L3 · Dividing 3-digit by 1-digit: standard algorithm

Learning goal

“I can divide a 3-digit number by a 1-digit number using the standard algorithm - sharing hundreds, then tens, then ones - and check my quotient by multiplying.”

Dividend — the number being shared or grouped. In 672 / 4, the dividend is 672.

Divisor — the number you divide by: the size of each group, or the number of groups. In 672 / 4, the divisor is 4.

Quotient — the answer to a division. The quotient of 672 / 4 is 168.

Remainder — what is left over when the sharing does not come out exact. (This lesson's divisions come out exact; remainders get their own lesson next.)

Worked example

Compute 672 / 4. Step 1: Share the hundreds: 6 hundreds / 4 = 1 hundred each, with 2 hundreds left over. Write 1 in the hundreds place of the quotient. Unbundle the 2 leftover hundreds into 20 tens: now there are 20 + 7 = 27 tens. Step 2: Share the tens: 27 tens / 4 = 6 tens each, with 3 tens left over. Write 6 in the tens place. Unbundle the 3 leftover tens into 30 ones: now there are 30 + 2 = 32 ones. Step 3: Share the ones: 32 ones / 4 = 8 ones each, nothing left over. Write 8. Quotient: 168. Check by multiplying: 168 x 4 = 672. Say it plainly: the algorithm is fair sharing done in three rounds - big pieces first, leftovers unbundled into the next smaller place each time.

Check yourself — explain it

After step 1, why do we work with 27 tens instead of just the 7 tens in 672?

Paired problem — example still visible

Compute 945 / 5, then check by multiplying. -> Hundreds: 9 / 5 = 1 r 4, giving 45 tens; tens: 45 / 5 = 9 r 0, giving 5 ones; ones: 5 / 5 = 1. Quotient 189; check 189 x 5 = 945.

Faded completion — last step is yours

"736 / 8: hundreds 7 / 8 = 0, so start with tens: 73 / 8 = 9 r 1; ones: 16 / 8 = ___. Quotient = ___" -> 2; 92

Ready to practise?

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

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