Back to Fluently divide multi-digit numbers using the standard algorithm

Fluently Divide Multi-Digit Numbers Using the Standard Algorithm

Show all steps of long division. Check every answer by multiplying: (divisor × quotient) + remainder = dividend.

Grade 6·22 problems·~35 min·Common Core Math - Grade 6·standard·6-ns-b-2

Work through problems with immediate feedback

Fluency Practice

$Long division setup for 756 ÷ 3. Three empty quotient digit positions labeled H, T, O are shown above the dividend.$

In the problem $756 \div 3$ , which digit of the quotient is found first using the standard algorithm?

The ones digit (6 ÷ 3 = 2)

The tens digit (5 ÷ 3)

The hundreds digit (7 ÷ 3 = 2)

All digits are found simultaneously.

Compute $756 \div 3$ using the standard algorithm. Show all four steps (Divide, Multiply, Subtract, Bring down) for each position.

Compute $1{,}428 \div 6$ . Write the quotient.

Compute $1{,}596 \div 38$ . Write the quotient.

Compute $261 \div 43$ . Check that the remainder is less than 43.

Varied Practice

In $216 \div 4$ , the first digit of the dividend (2) is smaller than the divisor (4). How should the algorithm proceed?

Combine the first two digits to form the first partial dividend: $21 \div 4 = 5$ R $1$ , then continue.

The problem cannot be solved because 4 > 2.

Write 2 above the first digit and continue.

Reverse the dividend: compute $612 \div 4$ instead.

Compute $431 \div 5$ . Write the quotient and remainder.

Compute $2{,}184 \div 6$ step by step.
$21 \div 6 =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ (write this digit above the hundreds).
Bring down 8: new partial dividend = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
$38 \div 6 =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . Bring down 4: new partial dividend = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
$24 \div 6 =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ R ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Quotient: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ R ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

21÷6:

new PD after 1st:

38÷6:

new PD after 2nd:

24÷6:

remainder:

quotient:

final remainder:

Compute $5{,}244 \div 52$ . Write the quotient and remainder.

When using a 2-digit divisor and your trial digit gives a remainder that is greater than or equal to the divisor, what should you do?

Decrease the trial digit by 1 and try again.

Accept the result — remainders can be any size.

Increase the trial digit by 1 and try again.

Start the problem over from the beginning.

Word Problems

A school is packing 136 students onto buses. Each bus holds 45 students.

Compute $136 \div 45$ using the standard algorithm. Write the quotient and remainder.

How many buses are needed to transport all 136 students?

3 buses

4 buses

3 buses and leave the extra student behind

$3\frac{1}{45}$ buses

A baker has 1,260 cookies to pack into boxes of 36.

How many full boxes can be packed? Are there any cookies left over?

A rope 1,125 cm long is cut into equal pieces of 25 cm each.

How many pieces are cut from the rope?

Mariana shares 25 inches of ribbon equally among 3 friends.

How much ribbon does each friend receive? Choose the correct answer and interpretation.

8 inches each (ignore the remainder)

9 inches each (round up the quotient)

$8\frac{1}{3}$ inches each (express the remainder as a fraction)

8 inches each, and 1 inch is wasted

Error Analysis

Tomas divides $1{,}428 \div 6$ . After the first step he has:

Divided: $14 \div 6 = 2$ (writes 2 above)
Multiplied: $2 \times 6 = 12$
Subtracted: $14 - 12 = 2$
He then writes the next quotient digit: $2 \div 6 = 0$ , then $28 \div 6 = 4$
His final answer: $204$

What step did Tomas skip that led to the wrong answer?

Tomas forgot to bring down the next digit of the dividend. He should have brought down the 2 from 1,428 to get 22, not 2.

Tomas used the wrong division fact. $14 \div 6$ is not 2.

Tomas should have started with the ones digit, not the thousands.

Tomas's answer of 204 is correct.

Carmen divides $186 \div 23$ .
Round $23 \approx 20$ ; $186 \div 20 \approx 9$ .
She tries 9: $9 \times 23 = 207 > 186$ — too large.
She tries 8: $8 \times 23 = 184$ ; remainder $= 186 - 184 = 2$ .
She checks: $2 < 23$ ✓. She writes quotient 8 R 2.
Then she writes: "Since the remainder 2 is very small, I'll just say the answer is 8."

Is Carmen's final answer correct? What should she report?

Carmen's computation is correct, but she should report the remainder: 8 R 2.

Carmen's answer of 8 is wrong; the correct quotient is 9.

Carmen should round up to 9 because the remainder is close to the divisor.

Carmen should try a larger trial digit because the remainder is too small.

Challenge / Extension

A library has 2,916 books to be sorted equally onto shelves. Each shelf holds 54 books. How many shelves are needed, and will any books be left on a partial shelf?

If you divide a number by 7 and get a quotient of 34 with remainder 5, what was the original number? Explain how you can find it without doing long division, and verify your answer.