L4 · Dividing 3-Digit by 1-Digit: Quotients with and without Remainders

Learning goal

“I can divide a 3-digit number by a 1-digit number one place at a time, write the quotient with a remainder when the sharing is not exact (like 41 r 4), and check every division by multiplying: quotient x divisor + remainder = the number I started with.”

Dividend — the number being shared or split up. In 468 / 4, the dividend is 468.

Divisor — the number of groups (or the size of each group). In 468 / 4, the divisor is 4.

Quotient — the result of the division: how many in each group. In 468 / 4 = 117, the quotient is 117.

Remainder — what is left over when the sharing cannot be finished exactly. In 250 / 6 = 41 r 4, the remainder is 4.

Worked example

468 / 4. Step 1 (hundreds): 4 hundreds / 4 = 1 hundred in each group. Write 1 in the hundreds place of the quotient. Step 2 (tens): 6 tens / 4 = 1 ten each, with 2 tens left over. Write 1 in the tens place. Trade the 2 leftover tens for 20 ones: now there are 20 + 8 = 28 ones. Step 3 (ones): 28 / 4 = 7. Write 7. Quotient: 117. Check by multiplying: 117 x 4 = 468 - division checked by its fact family. Say it plainly: long division is sharing by place value. Whatever a place cannot share gets TRADED down to the next place - never thrown away, never ignored.

Check yourself — explain it

The 2 leftover tens became 28 ones because...

Paired problem — example still visible

525 / 5 -> hundreds: 5 / 5 = 1; tens: 2 / 5 cannot make a whole ten each - write 0, trade 2 tens with the 5 ones -> 25 ones; ones: 25 / 5 = 5 -> 105. (Notice the 0 in the quotient - it holds the tens place!)

Faded completion — last step is yours

"693 / 3: hundreds 6 / 3 = 2; tens 9 / 3 = ___; ones 3 / 3 = 1. Quotient: ___." -> 3; 231

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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