Division by Two-Digit Numbers

In division by two-digit numbers we will practice dividing two, three, four and five digits by two-digit numbers.


Consider the following examples on division by two-digit numbers:

Let us use our knowledge of estimation to find the actual quotient. 

1. Divide 94 by 12

Round the number 

94 ÷ 12 → 90 ÷ 10 

Estimated quotient = 9 

In order to find the actual quotient, multiply the divisor 12 by the estimated quotient. 

12 × 9 = 108 

12 × 8 = 96

12 × 7 = 84

108 > 94

96 > 94

The actual quotient, we find is 7.

Check:

Division by 2 Digits





Quotient - 7

Remainder - 10

12 × 7 + 10 = 94

division by 2 digits number








2. Divide 96 by 16

Solution:

Division by Two Digit Numbers

16 x 6 = 96, so, 6 will be the quotient.

We search for the possible quotient. The divisor is a number of two digits.

So, 96 is taken as dividend.


Therefore, Quotient = 6


3. Divide 88 by 17

Solution:

division by 2-digit numbers

17 x 5 = 85 and 17 x 6 = 102,

85 < 88 but 102 > 88

So, 5 will be the quotient



Therefore, Quotient = 5, Remainder = 3


4. Divide 192 by 24

Solution: 

Division by Two Digit Numbers

19 < 24, so, 192 will be taken as dividend.

24 x 8 = 192. So, 8 will be the quotient.





Therefore, Quotient = 8


5. 510 ÷ 32 ⟶ 500 ÷ 30 ⟶ 50 ÷ 3

Estimated quotient = 16

Try:

32 × 16 = 512

32 × 15 = 480

512 > 510

The actual quotient is 15



6. Divide 275 by 24

Solution:

division by two digit numbers

(a) 27 > 24, 24 x 1 = 24, 24 x 2 = 48

So, 1 will be quotient.

Here, 27 is 27T or, 270

So, 1T or 10 is the quotient.

(b) 275 -240 = 35, 24 x 1. = 24,

So, 1 is the quotient.

24 x 11 + 11 = 264 + 11 = 275

Therefore, result is verified

Therefore, Quotient = 11, Remainder =11



7. Divide 803 by 70

Solution:

division by two digit numbers

(a) 80 > 70,

So, 80T will be taken as dividend

70 x 1 = 70, 70 x 2 = 140

So, 1T will be quotient.

(b) 803 - 700 = 103, 70 x 1 = 70, 70 x 2 = 140

So, 1 will be quotient.

70 x 11 + 33 = 770 + 33 = 803

Therefore, result is verified


Therefore, Quotient =11, Remainder = 33



8. Divide 345 by 49

Solution:

division by two digit numbers

34 < 49, So, 345 will be taken as dividend.

By trial 49 x 7 = 343 which is near to 345

So, 7 will be quotient.

Verification: 49 x 7 + 2 = 343 + 2 = 345


Therefore, Quotient = 7, Remainder = 2



9. Divide 1432 by 28.

Solution:

Divide 5-Digit by 2-Digit Number

I: 1 < 28            14 < 28

Therefore, take 143

II: We have 28 × 6 = 168; 28 × 5 = 140

Since 140 < 143, write 5 as first digit of the quotient. Write the product 26 × 5 = 140 below 143 and subtract.

III: 143 – 140 = 3; Bring down 2

32 > 28 We have 28 × 1 = 28 < 32.

28 × 2 = 56 > 32

Since 28 < 32, write 1 as the second digit of the quotient. Write the product 28 × 1 = 28 below and subtract.

IV: 32 – 28 = 4

Since 4 < 28, stop the division.


10. Divide 4963 by 14

Solution:

(I method)

division by two digit numbers

(a) 14 x 3 = 42 and 14 x 4 = 56, 42 < 49 and 56 > 49

So, 3H will be quotient.

(b) 4963 - 4200 = 763, 14 x 5 = 70 and 14 x 6 = 84

So, 5T will be quotient.

(c) 763 - 700 = 63, 14 x 4 = 56, 14 x 5 = 70

56 < 63, 70 > 63

Therefore, 4 is the quotient.

