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fact-minute

Grades 1–5 · printable + timed

Dividing by 9 Timed Test

Print it with the answer key on page 2, or run the timer here.

Operation
Fact range
Problems
Time limit

Division · 9s · 20 problems · 1 minute NameDateScore
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6
  7. 7
  8. 8
  9. 9
  10. 10
  11. 11
  12. 12
  13. 13
  14. 14
  15. 15
  16. 16
  17. 17
  18. 18
  19. 19
  20. 20
Answer key · Division · 9s · 20 problems NameDate
  1. 1 54 ÷ 9 6
  2. 2 36 ÷ 4 9
  3. 3 81 ÷ 9 9
  4. 4 54 ÷ 6 9
  5. 5 99 ÷ 11 9
  6. 6 18 ÷ 9 2
  7. 7 9 ÷ 1 9
  8. 8 108 ÷ 12 9
  9. 9 9 ÷ 1 9
  10. 10 9 ÷ 9 1
  11. 11 27 ÷ 9 3
  12. 12 9 ÷ 1 9
  13. 13 72 ÷ 8 9
  14. 14 90 ÷ 9 10
  15. 15 0 ÷ 9 0
  16. 16 81 ÷ 9 9
  17. 17 63 ÷ 9 7
  18. 18 99 ÷ 11 9
  19. 19 36 ÷ 9 4
  20. 20 54 ÷ 9 6
0 correct of 20

Correct 0 Wrong 0 Blank 20

0:00 elapsed of 1:00

Elapsed 0s Left 60s

A timed sheet on dividing by 9

Dividing by 9, from 0 ÷ 9 to 108 ÷ 9. Every problem on the sheet is drawn from that set and nothing outside it.

Choose 20, 50 or 100 problems and a limit of 1, 2 or 5 minutes, then print the sheet with its answer key on page two, or start the timer and type into the same grid. The problems are drawn again every time the page loads, so a second sheet is not a copy of the first. How the counts and limits work is on its own page, along with what a timed test does and does not measure.

Thirteen rows, with the answers

Dividing by 9: all thirteen facts and their answers.
Problem Answer
0 ÷ 9 0
9 ÷ 9 1
18 ÷ 9 2
27 ÷ 9 3
36 ÷ 9 4
45 ÷ 9 5
54 ÷ 9 6
63 ÷ 9 7
72 ÷ 9 8
81 ÷ 9 9
90 ÷ 9 10
99 ÷ 9 11
108 ÷ 9 12

Where dividing by 9 goes wrong

A number divisible by 9 has digits that sum to a multiple of 9 — 72 gives 7 + 2 = 9, and 108 gives 1 + 0 + 8 = 9. That rule makes dividing by 9 easier than multiplying by it: confirm from the dividend that 9 goes in at all, and only then count how many times.

Three that come up

How do you spot a multiple of 9?
Its digits add to 9 or to a multiple of 9. 63 gives 9, 108 gives 9.
Is dividing by 9 easier than multiplying by 9?
Often, because the digit-sum rule confirms the dividend before the child has to recall the quotient.
What about 99 ÷ 9?
It is 11, and the digit sum of 99 is 18, still a multiple of 9.

What the standards and the critics actually say

Common Core State Standards for Mathematics (PDF), page 23 — 3.OA.C.7 “By the end of Grade 3, know from memory all products of two one-digit numbers.” thecorestandards.org — CCSSI_Math Standards.pdf

NCTM — Procedural Fluency in Mathematics (position statement) “Timed tests do not assess fluency and can negatively affect students, and thus should be avoided.” nctm.org — Procedural Fluency in Mathematics

youcubed — Fluency Without Fear “For about one third of students the onset of timed testing is the beginning of math anxiety.” youcubed.org — Fluency Without Fear