Find the value of each expression mentally.

Jada uses partial quotients to find out how many groups of 7 are in 392.

1. Analyze Jada’s steps in the partial-quotients algorithm.

   

   Divide. 3 hundred ninety 2 divided by 7, 11 rows. First row: fifty 6. Second row: 9. Third row: 7. Fourth row: 40. Fifth row: 7, long division symbol with 3 hundred ninety 2 inside. Sixth row: minus 2 hundred eighty. Horizontal line. Seventh row: one hundred twelve. Eighth row: minus 49. Horizontal line. Ninth row: sixty 3. Tenth row: minus sixty 3. Horizontal line. Eleventh row: 0.

   1. Look at the 3 numbers above 392. What do they represent?
   2. Look at the 3 subtractions below 392. What do they represent?

2. Show another way you can decompose 392 to divide by 7.

3. Use a partial-quotients algorithm to find the value of .

Andre and Elena divide 2,315 by 5. Before they begin, Andre says, “I can already tell that the quotient is going to be less than 500.”

1. Decide if you agree with Andre without doing any calculations. Explain your reasoning.

2. Here is Andre and Elena’s work. Each student made one or more errors. Identify the errors each student made. Then show a correct computation.

   Andre’s Work

   

   Divide. 2 thousand 3 hundred 15 divided by 5, 11 rows. First row: 1 hundred 3. Second row: 3. Third row: sixty. Fourth row: 40. Fifth row: 5, long division symbol with 2 thousand 3 hundred 15 inside. Sixth row: minus two thousand. Horizontal line. Seventh row: 3 hundred 16. Eighth row: minus 3 hundred. Horizontal line. Ninth row: 16. Tenth row: minus 15. Horizontal line. Eleventh row: 0.

   Elena’s Work

   

   Divide. 2 thousand 3 hundred 15 divided by 5, 11 rows. First row: 4 hundred. Second row: 60. Third row: 100. Fourth row: 3 hundred. Fifth row: 5, long division symbol with 2 thousand 3 hundred 15 inside. Sixth row: minus 1 thousand 5 hundred. Horizontal line. Seventh row: 8 hundred 15. Eighth row: minus 5 hundred. Horizontal line. Ninth row: 3 hundred 15. Tenth row: minus 3 hundred. Horizontal line. Eleventh row: 15.

Here are 4 calculations to find the value of , but each one is unfinished.

Complete at least 2 of the unfinished calculations.

A

Divide. 3 thousand 2 hundred 94 divided by 3, 6 rows. First row: 90. Second row: 1 thousand. Third row: 3, long division symbol with 3 thousand 2 hundred 94 inside. Fourth row: minus 3 thousand, side note 3 times 1 thousand. Horizontal line. Fifth row: 2 hundred 94. Sixth row: minus 2 hundred 70, side note 3 times 90. Horizontal line.

B

Divide. 3 thousand 2 hundred 94 divided by 3, 12 rows. First row: 80. Second row: 2 hundred. Third row: 4 hundred. Fourth row: 4 hundred. Fifth row: 3, long division symbol with 3 thousand 2 hundred 94 inside. Sixth row: minus 1 thousand two hundred, side note 3 times 4 hundred. Horizontal line. Seventh row: 2 thousand 94. Eighth row: minus one thousand 2 hundred, side note 3 times 4 hundred. Horizontal line. Ninth row: 8 hundred 94. Tenth row: minus 6 hundred, side note 3 times 2 hundred. Horizontal line. Eleventh row: 2 hundred 94. Twelfth row: minus 2 hundred 40, side note 3 times 80. Horizontal line.

C

D