Andre calculated using a method that was different from Kiran's.
Andre subtracted 600 from 657. What does the 600 represent?
Andre wrote 10 above the 200, and then subtracted 30 from 57. How is the 30 related to the 10?
What do the numbers 200, 10, and 9 represent?
What is the meaning of the 0 at the bottom of Andre’s work?
How might Andre calculate ? Explain or show your reasoning.
10.3
Activity
What’s the Quotient?
Find the value of each quotient. Show your reasoning. Use vertical calculations at least once.
Student Lesson Summary
Another way to find the quotient of 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 :
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 () 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 using partial quotients. We can calculate with fewer steps by removing groups of larger sizes.