Unit 5, Lesson 10
Using Partial Quotients
Grade 6
Practice
Problem 1
Here is one way to find \(2,\!105 \div 5\) using partial quotients. Show a different way of using partial quotients to divide 2,105 by 5.
Partial quotient method of 2,105 divided by 5, 11 rows. First row: 421. Second row: 1. Third row: 20. Fourth row: 400. Fifth row: 5, long division symbol with 2,105 inside. Sixth row: minus 2,000. Horizontal line. Seventh row: 105. Eighth row: minus 100. Horizontal line. Ninth row: 5. Tenth row: minus 5. Horizontal line. Eleventh row: 0.
Problem 2
Andre and Jada both found \(657 \div 3\) by using partial quotients, but they did the calculations differently, as shown here.
Andre and Jada's calculation of a partial product problem, 657 divided by 3. Andre's calculation. 657 inside the division bar, divided by 3. 3 divides into 657, 200 times. Subtract 600 from 657 for a remainder of 57. 3 divides into 57, 10 times. Subtract 30 from 57 for a remainder of 27. 3 divides into 27, 9 times. Subtract 27 from 27 for a remainder of 0. Add all of Andre's partial quotients of 200, 10 and 9 for a total of 219. Jada's calcluation. 657 inside the division bar, divided by 3. 3 divides into 657, 50 times. Subtract 150 from 657 for a remainder of 507. 3 divides into 507, 100 times. Subtract 300 from 507 for a remainder of 207. 3 divides into 207, 60 times. Subtract 180 from 207 for a remainder of 27. 3 divides into 27, 9 times. Subtract 27 from 27 for a remainder of 0. Add all of Jada's partial quotients of 50, 100, 60 and 9 for a total of 219.
- How is Jada's work the same as Andre’s work? How is it different?
- Explain why they have the same answer.
Problem 4
Here is an incomplete calculation of \(534\div 6\).
Write the missing numbers (marked with “?”) that would make the calculation complete.
An incomplete calculation of 534 divided by 6, 8 rows. First row: 89. Second row: 9. Third row: 80. Fourth row: 6, long division symbol with 534 inside. Fifth row: minus question mark symbol. Horizontal line. Sixth row: question mark symbol. Seventh row: minus question mark symbol. Horizontal line. Eighth row: 0.