Verification: 14 x 354 + 7 = 4956 + 7 = 4963


Therefore, Quotient = 354, Remainder = 7



(II method)

division by two digit numbers

(a) 14 x 3 = 42, 14 x 4 = 56,

Therefore, 3H will be quotient.

49 - 42 = 7, 6 is carried down

(b) 14 x 5 = 70, 14 x 6 = 84,

Therefore, 5T will be quotient.

76 - 70 = 6, 3 is carried down.

14 x 4 = 56, 14 x 5 = 70,

Therefore, 4 will be quotient.

63 - 56 = 7 is the remainder

Quotient = 354

Remainder = 7

Verification:

Quotient x divisor + remainder

= 354 x 14 + 7

= 4956 +7

= 4963 (dividend)

So, result is verified



11. Divide 47320 by 35

Solution:

division by two digit numbers

(a) 47 Th is divided by 35, 35 x 1 = 35 < 47,

35 x 2 = 70 > 47, so, 1 Th is quotient.

47 - 35 = 12, 3 is carried down

(b) 123H is divided by 35, 35 x 3 = 105 < 123

35 x 4 = 140 > 123, so, 3 H is quotient

123 - 105 = 18, 2 is carried down.

(c) 182 T is divided by 35, 35 x 5 = 175 < 182

35 x 6 = 210 > 182, therefore, 5T is quotient.

182 - 175 = 7, 0 is carried down.

(d) 70 is divided by 35, 35 x 2 = 70,

2 is the quotient

70 - 70 = 0

Verification: 35 x 1352 + 0 = 47320.

So verified.

Therefore, Quotient = 1352 Remainder = 0



12. Divide 50360 by 43

Solution:

division by two digit numbers

(a) 50Th is divided by 43, 43 x 1 = 43 < 50.

So, 1 Th is quotient, 50 - 43 = 7,3 is taken down.

(b) 73 H is divided by 43, 43 x 1 = 43 < 73

43 x 2 = 86 > 73.

So, 1H is quotient, 73 - 43 = 30, 6 is taken down.

(c) 306 T is divided by 43, 43 x 7 = 301 < 306

7 T is quotient, 306 - 301 = 5, 0 is taken down

(d) 50 is divided by 43, 1 is quotient

50 - 43 = 7 is remainder

Verification: 1171 x 43 + 7 = 50353 + 7 = 50360.

Result is verified.

Quotient =1171 Remainder = 7


13. Divide 923 by 13

Solution:

Let us divide 923 by 13.

Step I: Since, the divisor is a 2-digit number, we consider 92 the 2-digit number on the extreme left of the dividend.

92 > 13, we  know that 13 x 7 = 91

We write 7 in the quotient.

Subtract 91 from 92.

Step II: Bring down 3 and write on the right side of the remainder. 13 is the new dividend.

Step III: Divide 13 by 13.

We know 13 x 1 = 13. Write 1 in the quotient. Subtract 13 from 13. The remainder is 0.

Divide 923 by 13

Hence, quotient = 71 and remainder = 0.


14. Divide 1749 by 27 and check your answer.

Solution:

Let us divide 1749 by 27.

Step I: The divisor 27 is greater than the 2-digit number on the extreme left of the dividend. So, we take the 3-digit number which is 174 and divide by 27. Write 6 in the quotient and subtract 162 from 174.

Step II: Bring down 9 and write on the right side of the remainder. 129 is the new dividend.

Step III: Divide 129 by 27.

Write 4 in the quotient and subtract 108 from 129. Remainder is 21

Divide 1749 by 27

Hence, quotient = 64 and remainder = 21

Verification: 

We know that 

Dividend = Quotient x Divisor + Remainder

             = 64 x 27 + 21

             = 1728 + 21

             = 1749

1749 is the dividend as given in the question.


15. Divide 15642 by 32

Solution:

Divide 5-Digit by a 2-Digit Number

I: 1 < 32             15 < 32

Therefore, take 156

II: We have 32 × 5 = 160 > 156

32 × 4 = 128 < 156

Since 128 < 156, write 4 as first digit of the quotient. Write the product 32 × 4 = 128 below 156 and subtract.

III: 156 – 128 = 28. Bring down 4.

