Table of 9

How to say the table of 9

Nine one is 9, nine twos are 18, nine threes are 27, nine fours are 36, nine fives are 45, nine sixes are 54, nine sevens are 63, nine eights are 72, nine nines are 81, nine tens are 90.

In Hindi

नौ एकम नौ, नौ दूनी अठारह, नौ तिया सत्ताईस, नौ चौके छत्तीस, नौ पंजे पैंतालीस, नौ छक्के चौवन, नौ सत्ते तिरसठ, नौ अट्ठे बहत्तर, नौ नवें इक्यासी, नौ दहाई नब्बे।

This is the traditional chant used in Hindi-medium schools. The words for the multiplier (एकम, दूनी, तिया and so on) vary a little from region to region. All the pahade from 2 to 20 are on the Hindi pahade page.

A quick way to work it out

Take ten times the number and remove one lot. For 9 × 7, ten sevens are 70, less 7 is 63. Up to 9 × 10, the two digits of every answer add up to 9 (63 gives 6 + 3), and the tens digit is one less than the number you multiplied by. So for 9 × 7 the tens digit is 6 and the units digit is whatever makes 9: that is 3.

Patterns in the table of 9

• Last digit. The last digits of the first ten answers are 9, 8, 7, 6, 5, 4, 3, 2, 1 and 0. Each digit from 0 to 9 appears exactly once, which happens only for numbers ending in 1, 3, 7 or 9. After × 10 the same order repeats.
• Odd and even. 9 is odd, so the answers go odd, even, odd, even: 9, 18, 27, 36, 45 and 54. An odd number times an odd number is odd, and times an even number is even.
• Digit totals. Add the digits of any answer, and add again if you get two digits: you always reach 9. For example 63 gives 6 + 3 = 9. This is true for every multiple of 9.
• Steps of 9. Each answer is 9 more than the one above it. So if 9 × 7 slips your mind, take 9 × 6 = 54 and add 9 to get 63.
• Total of the first ten. Add the first ten answers and you get 495. That is 55 × 9, because 1 + 2 + 3 and so on up to 10 is 55.

How the table of 9 is built

9 is not prime: it can be written as 3 × 3. So its table can be built from a smaller one. For example 9 × 6 is 3 × 18, and 3 × 6 = 18, so the answer is 3 × 18 = 54. The square of 9 is 9 × 9 = 81. On a multiplication chart the squares lie on the diagonal line from top left to bottom right.

How much is really new? Because 9 × 3 is the same as 3 × 9, a child who already knows the tables below 9 has met most of this one. Up to × 10, only 2 facts are new: 9 × 9 and 9 × 10.

Where you meet 9

A noughts and crosses grid has 9 squares (3 × 3) and Navratri lasts 9 nights. The digit-total rule is also the test for whether any number divides by 9.

Division facts from this table

Every line gives a division fact for free. From 9 × 7 = 63 you know that 63 ÷ 9 = 7 and 63 ÷ 7 = 9. To divide a number by 9, look for it in the answers above: 81 is on line 9, so 81 ÷ 9 = 9. More on this in division from tables.

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All tables: 1 to 10, 11 to 20, 21 to 30. Methods: table tricks.