Long Division Method with Regrouping and without Remainder

We will discuss here how to solve step-by-step the long division method with regrouping and without remainder.

Consider the following examples:

A. Dividing a 2-Digits Number by 1-Digit Number With Regrouping and Without Remainder:

Dividing a 2-Digits Number by 1-Digit Number With Regrouping

Division by Regrouping 2-digit Numbers

1. Divide 92 by 4.

Solution:

Step I: Arrange the numbers in columns.

Divide 9 tens by 4.

4 × 2 = 8, 8 < 9

and 4 × 3 = 12, 12 > 9

So, 9 - 8 = 1

We have 1 ten left.


Step II:

Bring down 2 ones.

We now have 1 ten and 2 ones = 12 ones as the new dividend.

On reciting the table of 4,

we get 4 × 3 = 12

So, the quotient is 23.


B. Dividing a 3-Digits Number by 1-Digit Number With Regrouping and Without Remainder:

Division by Regrouping 3-digit Numbers

1. 468 ÷ 3

Let us follow the division along with the given steps.

Long Division Method with Regrouping and without Remainder

Step I: Begin with hundreds digit

4 hundreds ÷ 3 = 1 hundred with remainder 1 hundred

Step II: Bring down 6 tens to the right of 1 hundred

1 hundred + 6 tens = 16 tens

Step III: 16 tens ÷ 3 = 5 tens with remainder 1 ten

Step IV: Bring down 8 ones to the right of 1 ten

1 ten + 8 ones = 18 ones

Step V: 18 ones ÷ 3 = 6 ones

Therefore, 468 ÷ 3 = 156


2. Divide 675 by 3.

Solution: 

Dividing a 3-Digits Number by 1-Digit Number With Regrouping

Step I: Divide the 6 hundreds. (3 × 2 = 6)

Subtract the hundreds: 6 - 6 = 0

Step II: Divide the 7 tens. (3 × 2 = 6)

Subtract the tens: 7 - 6 = 1,

i.e., 1 ten is left.

So, bring down 5 ones.

Step III: Now, we have 10 ones (1 ten) + 5 ones = 15 ones.

Divide 15 ones by 3. (3 × 5 = 15)

Subtract the ones:

15 - 15 = 0

Therefore, Quotient = 225, Remainder = 0.


C. Dividing a 4-Digits Number by 1-Digit Number With Regrouping and Without Remainder:

1. 9120 ÷ 5

Let us follow the division along with the given steps.

Long Division with Regrouping and without Remainder

Step I: Begin with thousands digit

9 thousands ÷ 5 = 1 thousand with remainder 4 thousands

Step II: Bring down 1 hundred to the right of 4 thousands

Step III: Now 4 thousands + 1 hundred = 41 hundreds

Step IV: Now 41 hundreds ÷ 5 = 8 hundreds with remainder 1 hundred

Step V: Bring down 2 tens to the right of 1 hundred

Step VI: Now 1 hundred + 2 tens = 12 tens

Step VII: So, 12 tens ÷ 5 = 2 with remainder 2 tens

Step VIII: Bring down zero to the right of 2 tens

So, 2 tens + 0 ones = 20 ones

Now 20 ones ÷ 5 = 4 ones

Therefore, 9120 ÷ 5 = 1824





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3rd Grade Math Lessons

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