Informative line

Operation On Whole Numbers

Addition and Subtraction  of Numbers Ending with Zeros

  • The numbers ending with zeros are easy to add and subtract.
  • For example, if we have two numbers with zeros at the end, to add or subtract, then

In addition:

If both numbers have two zeros, then write two zeros in the sum and add the remaining digits.

In subtraction:

If both numbers have two zeros, then write two zeros in the difference and subtract the remaining digits.

  • The best way to see how it works, consider an example:

Example: Add \(50,000\) with \(90,000\)

  • Arrange one number above the other.

\(\begin {array}\ &9&0&0&0&0\\ +&5&0&0&0&0\\ \hline\\ \hline \end {array}\)

  • Here, the numbers have four zeros each.

\(\begin {array}\ &9&0&0&0&0\\ +&5&0&0&0&0\\ \hline\\ \hline \end {array}\)

  • Now, write \(4\) zeros in the sum, because zero plus zero equals zero.

\(\begin {array}\ &9&0&0&0&0\\ +&5&0&0&0&0\\ \hline &&0&0&0&0\\ \hline \end {array}\)

  • Now, add the remaining digits.

\(9+5=14\)

Therefore,

\(\begin {array}\ &9&0&0&0&0\\ +&5&0&0&0&0\\ \hline 1&4&0&0&0&0\\ \hline \end {array}\)

Illustration Questions

Add \(80000+2000\)

A \(10,000\)

B \(82,000\)

C \(100,000\)

D \(78,000\)

×

Given: \(80000+2000\)

Write one number below the other in left alignment.

\(\begin {array}\ &8&0&0&0&0\\ +&&2&0&0&0\\ \hline \\ \hline \end {array}\)

If we have both number with zeros at the end, then we calculate sum or difference by writing same number of zeros in sum and difference.

Here, one number has \(4\) zeros and another has \(3,\) both the numbers have at least \(3\) zeros.

\(\begin {array}\ &8&0&0&0&0\\ +&&2&0&0&0\\ \hline \\ \hline \end {array}\)

Now, place \(3\) zeros in the sum because zero plus zero equals zero.

\(\begin {array}\ &8&0&0&0&0\\ +&&2&0&0&0\\ \hline &&&0&0&0\\ \hline \end {array}\)

Now, add the remaining digits.

\(80+2=82\)

Therefore,

\(\begin {array}\ &8&0&0&0&0\\ +&&2&0&0&0\\ \hline &8&2&0&0&0\\ \hline \end {array}\)

Hence, option (B) is correct.

Add \(80000+2000\)

A

\(10,000\)

.

B

\(82,000\)

C

\(100,000\)

D

\(78,000\)

Option B is Correct

Operations with Whole Numbers

  • There are four operations that can be performed while working with whole numbers.
  • These four operations are:-
  1. Addition
  2. Subtraction
  3. Multiplication
  4. Division

Addition of whole numbers

  • To add the whole numbers, first line up the numbers vertically so that the ones, tens, hundreds, thousands digits are in the same column, then draw a line.
  • Next add the digits at ones place.
  • If sum is greater than \(9\), then \(1\) is carried onto the tens column and the ones digit is written under the ones column.
  • Repeat the procedure for other columns too.

For example: Solve \(2515+3476\)

We need to line up the digits according to their place values and then add vertically.

Thus, sum of \(2515\) and \(3476\) is \(5991\) as shown.

Illustration Questions

What is the sum of \(1024\) and \(2028\)?

A \(302428\)

B \(3050\)

C \(30428\)

D \(3052\)

×

First, we need to line up the digits according to their place values.

 

image

Then, add the numbers.

image

Sum of \(1024\) and \(2028\) is \(3052\) .

Hence, option (D) is correct.

What is the sum of \(1024\) and \(2028\)?

A

\(302428\)

.

B

\(3050\)

C

\(30428\)

D

\(3052\)

Option D is Correct

Subtraction of Whole Numbers

  • To subtract the whole numbers, write the smaller number under the larger by writing down the ones, tens, hundreds, thousands digits under the same column, then draw a line.
  • Start subtracting from ones place.
  • If bottom digit is greater than the top digit, then borrow \(10\) from the digit to the left and add it to the top digit.

For example: Subtract \(223\) from \(518\)

\(\begin{array}\\ &&5&1&8\\ &-&2&2&3\\ \hline\\ \end{array}\)

Here, 2 is greater than \(1\) in the tens column, so we borrow from digit \(5\) in hundreds column, that make \(1\)into a \(11\) and \(5\)  into \(4\).

  • Thus difference of \(518\) and \(223 \) is \(295\) as shown.

Illustration Questions

What is the difference between \(1235\) and \(770\)?

A \(465\)

B \(564\)

C \(456\)

D \(654\)

×

First, we line up the digits according to their place values with the larger number written at the top.

image

Then, subtract the numbers.

image

Difference of \(1235\) and \(770\) is \(465\).

Hence, option (A) is correct.

What is the difference between \(1235\) and \(770\)?

A

\(465\)

.

B

\(564\)

C

\(456\)

D

\(654\)

Option A is Correct

Multiplication of Whole Numbers

  • To multiply whole numbers, write the multiplier under the multiplicand and draw a line.
  • A number which is to be multiplied by another number, is called multiplicand.
  • The number with which we multiply is called 'multiplier'.
  • Multiply the multiplier by each digit of the multiplicand.
  • Write the ones digit of each partial product in the same column as the multiplying digit.
  • If there is a tens digit, carry it and add it to the next product.
  • Remember to place a zero for each digit with which we have already multiplied.

