# MSC 8 – Multiplying by 9

Recall the x9 table.

```9 x 1  = 09
9 x 2  = 18
9 x 3  = 27
9 x 4  = 36
9 x 5  = 45
9 x 6  = 54
9 x 7  = 63
9 x 8  = 72
9 x 9  = 81
9 x 10 = 90
```

If you look closely at the consecutive products of 9, you will see a pattern.The first digit of the product is in increasing order from 0 to 9; while the second digit is decreasing from 9 to 0.

There is also a pattern on how we arrive at the product.  When 9 is multiplied to a number, we see that the product is a 2-digit number and the first digit of this product is always one less than the number being multiplied by 9.The second digit of the product is the number which when added to the first digit would give a total of 9.

Another way of getting this table is to consider 9 as (10 -1). Thus

```
9 x 1 = (10 -1) x 1 = 10 – 1 or 09;
9 x 2 = (10 -1) x 2 = 20 – 2 or 18;
9 x 3 = (10 -1) x 3 = 30 – 3 or 27
```

and so on. This is the general method we will use to multiply by 9

Example 8.1: 23 x 9 = 207

23 x 9 = 23 x (10 – 1) = 230 – 23 = 207

Example 8.2: 357 x 9 = 3213

357 x 9 = 357 x (10 – 1) = 3570 – 357 = 3213

We can develop a further short-cut for this method.

Step 1) Place a bar separating the last digit from the other digits of the multiplicand.
Step 2) Add 1 to the left hand part
Step 3) Subtract the result from the number. The difference is the first part of the answer.
Step 4) The second part is the ten’s complement of the last digit of the multiplicand (which simply means we subtract the last digit from 10)

Example 8.3: 23 x 9 =

Step 1)  Place a bar separating the last digit 3 from the other digits of the multiplicand, so we place a bar between 2 and 3

2 | 3

Step 2) Add 1 to the left hand part, so we add 1 to 2 to get 3.

2 + 1 = 3

Step 3)  Subtract the result from the number. The difference is the first part of the answer, so we subtract  3 from 23, to get the first part of the answer, 20

23 – 3 = 20
Step 4) The second part is the ten’s complement of the last digit of the multiplicand, which simply means we subtract the last digit 3 from 10 to get the second part 7.

10 – 3 = 7

The first part is 20, and the second part is 7.

2 | 3 x 9 = 20 | 7 or 207

Example 8.4: 357 x 9 =

Step 1) 35|7
Step 2) 35 + 1 = 36
Step 3)357 – 36 = 321
Step 4) 10 – 7 = 3

35 | 7 x 9 = 321|3 or 3213

Since the steps are very simple we can combine some of them.

Example 8.5: 1248 x 9 =

Step 1)  Subtract 125 ( or 124 + 1 ) from 1248 to get the first part.

1248 – 125 = 1123
Step 2) Subtract 8 from 10 to get the second part

10 – 8 = 2

Combine the first part 1123 and the second part 2

1248 x 9 = 1123|2

If the multiplicand is long or complicated we can always resort to written subtraction, which is simpler than multiplication.

Example 8.6: 35,784 x 9 =

(34,784 – 3,479 ) | (10 – 4 )

32,205 | 6

35,784 x 9 = 322,056

Example 8.7: Dealers are given 10% discounts of the selling prices. What is the dealer’s price for an item worth P 1150?

Solution: When you are given a 10% discount, you pay 90% of the cost.

1150 – 115 = P1,035

Here’s how to use your fingers in multiplying by 9:

Spread out your hands and represent each of your fingers with the numbers from 1 to 10 as shown. When multiplying a number by 9, say 9 x 4, simply bend the finger that represents 4.  Count the number of fingers on the left of that finger – this will serve as the first digit of your product and the number of fingers on the right side of your bent finger represents the second digit of your answer. Exercise 8; Use (10-1) in multiplying by 9

1. )      6 x 9 =
2. )      9 x 9 =
3. )      35 x9 =
4. )      49 x 9 =
5. )      82 x 9 =
6. )      148 x 9 =
7. )      285 x 9 =
8. )      0. 9 x 68 =
9. )      90% of 675 =
10. )  45% of 740 =