Lecture Notes on Long Division

Summary

This lecture covers the method of long division for dividing numbers by both single-digit and multi-digit divisors. It involves a systematic way of breaking down larger numbers to find how many times a divisor can fit into them, step-by-step calculations to simplify the process, and several examples to demonstrate the technique.

Detailed Notes

Example 1: Dividing 228 by 4

• Step 1: 4 goes into 22 five times (4x5=20).
• Step 2: Subtract 20 from 22 to get 2.
• Step 3: Bring down the 8 to get 28.
• Step 4: 4 goes into 28 seven times exactly (4x7=28).
• Result: The answer is 57 with a remainder of 0.

Practice Problem: Dividing 182 by 7

• Step 1: 7 goes into 18 two times (7x2=14).
• Step 2: Subtract 14 from 18 to get 4.
• Step 3: Bring down the 2 to get 42.
• Step 4: 7 goes into 42 six times (7x6=42).
• Result: The answer is 26 with a remainder of 0.

Example 2: Dividing 1720 by 8

• Step 1: 8 goes into 17 two times (8x2=16).
• Step 2: Subtract 16 from 17 to get 1.
• Step 3: Bring down the next digit to get 12.
• Step 4: 8 goes into 12 one time (8x1=8).
• Step 5: Subtract 8 from 12 to get 4.
• Step 6: Bring down the 0 to get 40.
• Step 7: 8 goes into 40 five times (8x5=40).
• Result: The answer is 215 with a remainder of 0.

Example 3: Dividing 1125 by 25

• Step 1: 25 goes into 112 four times (25x4=100).
• Step 2: Subtract 100 from 112 to get 12.
• Step 3: Bring down the 5 to get 125.
• Step 4: 25 goes into 125 exactly five times (25x5=125).
• Result: The answer is 45 with a remainder of 0.

Example 4: Dividing 2946 by 32

• Step 1: 32 goes into 249 seven times (32x7=224).
• Step 2: Subtract 224 from 249 to get 25.
• Step 3: Bring down the 6 to get 256.
• Step 4: 32 goes into 256 eight times (32x8=256).
• Result: The answer is 78 with a remainder of 0.

Example 5: Dividing 94,000,245 by 75

• Detailed steps and operations include subtracting from groups like 94 by 75, esult in partial quotients: 9, 2, 5, 6.
• Result: The answer is approximately 1256.6.

Example 6: Dividing 216,741 by 84

• Steps especially emphasize making a list of multiples of the divisor and sequentially subtracting from the dividend.
• Result: The answer is 2580.25.

Conclusion

Long division is a methodical process that helps break down division of large numbers by smaller divisors, step-by-step reducing the problem until the entire dividend is accounted for. It employs subtraction of multiples of the divisor and the periodic bringing down of digits from the dividend to refine the quotient and remainder until complete resolution. By following each example given, one can hone their skills in this essential mathematical procedure.