Calculations On The Fly

Introduction

If we can do calculations under water we can keep better track of the dive since we can anticipate things like how much gas we are going to use, how far we will travel and how much decompression we need to do. It's also useful on land to do fast dive plans.

We can also use it to help us change or adjust a dive plan during the dive if the conditions or the goal of the dive changes. Of course, the best thing would be if we could do that while diving, without stopping or taking out a pen and paper. That would be the ultimate flexibility.

Before we can start doing any useful calculations however we need to learn and practise how to do calculations in our head. Let's call that a mental skill. Just as we have physical skills we can practise and become better at, we have mental skills. And a good diver needs them both.

Some of you reading this may think that math is boring and something you don't have any talent or interest in. But it doesn't require any talent or any God-given gift - just the will to learn and time to practice. So let's get started!

Multiply with 10

This is done by moving the decimal point to the right (add a zero if neccessary).

Example 1: 23 * 10
23 * 10 = 230

Example 2: 23.5 * 10
23.5 * 10 = 235

Example 3: 23.53 * 10
23.53 * 10 = 235.3

Divide by 10

This is done by moving the decimal point to the left.

Example 1: 3.1 / 10
3.1 / 10 = 0.31

Example 2: 31 / 10
31 / 10 = 3.1

Multiply with 2

This is done by adding the number to itself.

Example 1: 34 * 2
34 + 34 = 68

Sometimes it's easier to split the number up (similar to what you would do if you did it on paper)

Example 1: 34 * 2
(We split it up into 30 and 4) 30 * 2 = 60
4 * 2 = 8
60 + 8 = 68

Divide by 2

This is the same as taking half of something. Often it's easier to split it up into manageble chunks of any size, divide each chunk and then add them together. That works with multiplication too.

Example 1: 176 / 2
(We split them into 100, 70 and 6)
100 / 2 = 50
70 / 2 = 35
6 / 2 = 3
50 + 35 + 3 = 88

Example 2: 176 / 2
160 / 2 = 80 (since 2 * 8 = 16)
We have 176-160 = 16 still left so
16 / 2 = 8
We add them together:
80 + 8 = 88

Percentages

Working with percentages is the same as working with fractions of 100. 10% is 10/100. 10/100 is also 1/10 or 0.1 if you so like.

Here are some percentages that you may have to calculate and some hints on how to calculate them.

• 5% (half of 10%)
• 10% (divide by 10)
• 20% (10% * 2)
• 25% (divide by 2 twice)
• 30% (10% * 3 or 10% + 10% + 10%)
• 40% (10% * 4 or 50% - 10%)
• 50% (divide by 2)
• 60% (10% * 6 or 50% + 10%)
• 70% (10% * 7)
• 75% (100% - 25%)
• 80% (10% * 8 or 100% - 20%)
• 90% (10% * 9 or 100% - 10%)

Fractions

Some fractions that you may have to calculate are:

• 1/2 (50%)
• 1/3 (33%)
• 1/4 (25% or 50% / 2 or 100% / 2 / 2)
• 1/5 (20%)
• 1/6 (17% or 33% / 2)
• 1/7 (14%)
• 1/8 (12.5% or 25% / 2)

Some examples

What is 20% of 60?
10% of 60 = 6
20% is twice of that so,
6 + 6 = 12

What is 20% of 36?
10% of 36 = 3.6
20% is twice of that so,
3.6 + 3.6 = 7.2

What is 40% of 92?
10% of 92 = 9.2
20% is twice of that so,
9.2 + 9.2 = 18.4
and 40% is twice of 20% so,
18.4 + 18.4 = 36.8

Often it is very useful to round the number before calculating if you only need the result "almost right".

What is 40% of 92?
10% of 90 = 9
9 * 4 = 36
So a little more than 36

What is 80% of 150?
10% of 150 = 15
20% is twice, 15 + 15 = 30
80% is 100% - 20% so
150 - 30 = 120

What is 1/6 of 3100?
Let's do 1/6 of 31 first
6 * 5 = 30 and 6 * 6 = 36 so
it's a little more than 5 (5 1/6 to be exact, which is 5.17)
So 1/6 of 3100 is 517 or
a little more than 500.

What is 15% of 354?
10% of 354 is 35.4
5% is half so 35.4 / 2 = 17.7
15% is 10% + 5% so
35.4 + 17.7 = 53.1

What is 15% of 354? (in a different way)
10% of 360 is 36
5% is 18
15% is 36 + 18 = 54
so a little less than 54

What is 25% of 210?
50% is 210 / 2 = 105
25% is 105 / 2 = 52.5

Summary

Now, keep on practicing by taking any number between 1 and 100 and calculate percentages or fractions of that. If you feel that you need know some more of theory behind, pick an old school book or something from the bookstore - there is no shame in that. In the next part we will start doing some useful calculations.

Good luck!

Peter