Trick to Multiply by 9

Last Updated : 18 Oct, 2024

The multiplication trick for 9 follows a simple pattern, making it easy to calculate and less time-consuming:

For any number you multiply by 9 (from 1 to 9), subtract 1 from the number you are multiplying. This gives the last digit of the answer.

Examples:

(9 × 4)
Here, subtract 1 from 4: ( 4 - 1 = 3 ).
To get the second digit, subtract the first digit of your answer from 9.
( 9 - 3 = 6 ), so ( 9 × 4 = 36 ).
( 9 × 5 )
Subtract 1 from 5: ( 5 - 1 = 4 ). Subtract 4 from 9: ( 9 - 4 = 5 ). So, ( 9 × 5 = 45 ).
This pattern works for all multiplication facts of 9 up to 9 × 9.

Other then these there are two more tricks we can use:

Using Fingers
Using 10s

Using Fingers to Multiply by 9

This trick works for multiplying any single-digit number (1–9) by 9, using your fingers.

Step 1: Hold your hands out with fingers spread apart.

Step 2: Pick the number you're multiplying by 9.

For example, if you’re multiplying 4 × 9, focus on your 4th finger (your left-hand ring finger).

Step 3: Bend the finger corresponding to that number. In this case, bend your 4th finger.

Step 4: Count the fingers on each side of the bent finger.

The number of fingers on the left side represents the tens digit.
The number of fingers on the right side represents the ones digit.
For 4 × 9:You have 3 fingers on the left, and 6 fingers on the right. So, 4 × 9 = 36.

Multiplying by 9 Using 10s

Think of multiplying by 9 as multiplying by 10 and then subtracting the original number.

Formula: 9 × n = (10 × n) − n

Example:

9 × 7 = (10 × 7) − 7 = 70 − 7 = 63
9 × 32 = (10 × 32) - 32 = 320 - 32 = 288
9 × 123 = (10 × 123) - 123 = 1230 - 123 = 1107

Pattern Trick for the 9 Times Table

Write the multiples of 9 from 1 to 10. You will notice these patterns:

Tens digit increases from 0 to 9 (0, 1, 2, ..., 9).
Ones digit decreases from 9 to 0 (9, 8, 7, ..., 0).

Thus, we can write the table of 9 simply by writing 0 to 9 in the tens place and 9 to 0 in the ones place.

Multiplier	Tens Digit	Ones Digit	Result
9 × 1	0	9	09
9 × 2	1	8	18
9 × 3	2	7	27
9 × 4	3	6	36
9 × 5	4	5	45
9 × 6	5	4	54
9 × 7	6	3	63
9 × 8	7	2	72
9 × 9	8	1	81
9 × 10	9	0	90

Conclusion

Learning the trick to multiply by 9 can make math quicker and easier, whether you're solving problems in your head or on paper. By simply subtracting 1 from the number you're multiplying and then using a simple subtraction from 9, you can solve these multiplications fast. For larger numbers, the formula 9 × n = (10 × n) − n is another handy tool to get the right answer quickly.

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