One way to find the quotient of is by using partial quotients, in which we keep subtracting 3 groups of some amount from 948. We can organize the steps and record the partial quotients in a vertical calculation.

Here are two calculations for finding :

2 partial quotients methods of 948 divided by 3. First calculation, 11 rows. First row: 316. Second row: 1. Third row: 15. Fourth row: 300. Fifth row: 3, long division symbol with 948 inside. Sixth row: minus 900, 3 groups of 300. Horizontal line. Seventh row: 48. Eighth row: minus 45, 3 groups of 15. Horizontal line. Ninth row: 3. Tenth row: minus 3, 3 groups of 1. Horizontal line. Eleventh row: 0. Second calculation, 11 rows. First row: 316. Second row: 150. Third row: 150. Fourth row: 16. Fifth row: 3, long division symbol with 948 inside. Sixth row: minus 48, 3 groups of 16. Horizontal line. Seventh row: 900. Eighth row: minus 450, 3 groups of 150. Horizontal line. Ninth row: 450. Tenth row: minus 450, 3 groups of 150. Horizontal line. Eleventh row: 0

• In the calculation on the left, first we subtract 3 groups of 300, then 3 groups of 15, and then 3 groups of 1. Adding up the partial quotients ( ) gives us 316.
• The calculation on the right shows a different amount per group subtracted each time (3 groups of 16, 3 groups of 150, and 3 more groups of 150), but the total amount in each of the 3 groups is still 316.

There are other ways of calculating using partial quotients. We can calculate with fewer steps by removing groups of larger sizes.

Long division is another method for calculating quotients. It relies on place value to perform and record the division.

When we use long division, we work from left to right and with one digit at a time, starting with the leftmost digit of the dividend. We remove the largest group possible each time, using the placement of the digit to indicate the size of each group.

Here is an example of how to find using long division.

Long division of 948 divided by 3. 8 rows. First row: 316. Second row: 3, long division symbol with 948 inside. Third row: minus 9, 3 groups of 3 hundreds. Horizontal line. Fourth row: 4. Fifth row: minus 3, 3 groups of 1 ten. Horizontal line. Sixth row: 18. Seventh row: minus 18, 3 groups of 6 ones. Horizontal line. Eight row: 0.

• We start by dividing 9 hundreds into 3 groups, which means 3 hundreds in each group. Instead of writing 300, we simply write 3 in the hundreds place, knowing that it means 3 hundreds.

• There are no remaining hundreds, so we work with the tens. We can make 3 groups of 1 ten out of 4 tens, so we write 1 in the tens place above the 4 of 948. Subtracting 3 tens from 4 tens, we have a remainder of 1 ten.

• We know that 1 ten is 10 ones. Combining these with the 8 ones from 948, we have 18 ones. We can make 3 groups of 6 ones, so we write 6 in the ones place.

In total, there are 3 groups of 3 hundreds, 1 ten, and 6 ones in 948, so .