A learner decomposes a dividend into convenient, known multiples of a one-digit divisor, finds the corresponding partial quotients, and adds them to determine the total quotient; for example, can be viewed as . This reasoning connects multiplication and division and can include a remainder when the decomposition does not divide evenly, but does not extend to formal long division, multi-digit divisors, or generalized partial-quotient algorithms.
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Detailed Explanation: Use partial quotients informally
To use partial quotients, break the dividend into parts that are easy to divide. Divide each part, then add the answers.
Example: Find .
- Break into convenient parts:
- Divide each part by :
- Add the partial quotients:
So,
Check with multiplication: .
Learn by doing: Use partial quotients informally
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Practice:
Division as Fraction - With Remainder 2 x 1
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Download/Modify Free Grade 3 'Use partial quotients informally' Worksheet
Print this free 'Use partial quotients informally' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Division as Fraction - With Remainder 2 x 1
- Division as Fraction - No Remainder 2 x 1
- Division Equation - With Remainder 2 x 1
- Digit Solving - Long Division (Next Step) - One Step, With Remainder - Identify Quotient
- Digit Solving - Long Division (Next Step) - One Step, No Remainder - Identify Quotient
- Division Cards Model - Deck and Hand Size to Player Count - No Remainder (1 Digit)
- Division Cards Model - Deck and Hand Size to Player Count - No Remainder (2 Digit)
- Division Cards Model - Deck and Player Count to Hand Size - With Remainder (1 Digit)
Units Teaching This Skill
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