Skip to content

Divide Up to Four-Digit Dividends by Two-Digit Divisors Using Area Models or Partial Quotients

Students use the partial quotients strategy or area model to divide up to four-digit dividends by two-digit divisors. They subtract multiples of the divisor from the dividend in stages, recording each partial quotient, then summing to find the total quotient.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Divide Up to Four-Digit Dividends by Two-Digit Divisors Using Area Models or Partial Quotients

Grade 5 · Whole Number Division with Multi-Digit Dividends · question 1 of 3

0 of 20

20 rungs. A star at the top.

187 ÷ 11 =

How it is taught

0:00 of 5:46

Partial quotients take friendly chunks of the divisor at a time.

Each chunk is a piece of the quotient you add at the end.

Read it: Dividing in chunks

864 ÷ 24: take out 30 twenty-fours, which is 720, and 144 is left. Take out 6 more twenty-fours, which is 144, and 0 is left. 30 + 6 = 36, so 864 ÷ 24 = 36.

  1. Take out an easy chunk of the divisor, such as 10 or 30 of them.
  2. Subtract to see what is left, and take out another chunk.
  3. When nothing is left, add the chunks: that sum is the quotient.

Each chunk is a number of 24s, so the chunks together count how many 24s are in 864.

Tens of the divisor are easy to multiply: 30 × 24 is 3 × 24 with a 0 after it, 720.

Any chunk that fits works; bigger chunks just take fewer steps.

Take out chunks of the divisor until nothing is left, then add the chunks.

Adding what was taken out: 720 + 144 = 864, the number we started with.

Add how many 24s were taken out: 30 + 6 = 36.

1035 ÷ 23 = ___ — 45. Take 40 + 5 groups of 23: 45.

1,248 ÷ 24

One thousand two hundred forty-eight stickers, shared evenly among twenty-four classmates. How many does each one get?

Write it out: one thousand two hundred forty-eight inside the division house, twenty-four outside. Twenty-four is a two-digit divisor, so guessing one digit at a time is hard — partial quotients is easier.

Instead of the exact answer, take out a big, friendly chunk. How many twenty-fours fit inside one thousand two hundred forty-eight?

Forty is a safe guess. Twenty-four times forty is nine hundred sixty, and that fits. Write forty in the partial-quotients column.

Twenty-four times forty is nine hundred sixty. Write minus nine hundred sixty underneath.

One thousand two hundred forty-eight minus nine hundred sixty leaves two hundred eighty-eight.

Keep going with what is left. Twenty-four times ten is two hundred forty, which fits inside two hundred eighty-eight. Write ten in the column.

Twenty-four times ten is two hundred forty. Write minus two hundred forty.

Two hundred eighty-eight minus two hundred forty leaves forty-eight.

Almost there. Twenty-four times two is forty-eight — exactly what is left. Write two in the column.

Twenty-four times two is forty-eight. Write minus forty-eight.

Forty-eight minus forty-eight is zero. Nothing left over, so there is no remainder.

Here is the step everyone forgets: add the partial quotients. Forty plus ten plus two is fifty-two.

One thousand two hundred forty-eight divided by twenty-four is fifty-two. Each classmate gets fifty-two stickers. Your chunks do not have to match mine — any friendly numbers that add up will land on the same answer.

1,248 stickers, 24 classmatesHow many does each one get?241248Partial quotients40−96028810−240482−480+52ANSWER5240 + 10 + 2
Grade 5 · Sharing 1,248 stickers among 24 classmates

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free