Basic Long Division (No Remainder)

Calculate $96 \div 4$

Set up the problem: Write 4 outside and 96 inside the division bracket = $4\overline{\smash{)}96}$

Divide: How many 4s in 9?: $9 \div 4 = 2$ (with remainder) = Write 2 above the 9

Multiply: $2 \times 4$: $2 \times 4 = 8$ = Write 8 below the 9

Subtract: $9 - 8$: $9 - 8 = 1$ = Write 1 below

Bring down the 6: Bring down the 6 next to the 1 = Now we have 16

Divide: How many 4s in 16?: $16 \div 4 = 4$ exactly = Write 4 above the 6

Multiply and subtract: $4 \times 4 = 16$, then $16 - 16 = 0$ = Remainder is 0

Answer: $96 \div 4 = 24$

Long Division with Two-Digit Divisor

Calculate $468 \div 12$

Set up the problem: Write 12 outside and 468 inside the division bracket = $12\overline{\smash{)}468}$

Divide: How many 12s in 4?: $4 \div 12 = 0$ (too small) = Look at first two digits: 46

Divide: How many 12s in 46?: $46 \div 12 = 3$ (since $12 \times 3 = 36$ and $12 \times 4 = 48$ is too big) = Write 3 above the 6

Multiply: $3 \times 12$: $3 \times 12 = 36$ = Write 36 below 46

Subtract: $46 - 36$: $46 - 36 = 10$ = Write 10 below

Bring down the 8: Bring down the 8 next to 10 = Now we have 108

Divide: How many 12s in 108?: $108 \div 12 = 9$ (since $12 \times 9 = 108$) = Write 9 above the 8

Multiply and subtract: $9 \times 12 = 108$, then $108 - 108 = 0$ = Remainder is 0

Answer: $468 \div 12 = 39$

Long Division with Remainder

Calculate $157 \div 6$

Set up the problem: Write 6 outside and 157 inside the division bracket = $6\overline{\smash{)}157}$

Divide: How many 6s in 15?: $15 \div 6 = 2$ (since $6 \times 2 = 12$ and $6 \times 3 = 18$ is too big) = Write 2 above the 5

Multiply: $2 \times 6$: $2 \times 6 = 12$ = Write 12 below 15

Subtract: $15 - 12$: $15 - 12 = 3$ = Write 3 below

Bring down the 7: Bring down the 7 next to 3 = Now we have 37

Divide: How many 6s in 37?: $37 \div 6 = 6$ (since $6 \times 6 = 36$) = Write 6 above the 7

Multiply and subtract: $6 \times 6 = 36$, then $37 - 36 = 1$ = Remainder is 1

Answer: $157 \div 6 = 26$ remainder $1$, or $26\text{ R}1$

Mistake: Forgetting to bring down the next digit

Why: After subtracting, students sometimes try to divide the small remainder instead of bringing down the next digit.

Correct: Always bring down the next digit after subtracting. If you have 3 remaining and the next digit is 7, you now work with 37.

Mistake: Using a quotient that's too large

Why: Students guess a number that, when multiplied by the divisor, gives a result larger than what they're dividing into.

Correct: If your multiplication result is bigger than the number you're working with, try a smaller quotient. For example, if dividing 32 by 7, try 4 (not 5, because $7 \times 5 = 35 > 32$).

Mistake: Placing digits in the wrong position in the quotient

Why: Students write the quotient digits without aligning them properly above the correct digits of the dividend.

Correct: Each digit in the quotient should be written directly above the last digit you brought down.

Mistake: Stopping too early with a remainder

Why: Students get a non-zero remainder and think they're done, even though there are more digits to bring down.

Correct: Keep going until you've brought down every digit. Only then is the remaining number your final remainder.

Splitting Items Equally

When you need to divide items among a group of people fairly.

A teacher has 156 pencils to distribute equally among 12 students. $156 \div 12 = 13$ pencils per student.

Calculating Unit Price

Finding how much one item costs when you know the total cost of multiple items.

A pack of 8 notebooks costs 24 dollars. Each notebook costs $24 \div 8 = 3$ dollars.

Planning and Scheduling

Figuring out how to organize time or resources into equal parts.

A road trip is 420 kilometers. If you drive 60 kilometers per hour, the trip takes $420 \div 60 = 7$ hours.

Q: How do I know which number to try first?

A: Estimate! Ask yourself: 'How many times does the divisor fit into this number without going over?' If $12 \times 3 = 36$ and $12 \times 4 = 48$, and you're dividing into 46, use 3.

Q: What if the divisor is bigger than the first digit?

A: Use more digits! If dividing 468 by 12, you can't fit 12 into 4, so look at 46 instead.

Q: What do I do with the remainder?

A: It depends on the context. Sometimes you write it as 'R3', sometimes as a fraction (like $\frac{3}{7}$), and sometimes you round up or down based on the situation.