Example1: Multiply \(224\) by \(8\)

  • We need to line up the digits according to place value.

 Example 2: \(517×32\)

  • We need to line up the digits according to their place values.

  • First multiply each digit of multiplicand by 2.

  • Now, we multiply each digit of the multiplicand by 3 and then add the products. 
  • Thus, \(16544\) is the product of \(517\) and \(32\).

Illustration Questions

What is the product of \(312 \) and \(17\)?

A \(329\)

B \(295\)

C \(5304\)

D \(31217\)

×

First, we need to line up the digits according to their place values.

image

Then, multiply each digit of multiplicand by \(7\).

image

Now, multiply each digit of multiplicand by \(1\) and then add products.

image

\(5304\) is the product of \(312 \) and \(17\).

Hence, option (C) is correct.

What is the product of \(312 \) and \(17\)?

A

\(329\)

.

B

\(295\)

C

\(5304\)

D

\(31217\)

Option C is Correct

Division of Whole Numbers

How do you divide whole numbers?

  • To divide whole numbers,
  1. Put divisor outside the division box.
  2. Put dividend inside the division box.
  3. Start from the left of the dividend, take as many digits as necessary to form a number that will contain the divisor at least once but less than ten times.
  • Now divide that partial dividend by the divisor and obtain the first digit of the quotient.
  • Write the quotient over the last digit of the partial dividend and bring down the next digit of the dividend and write it next to the remainder.
  • Continue the process until there are no more digits in the dividend.

Example 1: Divide \(9189\) by \(9\).

  • Here \(9189\) is the dividend and \(9\) is the divisor.
  • On division we get, \(1021\) as the quotient.

Example 2: Divide \(27725\) by \(25\).

  • Here, \(27725\) is the dividend and \(25\) is the divisor.
  • So, \(1109\) is the quotient.

Example 3: Divide \(38745\) by \(315\).

  • Here, \(38745\)  is the dividend and \(315\) is the divisor.
  • So, \(123\)  is the quotient.

So, \(123\)  is the Quotient.


  • Now, we multiply each digit of the multiplicand by 3 and then add the products. 
  • Thus, \(16544\) is the product of \(517\) and \(32\).

4. Division of whole numbers:

  • To divide whole numbers,
  1. Put divisor outside the division box.
  2. Put dividend inside the division box.
  3. Start from the left of the dividend, take as many digits as necessary to form a number that will contain the divisor at least once but less than ten times.
  • Now divide that partial dividend by the divisor and obtain the first digit of the quotient.
  • Write the quotient over the last digit of the partial dividend and bring down the next digit of the dividend and write it next to the remainder.
  • Continue the process until there are no more digits in the dividend.

For example: Divide \(9189\) by \(9\)

  • Here \(9189\) is the dividend and \(9\) is the divisor.
  • On division we get, \(1021\) as the quotient.

Example 2: Divide \(27725\) by \(25\)

  • Here, \(27725\) is the dividend and \(25\) is the divisor.
  • So, \(1109\)s the quotient.

Example 3: Divide \(38745\) by \(315\) 

  • Here, \(38745\)  is the dividend and \(315\) is the divisor. 

So, \(123\)  is the Quotient.

Illustration Questions

Find the result of \(552\div12\).

A \(36\)

B \(35\)

C \(45\)

D \(46\)

×

Given:

Divisor \(=12\)

Dividend \(=552\)

Put these values under division sign.

image

On performing the above division, we get:

image

Thus, the result of \(552\div12\) is \(46\).

Hence, option (D) is correct.

Find the result of \(552\div12\).

A

\(36\)

.

B

\(35\)

C

\(45\)

D

\(46\)

Option D is Correct

Multiplication and Division of Numbers Ending with Zeros

  • The numbers ending with zeros are easy to multiply and divide.
  • For example, if we have two numbers with zeros at the end, to multiply or divide, then:

In multiplication:

  • Multiply the numbers without zeros, then place the total zeros at the end of the product.

For example, multiply \(300\) by \(20\)

  • First, multiply the number without zeros,

\(3×2=6\)

  • Now, place the total zeros at the end of the product.

\(3\underbrace{00}_{2\text{ zeros}}×2\underbrace{0}_{1 \text{ zero}}=6\underbrace{000}_{\text{Total 3 zeros}}\)

In Division:

  • First, remove the common zeros, then divide the remaining digits.

For example, divide \(90000\) by \(300\)

First, remove the common zeros.

Since, the numbers have two zeros common, we remove these zeros.

\(\therefore\;90000\div300\)

\(=900\div3\)

Now, divide the remaining digits.

\(900\div3=300\)

Illustration Questions

What is the product of \(20000\) and \(250\)?

A \(50,000\)

B \(500,000\)

C \(5,000,000\)

D \(5,000\)

×

Given: \(20000\) and \(250\)

If we have two numbers with zeros at the end to multiply, then multiply the numbers without zeros first and then place the total number of zeros at the end of the product.

Multiply the numbers without zeros.

\(2×25=50\)

Now, place the total zeros at the end of the product.

\(2\underbrace{0000}_{\text{4 zeros}}×25\underbrace{0}_{\text{1 zero}}=50\underbrace{00000}_{\text{Total 5 zeros}}\)

Hence, option (C) is correct.

What is the product of \(20000\) and \(250\)?

A

\(50,000\)

.

B

\(500,000\)

C

\(5,000,000\)

D

\(5,000\)

Option C is Correct

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