284 > 32. We have 32 × 9 = 288 > 284.

32 × 8 = 256 < 284.

Since 256 < 284, write 8 as the second digit of the quotient. Write the product 32 × 8 = 256 below 284 and subtract.

IV: 284 - 256 = 28. Bring down 2. 282 > 32. We have 32 × 9 = 288 > 282

32 × 8 = 256 < 282.

V: Write 8 as the third digit of the quotient. Write the product 32 × 8 = 256 below 282 and subtract.

282 – 256 = 26.

Since 26 < 32, stop the division.


Division Activity

Objective: Dividing a 2-digit number by 9 using short cut method.

Materials Required: Pen and paper only.

Procedure/Demonstration: We can divide any 2-digit number by 9 quickly.


Type 1: When the sum of the digits is less than 9.

In this case, the tens digit of the dividend gives quotient and the sum of the two digits gives remainder.

Division Short Cut Method


Type 2: When the sum of the digits is greater than or equal of 9 but less than 18. In this case, 1 more than the tens digit of the dividend gives quotient. To get the remainder, subtract 9 from the sum of the digits of the dividend.

75 ÷ 9 gives quotient = 7 + 1 = 8 and remainder = 12 - 9 = 3

63 ÷ 9 gives quotient = 6 + 1 = 7 and remainder = 9 - 9 = 0


Worksheet on Division by 2-Digit Numbers:

1. Divide the following:

(i) 8629 ÷ 12

(ii) 38245 ÷ 32

(iii) 16928 ÷ 11

(iv) 28724 ÷ 33

(v) 86458 ÷ 15

(v) 7542 ÷ 19


Answer:

1. (i) Quotient: 719; Remainder: 1

(ii) Quotient: 1195; Remainder: 5

(iii) Quotient: 1538; Remainder: 10

(iv) Quotient: 870; Remainder: 14

(v) Quotient: 5763; Remainder: 13

(v) Quotient: 396; Remainder: 18

You might like these

Related Concept

Addition

Word Problems on Addition

Subtraction

Check for Subtraction and Addition

Word Problems Involving Addition and Subtraction

Estimating Sums and Differences

Find the Missing Digits

Multiplication

Multiply a Number by a 2-Digit Number

Multiplication of a Number by a 3-Digit Number

Multiply a Number

Estimating Products

Word Problems on Multiplication

Multiplication and Division

Terms Used in Division

Division of Two-Digit by a One-Digit Numbers

Division of Four-Digit by a One-Digit Numbers

Division by 10 and 100 and 1000

Dividing Numbers

Estimating the Quotient

Division by Two-Digit Numbers

Word Problems on Division






4th Grade Math Activities

From Division by Two-Digit Numbers to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Intersecting Lines | What Are Intersecting Lines? | Definition

    Jun 14, 24 11:00 AM

    Intersecting Lines
    Two lines that cross each other at a particular point are called intersecting lines. The point where two lines cross is called the point of intersection. In the given figure AB and CD intersect each o…

    Read More

  2. Line-Segment, Ray and Line | Definition of in Line-segment | Symbol

    Jun 14, 24 10:41 AM

    Line-Segment, Ray and Line
    Definition of in Line-segment, ray and line geometry: A line segment is a fixed part of a line. It has two end points. It is named by the end points. In the figure given below end points are A and B…

    Read More

  3. Definition of Points, Lines and Shapes in Geometry | Types & Examples

    Jun 14, 24 09:45 AM

    How Many Points are There?
    Definition of points, lines and shapes in geometry: Point: A point is the fundamental element of geometry. If we put the tip of a pencil on a paper and press it lightly,

    Read More

  4. Subtracting Integers | Subtraction of Integers |Fundamental Operations

    Jun 13, 24 04:32 PM

    Subtraction of Integers
    Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.

    Read More

  5. 6th Grade Worksheet on Whole Numbers |Answer|6th Grade Math Worksheets

    Jun 13, 24 04:17 PM

    6th Grade Worksheet on Whole Numbers
    In 6th Grade Worksheet on Whole Numbers contains various types of questions on whole numbers, successor and predecessor of a number, number line, addition of whole numbers, subtraction of whole number…

    Read More