Trick 9 : Consider the division by divisors of more than one digit, and when the divisors are slightly greater than powers of 10.
Consider the division by divisors of more than one digit, and when the divisors are slightly greater than powers of 10.
Example 1 : Divide 1225 by 12.
Step 1 : (From left to right ) write the Divisor leaving the first digit, write the other digit or digits using negative (-) sign and place them below the divisor as shown.
12
-2
¯¯¯¯
Step 2 : Write down the dividend to the right. Set apart the last digit for the remainder.
i.e.,, 12 122 5
- 2
Step 3 : Write the 1st digit below the horizontal line drawn under the dividend. Multiply the digit by –2, write the product below the 2nd digit and add.
i.e.,, 12 122 5
-2 -2
¯¯¯¯¯ ¯¯¯¯
10
Since 1 x –2 = -2 and 2 + (-2) = 0
Step 4 : We get second digits’ sum as ‘0’. Multiply the second digits’ sum thus obtained by –2 and writes the product under 3rd digit and add.
12 122 5
- 2 -20
¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯
102 5
Step 5 : Continue the process to the last digit.
i.e., 12 122 5
- 2 -20 -4
¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯
102 1
Step 6: The sum of the last digit is the Remainder and the result to its left is Quotient.
Thus Q = 102 and R = 1 Example 2 : Divide 1697 by 14.
14 1 6 9 7
- 4 -4–8–4
¯¯¯¯ ¯¯¯¯¯¯¯
1 2 1 3
Q = 121, R = 3.
Example 3 : Divide 2598 by 123.
Note that the divisor has 3 digits. So we have to set up the last two digits of the dividend for the remainder.
1 2 3 25 98 Step ( 1 ) & Step ( 2 )
-2-3
¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Now proceed the sequence of steps write –2 and –3 as follows :
1 2 3 2 5 9 8
-2-3 -4 -6
¯¯¯¯¯ -2–3
¯¯¯¯¯¯¯¯¯¯
2 1 1 5
Since 2 X (-2, -3)= -4 , -6; 5 – 4 = 1
and (1 X (-2,-3); 9 – 6 – 2 = 1; 8 – 3 = 5.
Hence Q = 21 and R = 15.
Example 4 : Divide 239479 by 11213. The divisor has 5 digits. So the last 4 digits of the dividend are to be set up for Remainder.
1 1 2 1 3 2 3 9 4 7 9
-1-2-1-3 -2 -4-2-6 with 2
¯¯¯¯¯¯¯¯ -1-2-1-3 with 1
¯¯¯¯¯¯¯¯¯¯¯¯¯
2 1 4 0 0 6
Hence Q = 21, R = 4006.
Example 5 : Divide 13456 by 1123
1 1 2 3 1 3 4 5 6
-1–2–3 -1-2-3
¯¯¯¯¯¯¯ -2-4 –6
¯¯¯¯¯¯¯¯¯¯¯¯¯
1 2 0–2 0
Note that the remainder portion contains –20, i.e.,, a negative quantity. To over come this situation, take 1 over from the quotient column, i.e.,, 1123 over to the right side, subtract the remainder portion 20 to get the actual remainder.
Thus Q = 12 – 1 = 11, and R = 1123 - 20 = 1103.
Example 1 : Divide 1225 by 12.
Step 1 : (From left to right ) write the Divisor leaving the first digit, write the other digit or digits using negative (-) sign and place them below the divisor as shown.
12
-2
¯¯¯¯
Step 2 : Write down the dividend to the right. Set apart the last digit for the remainder.
i.e.,, 12 122 5
- 2
Step 3 : Write the 1st digit below the horizontal line drawn under the dividend. Multiply the digit by –2, write the product below the 2nd digit and add.
i.e.,, 12 122 5
-2 -2
¯¯¯¯¯ ¯¯¯¯
10
Since 1 x –2 = -2 and 2 + (-2) = 0
Step 4 : We get second digits’ sum as ‘0’. Multiply the second digits’ sum thus obtained by –2 and writes the product under 3rd digit and add.
12 122 5
- 2 -20
¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯
102 5
Step 5 : Continue the process to the last digit.
i.e., 12 122 5
- 2 -20 -4
¯¯¯¯¯ ¯¯¯¯¯¯¯¯¯¯
102 1
Step 6: The sum of the last digit is the Remainder and the result to its left is Quotient.
Thus Q = 102 and R = 1 Example 2 : Divide 1697 by 14.
14 1 6 9 7
- 4 -4–8–4
¯¯¯¯ ¯¯¯¯¯¯¯
1 2 1 3
Q = 121, R = 3.
Example 3 : Divide 2598 by 123.
Note that the divisor has 3 digits. So we have to set up the last two digits of the dividend for the remainder.
1 2 3 25 98 Step ( 1 ) & Step ( 2 )
-2-3
¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Now proceed the sequence of steps write –2 and –3 as follows :
1 2 3 2 5 9 8
-2-3 -4 -6
¯¯¯¯¯ -2–3
¯¯¯¯¯¯¯¯¯¯
2 1 1 5
Since 2 X (-2, -3)= -4 , -6; 5 – 4 = 1
and (1 X (-2,-3); 9 – 6 – 2 = 1; 8 – 3 = 5.
Hence Q = 21 and R = 15.
Example 4 : Divide 239479 by 11213. The divisor has 5 digits. So the last 4 digits of the dividend are to be set up for Remainder.
1 1 2 1 3 2 3 9 4 7 9
-1-2-1-3 -2 -4-2-6 with 2
¯¯¯¯¯¯¯¯ -1-2-1-3 with 1
¯¯¯¯¯¯¯¯¯¯¯¯¯
2 1 4 0 0 6
Hence Q = 21, R = 4006.
Example 5 : Divide 13456 by 1123
1 1 2 3 1 3 4 5 6
-1–2–3 -1-2-3
¯¯¯¯¯¯¯ -2-4 –6
¯¯¯¯¯¯¯¯¯¯¯¯¯
1 2 0–2 0
Note that the remainder portion contains –20, i.e.,, a negative quantity. To over come this situation, take 1 over from the quotient column, i.e.,, 1123 over to the right side, subtract the remainder portion 20 to get the actual remainder.
Thus Q = 12 – 1 = 11, and R = 1123 - 20 = 1103.
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