# 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: Quotient - 7

Remainder - 10

12 × 7 + 10 = 94 2. Divide 96 by 16

Solution: 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: 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: 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: (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: (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: 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 4963 by 14

Solution:

(I method) (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) (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

10. Divide 47320 by 35

Solution: (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

11. Divide 50360 by 43

Solution: (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

12. 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 = 91We 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. Hence, quotient = 71 and remainder = 0.

 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 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.

## You might like these

• ### Money Bills | Prepare a Bill for the Purchases | Copy of an Invoice

We often buy things and then we get money bills of the items. The shopkeeper gives us a bill containing information about what we purchase. Different items purchased by us, their rates and the total

• ### Worksheet on Bills | Bills & Billing of Different Items |Cost of items

We will practice the questions given in the worksheet on bills and billing of different items. We know bill is a slip of paper on which a shopkeeper notes down the requirements of a buyer

• ### Estimating Products | Estimation in Multiplication | Rounding Numbers

To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers. Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate

• ### Worksheet on Word Problems on Addition and Subtraction Together | Ans

In 4th grade worksheet on word problems on addition and subtraction, all grade students can practice the questions on word problems based on addition and subtraction. This exercise sheet on

• ### Estimating Sums and Differences | Estimations | Practical Calculations

For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is required rather than an exact answer. To do this, numbers are rounded off to a

• ### Worksheet on Forming Numbers with Digits | Smallest & Greatest Numbers

In the worksheet on forming numbers with digits, the questions will help us to practice how to form different types of smallest and greatest numbers using different digits. We know that all the numbers are formed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

• ### Worksheets on Comparison of Numbers | Find the Greatest Number

In worksheets on comparison of numbers students can practice the questions for fourth grade to compare numbers. This worksheet contains questions on numbers like to find the greatest number, arranging the numbers etc…. Find the greatest number:

• ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the

• ### Even and Odd Numbers | Definition | Properties | Examples | Questions

A number which is a multiple of 2 is an even number and that which is not multiple of 2 is an odd number. All those numbers that can be put into pairs are called even numbers, that is, all those numbers which come in the table of two are even numbers.

• ### Successor and Predecessor | Successor of a Whole Number | Predecessor

The number that comes just before a number is called the predecessor. So, the predecessor of a given number is 1 less than the given number. Successor of a given number is 1 more than the given number. For example, 9,99,99,999 is predecessor of 10,00,00,000 or we can also

• ### Worksheets Showing Numbers on Spike Abacus | Number in Figures

Worksheets showing numbers on spike abacus for 4th grade math questions to practice after learning 1 digit, 2 digits, 3 digits, 4 digits and 5 digits numbers on spike abacus.

• ### Numbers Showing on Spike Abacus | Spike Abacus | Name of a Number

Numbers showing on spike abacus helps the students to understand the number and its place value. Spike abacus is very helpful to understand the concept of magnitude and name of a number.

• ### 4th Grade Division Worksheet | Simple Division | Math Division|Answers

In 4th grade division worksheet we will solve division by 2-digit numbers, division by 10 and 100, properties of division, estimation in division and word problems on division.

• ### Worksheet on Word Problems on Division | Solve Division Problems

In worksheet on word problems on division, all grade students can practice the questions on word problems involving division. This exercise sheet on word problems on division can be practiced by the students to get more ideas to solve division problems.

• ### Worksheet on Estimating the Quotient | Questions on Estimate Quotient

In worksheet on estimating the quotient, all grade students can practice the questions on estimate the quotient. This exercise sheet on estimating quotient can be practiced by the students to get more ideas. Find the estimated quotient for the following divisions:

Related Concept