Division with remainder, divisibility by 9 and 3
Find out why the remainder is smaller than the divisor, build the dividend with a = bq + r and test divisibility by 9 and 3 by the digit sum.
- Ukraine: grade 5
Guide
This follows the Ukrainian books: Year 5 item 19 "Division with remainder"; Year 6 part 1 item 3 "Tests of divisibility by 9 and by 3". Division is written in the long (corner) layout shown under the exercise. The child fills the boxes or types a number.
In division with remainder the dividend a = bq + r, where b is the divisor, q the partial quotient and r the remainder, with r < b. If r = 0 the number divides exactly. Example: 189 = 13 · 14 + 7.
Test for 9: a number is divisible by 9 exactly when its digit sum is divisible by 9. The same for 3. For example 4869: 4 + 8 + 6 + 9 = 27, so it is divisible by 9 and by 3.