As we know that the division is to distribute a given value or quantity into groups having equal values. In long division, values at the individual place (Thousands, Hundreds, Tens, Ones) are dividend one at a time starting with the highest place.
Division by One-Digit Divisor
1. Find the quotient and remainder of 649 ÷ 9.
Solution:
Step I: We start dividing the hundreds first. Since 6 hundreds cannot be divided into 9 groups of hundreds, the quotient at hundreds column is zero. Step II: 6 Hundreds are now changed into 60 tens and added to 4 tens, making 64 tens. Step III: 64 tens give 9 groups of 7 tens each and 1 ten is left over. Step IV: 1 ten give 10 ones, 10 ones + 9 ones = 19 ones Step V: 19 ones can be put into 2 groups of 9 and 1 one is left over. |
q = 72; r = 1 |
Thus, 649 when divided into 9 groups each group gets 7 tens and 2 ones or 72 ones and 1 one is left over.
Division by Two-Digit Divisors
2. Divide 2698 by 21.
Solution:
Recall the process of long division.
Step I: 2 thousands cannot be divided into 21 groups of thousand. So, 0 is placed as quotient in the thousands column. Step II: 2 thousands give 20 hundreds. 20 hundreds + 6 hundreds give 26 hundreds. 26 hundreds make 1 group of 21 hundreds. 5 hundreds are left. Step III: 5 hundreds give 50 tens. |
q = 128; r = 10 |
So, 50 tens + 9 tens = 59 tens
59 tens are to be divided into 21 groups of tens
59 tens ÷ 21 makes 2 groups with 17 tens left.
2 is placed in the quotient in the tens column.
Step IV: 17 tens = 170 ones
170 ones + 8 ones = 178 ones
178 ones ÷ 21 makes 8 groups with 10 ones left.
Thus, in division of 2,698 by 21, we get 128 as quotient and 10 as remainder.
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