Another way to find the quotient of $345 \div 3$ is by using partial quotients, in which we keep subtracting 3 groups of some amount from 345. We can organize the steps and record the partial quotients in a vertical calculation.

Here are two calculations for finding $345 \div 3$:

2 partial quotients methods of 345 divided by 3. First calculation, 11 rows. First row: 115. Second row: 5. Third row: 10. Fourth row: 100. Fifth row: 3, long division symbol with 345 inside. Sixth row: minus 300, 3 groups of 100. Horizontal line. Seventh row: 45. Eighth row: minus 30, 3 groups of 10. Horizontal line. Ninth row: 15. Tenth row: minus 15, 3 groups of 5. Horizontal line. Eleventh row: 0. Second calculation, 11 rows. First row: 115. Second row: 50. Third row: 50. Fourth row: 15. Fifth row: 3, long division symbol with 345 inside. Sixth row: minus 45, 3 groups of 15. Horizontal line. Seventh row: 300. Eighth row: minus 150, 3 groups of 50. Horizontal line. Ninth row: 150. Tenth row: minus 150, 3 groups of 50. Horizontal line. Eleventh row: 0

• In the calculation on the left, first we subtract 3 groups of 100, then 3 groups of 10, and then 3 groups of 5. Adding up the partial quotients ($100+10+5$) gives us 115.
• The calculation on the right shows a different amount per group subtracted each time (3 groups of 15, 3 groups of 50, and 3 more groups of 50), but the total amount in each of the 3 groups is still 115.

There are other ways of calculating $345 \div 3$ using partial quotients. We can calculate with fewer steps by removing groups of larger sizes.