Long Division Explained

Division Basics

• Division is splitting into equal parts or groups.
• Division with a remainder does not go past the integer.
• The goal is to find out how many times 34 can fit into 731.
• The result is known as the quotient.
• If 34 doesn't divide 731 perfectly, there will be a remainder.
• This type of division leads to the Euclidean equality.

Steps for Division

• Break down the division into smaller parts.
• Start from left to right.
• First, consider how many times 34 goes into 7, recognizing it doesn't work because 7 is too small.
• Then, determine how many times 34 goes into 73.

Estimating the Quotient

• Do quick calculations to the side as needed.
• Multiplying 34 by 2 results in 68.
• Multiplying 34 by 3 exceeds 73, so 2 is the correct quotient.
• Write the 2 in the quotient position.

Calculating Remainder

• Multiply 2 by 34.
• From previous steps, 2 x 34 = 68.
• Subtract 68 from 73.
• 73 - 68 = 5.

Iterating the Process

• Bring down the next digit (1) next to the 5, resulting in 51.
• Determine how many times 34 goes into 51.

Final Steps

• 34 goes into 51 only once.
• Write 1 next to 2 in the quotient.
• Calculate 1 x 34 = 34.
• Subtract 34 from 51.
• 51 - 34 = 17.
• Since there are no more numbers to bring down, the division is complete.

Division Terminology

• 731 (the original number being divided) is the dividend.
• 34 (the number dividing the dividend) is the divisor.
• 21 (the result of the division) is the quotient.
• 17 (what is left over after division) is the remainder.

Euclidean Equality

• It represents the division.
• 731 = 21 x 34 + 17.
• Dividend = (Quotient x Divisor) + Remainder.
• Euclidean is from the Greek mathematician Euclid.
• Euclid studied arithmetic and divisibility thousands of years ago.