# MSC 11 – Division by 9

Most of us want to avoid the number 9 in almost all calculations. But we can make calculations easier by thinking of 9 as (10 – 1). This fact is particularly useful in division by 9.

Every 10 contains a 9 and a remainder of 1. So every multiple of ten that is less than 90 will have a quotient and remainder equal to its tens digit.

So                           20/9 = 2 r 2

40/9 = 4 r 4

and                        70/9 = 7 r 7.

Extending this observation, we can readily obtain the quotient when small numbers are divided by 9.

Take the case of 34. When divided by 9, the quotient is equal to the tens digit, 3 and the remainder is equal to the sum of the tens and units digits, 3 + 4 or 7.

Similarly,

42/9 =  4 r  (4+2) = 4 r 6

71/9 = 7 r (7+1)  = 7 r 8

26/9 = 2 r (2+6) = 2 r 8

69/9 = 6 r (6+9) = 6 r 15

But wait!  Since the remainder 15 is greater than 9, we can divide 15 by 9 to get 1 r 6.

So 69/9 = 6 r 15  = (6+1) r 6 = 7 r 6.

At this point, we would like to stress that the following results are equivalent:

69/9 = 6 r 15 = 7 r 6 = 8 r -3 but 7 r 6 is the best form.

Example 11.1:                    1321/9

We can write the procedure as:     1 3 2 1 / 9

Step 1. Bring down the first digit (1) to the answer row.

1 3 2 1 / 9
1

Step 2. Add the next digit of the dividend to this number to get the next digit of the quotient: (1+3=4)
1 3 2 1 / 9
1 4

Step 3. Repeat the preceding procedure to get the next digit of the quotient:    (4+2=6)
1 3 2 1 / 9
1 4 6

Step 4. The last sum is the remainder: (6+1=7)                                                   1 3 2 1 / 9
1 4 6 r 7

Example 11.2:             2023/9

2 0 2 3 / 9
2 2 4 r 7

To check: the sum of the digits of the dividend should be equal to the remainder.

2 + 0 + 2 + 3 = 7

Example 11.3:            4352/9

4   3    5    2 / 9
4   7   12  r 14

Here, we see that we have a 12 and a 14 in the quotient. The 1 in the 12 must be carried over to the 7 to yield 482.  There is also one 9 in the remainder 14.

So the final answer is 483 r 5.

We can modify our procedure to avoid double digits in the quotient.

4   3   5    2 / 9
4

Before writing down the 7 (4 + 3), we see that the next addition 7 + 5 will give a two digit result, 12. So we anticipate the carry operation and write down 8 instead of 7.

4   3   5    2 / 9
4   8

We then proceed as before

4   3   5    2 / 9
4   8

8 + 5 = 13. But since we have performed the carry operation in the previous step, we will write down only the last digit 3.

4   3   5    2 / 9
4   8   3

Finally we have the remainder: 3 + 2 = 5

4   3   5    2 / 9
4   8   3 r 5

check:         4 + 3 + 5 + 2 = 14; 1 + 4 = 5

The following are the decimal values of the remainder when dividing by 9.

1 – 1/9 = .1111… = 0.1

2 – 2/9 = .2222… = 0.2

3 – 3/9 = .3333… = 0.3

4 – 4/9 = .4444… = 0.4

5 – 5/9 = .5555… = 0.6

6 – 6/9 = .6666… = 0.7

7 – 7/9 = .7777… = 0.8

8 – 8/9 = .8888… = 0.9

Exercise 11: Divide the following numbers by 9

1. )      134 / 9 =
2. )      215 / 9 =
3. )      2231 / 9 =
4. )      4202 / 9 =
5. )      625 / 9 =
6. )      3030 / 9 =
7. )      7135 / 9 =
8. )      5672 / 9 =
9. )      3692 / 9 =
10. )      46893 / 9 =

Discover the 25 Math Short Cuts ( 25 MSC )!

# Converting Fahrenheit to Celsius

To convert Fahrenheit to Celsius, we use the following formula,

C = 5/9 (F – 32) = 10/18 (F – 32)

The trick here is to recognize that 5/9 is the same as 10/18.  Hence after deducting 32, we add a zero (multiply by 10) to the result and successively dividing by 2 and 9 (MSC 11 – Dividing by 9) to effectively divide by 18.

• Step 1.  Subtract 32
• Step 2.  Multiply by 10
• Step 3. Divide by 2
• Step 4. Divide by 9

Let us solve look at some examples.

Example 1:          100 oF = 37.8 oC

• Step 1.  Subtract 32:         100 – 32 = 68
• Step 2.  Multiply by 10:    68 x 10 = 680
• Step 3.  Divide by 2:         680 ÷ 2 = 340
• Step 4.  Divide by 9:         340 ÷ 9 = 37 r. 7  =  37.7…  =  37.8

Example 2:           145oF = 62.8oC

• Step 1.  Subtract 32:          145 – 32 = 113
• Step 2.  Multiply by 10:      113 x 10 = 1130
• Step 3.  Divide by 2:           1130 ÷ 2 = 565
• Step 4.  Divide by 9:           565 ÷ 9 = 62 r. 7  =  62.7…  =  62.8

Easy and simple!