Dividing 3-Digit by 1-Digit Number

Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step.

How to divide 3-digit numbers by single-digit numbers? 

Let us follow the examples to learn to divide 3-digit number by one-digit number. 


I: Dividing 3-digit Number by 1-Digit Number without Remainder:

1. Divide 248 by 2 and verify the result.

Solution: 

We proceed as follows:

Step I: Arrange the two given numbers as shown.

Divide 3-Digit by 1-Digit Number


Step II: Divide 2 hundreds by 2.

Start by looking at the first number (hundreds place) in the dividend.

Find a number in the table of 2 less than or equal to 2

We know 2 × 1 = 2.

So, 1 is the required number.

2 × 1 = 2, write 1 in hundreds place of the quotient and 2 below 2.

Subtract the number you got by multiplying the divisor, from the number in the dividend.

Subtract 2 from 2

2 - 2 = 0

Divide 3-Digit Number by 1-Digit Number


Step III: Divide 4 tens by 2.

Bring down the next digit, from the number in the dividend.

We have 4 there; now find a number in the table of 2 that divides it.

2 × 1 = 2

2 × 2 = 4

So, 2 is the required number.

2 × 2 = 4, write 2 in tens place of the quotient and 4 below 4.

Dividing 3-Digit Number by 1-Digit Number

Subtract the number you got by multiplying the divisor, from the number in the dividend.

Subtract 4 from 4

4 - 4 = 0


Step IV: Divide 8 ones by 2.

Bring down 8
Now see where does 8 come in the table of 2.

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

White 4 in the quotient and 8 under 8 and subtract.

8 - 8 = 0

Dividing 3-Digit by 1-Digit Number

Therefore, 248 ÷ 2 = 124



II: Dividing a 3-digit Number by a 1-Digit Number with Remainder: (Long Division)


Let us follow the examples to learn to divide 3-digit numbers by one-digit number with remainder.

1. Divide the following and verify the result: Long Division

625 ÷ 4

Solution: 

We proceed as follows:

Step I: Arrange the two given numbers as shown.

Divide 3-Digit by 1-Digit Number


Step II: Divide 6 hundreds by 4.

Start by looking at the first number (hundreds place) in the dividend.

Find a number in the table of 4 less than or equal to 6

We know 4 × 1 = 4.

So, 1 is the required number.

4 × 1 = 4, write 1 in hundreds place of the quotient and 4 below 6.

Subtract the number you got by multiplying the divisor, from the number in the dividend.

Subtract 4 from 6

6 - 4 = 2

Divide 3-Digit by 1-Digit Number


Step III: 

Bring down the next digit (tens places), from the number in the dividend.

We have 22 there; now find a number in the table of 4 that divides it.

4 × 1 = 2

4 × 2 = 8

4 × 3 = 12

4 × 4 = 16

4 × 5 = 20

So, 5 is the required number.

4 × 5 = 20, write 5 in tens place of the quotient and 20 below 22.


Divide 3-Digit by 1-Digit Number

Subtract the number you got by multiplying the divisor, from the number in the dividend.

Subtract 20 from 22

22 - 20 = 2


Step IV: Bring down 5

4 × 1 = 2

4 × 2 = 8

4 × 3 = 12

4 × 4 = 16

4 × 5 = 20

4 × 6 = 24

So, 6 is the required number.

4 × 6 = 24, write 6 in ones place of the quotient and 24 below 25.

Subtract the number you got by multiplying the divisor, from the number in the dividend.

Subtract 24 from 25

25 - 24 = 1.

Dividing 3-Digit by 1-Digit Number

Therefore, the quotient = 156 and remainder = 1.


Check: Dividend = Quotient × Divisor - Remainder

                         = 156 × 4 + 1

                         = 624 + 1

                         = 625 = Dividend


3. 645 ÷ 6

Division of Two-Digit by a One-Digit


Check:

107 × 6 = 642

642 + 3 = 645

Here we know, 645 ÷ 6 = 107 remainder is 3

645 is dividend

6 is divisor

107 is quotient

3 is remainder


The same method is used when dividing larger numbers.



Division Activity

Objective: Dividing a 3-digit number by 9 using short cut method.

Materials Required: Pen and paper only.

Procedure/Demonstration: We can divide any 3-digit number by 9 quickly.

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

In this case, the quotient is obtained by adding the number formed by hundreds and tens digits to the hundreds digit. The sum of the three digits gives the remainder.

213 ÷ 9, gives quotient = 21 + 2 = 23 and remainder = 2 + 1 + 3 = 6


Type 2: When the sum of the digits is greater than or equal of 9 but less than 18.

Here, we first add the number formed by hundreds and tens digits to the hundreds digit. 1 more than this sum is the quotient. To get the remainder, subtract 9 from the sum of the digits.


537 ÷ 9 gives quotient = 53 + 5 + 1 = 59 and

remainder = (9 + 8 + 7) - 9 = 15 - 9 = 6


Worksheet on Dividing 3-Digit by 1-Digit Number:

1. Find the quotient and the remainder, using long division method:

(i) 639 ÷ 3

(ii) 484 ÷ 2

(iii) 550 ÷ 5

(iv) 284 ÷ 4

(v) 504 ÷ 3

(vi) 840 ÷ 7

(vii) 248 ÷ 4

(viii) 655 ÷ 5

(ix) 616 ÷ 7

(x) 348 ÷ 4


Answer:

1. (i) Quotient: 213; Remainder: 0

(ii) Quotient: 242; Remainder: 0

(iii) Quotient: 110; Remainder: 0

(iv) Quotient: 71; Remainder: 0

(v) Quotient: 168; Remainder: 0

(vi) Quotient: 120; Remainder: 0

(vii) Quotient: 62; Remainder: 0

(viii) Quotient: 131; Remainder: 0

(ix) Quotient: 88; Remainder: 0

(x) Quotient: 87; Remainder: 0


2. Find the quotient and the remainder:

(i) 320 ÷ 6

(ii) 392 ÷ 6

(iii) 249 ÷ 7

(iv) 364 ÷ 8

(v) 193 ÷ 7

(vi) 492 ÷ 5

(vii) 524 ÷ 7

(viii) 419 ÷ 9

(ix) 270 ÷ 8

(x) 375 ÷ 7


Answer:

2. (i) Quotient: 53; Remainder: 2

(ii) Quotient: 65; Remainder: 2

(iii) Quotient: 35; Remainder: 4

(iv) Quotient: 45; Remainder: 4

(v) Quotient: 27; Remainder: 3

(vi) Quotient: 98; Remainder: 2

(vii) Quotient: 74; Remainder: 6

(viii) Quotient: 46; Remainder: 5

(ix) Quotient: 33; Remainder: 6

(x) Quotient: 53; Remainder: 4

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