Long Division (Standard Algorithm for Division)

Place value is the value of a digit based on its place in a number. The place value of a digit is 10 times the place value of the digit to its right.

Thousands place.

6 × 100 + 7 × 10 + 2 × 1, or 6 one hundreds, 7 tens, and 2 ones.

When I break a number up to divide using an area model, I break it apart by place value. When I divide a number using partial quotients I try to find the largest multiple of the divisor so that there is none of the greatest place value left after I subtract.

Students may use partial quotients or an area model. Some may think of the problem as 48 ÷ 12 = 4, and then multiply by 10 to get 40.

Divide, Multiply, Subtract, Bring down

When I divide, I can look at multiples of the divisor to help me find the dividend.

When there are no more digits to bring down and I have a remainder of 0, or when there are no more digits to bring down and the remainder is smaller than the divisor.

The standard algorithm is a very efficient way to divide.

I can start by making a list of multiples of 7. 4 is less than 7, so consider multiples of 7 close to 45. Multiply: 7 × 6 = 42. Subtract: 45 – 42 = 3. Bring down the 6 to make 36. Find multiples of 7 close to 36. Multiply: 7 × 5 = 35. Subtract: 36 – 35 = 1. Bring down the 4 to make 14. Find multiples of 7 close to 14. Multiply: 7 × 2 = 14. Subtract: 14 – 14 = 0. No numbers remain to bring down, and the remainder is 0. 4,564 ÷ 7 = 652.