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Division with remainders

Division with remainders

Japanese school year: Elementary 3

What you learn

Students learn how to calculate quotients and remainders when numbers do not divide evenly, recognizing that remainders must be smaller than divisors. This applies to everyday situations like packing items into equal bags. Prior knowledge of basic division using multiplication tables and simple subtraction is helpful.

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Key points

The dividend a equals divisor b × quotient q + remainder r. Use this formula to check your answer.

a=b×q+ra = b \times q + r

The remainder r is 0 or more, and must be smaller than divisor b. Use this to check your remainder.

0≤r<b0 \le r < b

When remainder r is 0, the number divides evenly, and dividend a matches divisor b × quotient q.

r=0  ⟺  a=b×qr = 0 \iff a = b \times q

Choose a set to practice.