Same Math › Grades 4–5 › Partial quotients
What is partial quotients division?
Partial quotients divides by taking away easy groups of the divisor, one chunk at a time, and keeping a tally. When nothing is left, you add up the groups.
- Take away easy groups: 100 groups of 6 is 600.
- Keep a tally of the groups on the right side.
- Add the tally: 100 + 20 + 7 = 127
Why schools teach it
Kids always know what the answer means
Long division asks for four steps at once (divide, multiply, subtract, bring down), and it's easy to get lost. Partial quotients turns division into subtraction with friendly numbers, and the answer always means the same thing: how many groups of 6 fit in 762.
In grades 4 and 5 the standards call for division strategies based on place value (4.NBT.B.6, 5.NBT.B.6). The standard long-division method is a 6th-grade standard (6.NS.B.2).
At the kitchen table
What to say, and what to skip
Say this
How many 6s can you easily take away? Can you do 100 groups?
What's left now?
Is there a bigger chunk you could take?
Any chunk that fits is correct. Bigger ones just mean fewer steps.How many groups did you take altogether?
That's the answer. Adding the tally is the last step.
Skip this
Do it the long-division way: divide, multiply, subtract, bring down.
That's a 6th-grade standard. Mixing the two now confuses both.- Marking it wrong because it took more steps.Taking 10 groups six times instead of 60 at once is slow, but correct.
- Expecting the biggest possible chunk every time.Speed comes with practice. Correct chunks come first.
See it in action
How a 4th grader solves 384 ÷ 8
Take away 40 groups of 8
40 × 8 = 320, 384 − 320 = 64Take away 8 more groups
8 × 8 = 64, 64 − 64 = 0Add the groups
40 + 8 = 48
A child who started with 10 groups at a time would take more steps and still get 48.
Free practice sheet
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Parents also ask
Why do some classes call it the Big 7?
Some classes start by listing easy multiples of the divisor, such as 1, 2, 5, 10, 20, 50 and 100 times, then use them as chunks. Ask the teacher which list your child's class uses.
What about remainders?
Whatever is left that's smaller than the divisor is the remainder. 50 ÷ 8 is 6 R 2.
Is it the same as long division?
It's the same math with more of the steps written down. Long division packs those steps into a shorter layout.
Does it work with two-digit divisors?
Yes. That's the 5th-grade version, like 552 ÷ 23.