ADDITION

 WELCOME .

ENJOY MATH WITH AMJID

ADDITION.

We have learnt that

We can show the number 999 as below :

If we add 1 more to 999. We will get smallest 4-digit number as shown below :

FORMING 4-DIGIT NUMBERS

Look at the following :

Similarly, we have

NUMBERS ON THE ABACUS

Look at the abacus shown on the right. We need 4 spikes to represent the 4-digit number. In the given figure of abacus, starting from the left, the spikes represent thousands, hundreds, tens and ones.

Let us now practise 4-digit numbers both in figures and words.

NUMBER NAMES
We know that number names are the numbers written in words. Each number is derived from the name of the place where digits are placed.

Example : Write the number names for the following numerals :
4823, 3475, 7780
Solution :

Number Names.

Four thousand eight hundred twenty three
Three thousand four hundred seventy five
Seven thousand seven hundred eighty

Example : Write the numerals for the following number names :
Eight thousand two hundred forty six
Five thousand six
Nine thousand thirty nine
Solution : 8246, 5006, 9039

PLACE VALUE AND FACE VALUE

We know that numbers are made-up of digits.
We also know that place value of a digit depends on its position
in the digits, but the face value of a digit remains unchanged.

Look at the place value chart :

the digit 4 is in thousands place, so its place value is 4 thousands or 4000.
the digit 7 is in hundreds place, so its place value is 7 hundreds or 700.
the digit 8 is in tens place, so its place value is 8 tens or 80.
the digit 6 is in ones place, so its place value is 6 ones or 6.

Example : Find the place value of the digits in the given numbers :
a. 2458
b. 3085
Solution :

Expanded form and standard form or short form :

To expand means to become more in number/size. When you pull a rubber band, it expands. Let us see, how it works with numbers. When we expand the number, we understand the value of each digit in its position.

See the numbers shown in the place value chart :

Now, begin with the place value of the digit in the thousands place. We expand like this :

Standard form or Short form :

Now, we express expanded form into standard form.
Take the help of place value chart.

COMPARING NUMBERS

We have already studied comparison of numbers.
Let us understand the rules to compare numbers.

Comparing numbers having different number of digits :

Example : Which is greater a. 315 or 86 ? b. 3896 or 485 ?
Solution : a. 315 has 3 digits and 86 has 2 digits.
So, 315 > 86
b. 3896 has 4 digits and 485 has 3 digits.
So, 3896 > 485

Comparing numbers with the same number of digits :

Example : Which is greater a. 315 or 86 ? b. 3896 or 485 ?
Solution : a. 315 has 3 digits and 86 has 2 digits.
So, 315 > 86
b. 3896 has 4 digits and 485 has 3 digits.
So, 3896 > 485

Comparing numbers with the same number of digits :

Example 1 : Which is greater 8742 or 5125 ?
Solution : We write the numbers as shown below :

Here, 8 is greater than 5. 8 > 5.
So, 8742 > 5125

Example 2 : Compare the numbers 3285 or 3876.
Solution : We write the numbers as shown below :

Here, 2 is less than 8. 2 < 8.
So, 3285 < 3876

ASCENDING AND DESCENDING ORDER

Ascending order means arranging numbers from the smallest number to the greatest number.

Example 1 : Arrange the numbers 3747, 1674, 1528 and 6409 in ascending order.
Solution : Here, 1528 is the smallest number.
The next number greater than 1528 is 1674.
The next numbers in greater order are 3747 and 6409.
So, the required ascending order is
1528 < 1674 < 3747 < 6409
or
1528, 1674, 3747, 6409
Descending order means arranging numbers from the greatest number to the smallest number.

Example 2 : Arrange the numbers 6115, 3242, 8056 and 1789 in descending order.
Solution : Here, 8056 is the greatest number.
The next number smaller than 8056 is 6115.
The next numbers in smaller order are 3242 and 1789.
So, the required descending order is
8056 > 6115 > 3242 > 1789.
or
8056, 6115, 3242, 1789.

PREDECESSOR AND SUCCESSOR OF A NUMBER

1 less than any given number is called the predecessor of that number.

FORMATION OF GREATEST AND SMALLEST NUMBERS

We have already studied in the previous class, the procedure of forming the greatest and the smallest 3-digit numbers with the given three digits (without repeating the digits).

We shall follow the same procedure here to form the greatest and the smallest 4-digit numbers with the given four digits (without repeating the digits).

Example 1 : Write the greatest 4-digit number (without repeating the digits) from the following four digits : 7, 2, 9, 1.
Solution : Greatest 4-digit number is 9721.

Example 2 : Write the smallest 4-digit number (without repeating the digits) from the following four digits : 5, 0, 3, 1.
Solution : Smallest 4-digit number is 1035.

ROUNDING THE NUMBER TO THE NEAREST TEN

Suppose we want to round 32 to the nearest ten. To do this, we must know whether it is nearer to 30 or 40. 35 is half way between 30 and 40 and as 32 < 35. So 32 is nearer to 30 than 40.

To the nearest tens 42 rounds to 40.
35 is rounded to 40.
39 is rounded to 40.
Similarly, 457 is rounded to 460. 1123 is rounded to 1120.
The number 8583863 is rounded to 8583860.