Partial –Quotients Division Algorithm
To find the number of 8s in 453, first find all the partial quotients. Record them in a column to the right of the
problem. Then add the partial quotients to find the final quotient or answer.
EXAMPLE
(dividend)
(divisor)
456 ÷ 8
Ask: How many 8s are in 456 (at least 50).
The first partial quotient is 50.
50 X 8 = 400
Subtract 400 from 456.
8 456
400 50
56
56
7
0 57
Ask: How many 8s are in 56? (7)
The second partial quotient is 7.
7 X 8 = 56
Subtract 56 from 56.
The difference is 0. So there is no remainder.
Add the partial quotients. The answer is 57.
456 ÷ 8 = 57
Long Division (Standard) with Models
Use base-10 blocks to model the dividend. Then make trades until you have the correct number of equal groups.
(dividend)
3 hundreds cannot be divided into 6 equal groups. So rename 3 hundreds as 30 tens.
377 ÷ 6
6
6 377
36
1
Divide 37 tens into 6 equal groups. Each group has 6 tens and 1 ten remains.
1 ten cannot be divided into 6 equal groups. So rename 1 ten as 10 ones. There are
now 17 ones.
Divide 17 ones into 6 equal groups.
5 ones remain.
Divide 17 ones into
377 ÷ 6
(divisor)
62 R5
6
6 377
36
17
62
6 377
36
17
12
5