than’ and ‘less than’ symbols and ordering of numbers.
• Number patterns, place values and addition and subtraction of multi-digit numbers.