9.5 Your Own Formulas

In the last section, you worked out formulas that could be used in a spreadsheet. This section gives you more practice in deriving formulas both by looking at number tricks and rearranging existing formulas.

Activity Symbol Activity: Think of a Number

Try this number puzzle: “Think of a number. Add 5. Double it. Subtract 8. Divide by 2. Take away the number you first thought of. Add 4.” [ If you use your calculator, remember to press the Equals sign after each instruction. ]

Now if 1 represents the letter “A,” 2 represents the letter “B,” 3 represents the letter “C,” and so on, work out the letter represented by your answer and write down the name of an animal beginning with this letter.

Start by choosing 3 as the initial number.

Answer Symbol

Answer

The instructions work out as follows.

Starting with 3  
Add 5:
three plus five equals eight
Double it:
eight multiplication two equals 16
Subtract 8:
16 minus eight equals eight
Divide by 2:
eight division two equals four
Subtract your number:
four minus three equals one
Add 4:
one plus four equals five

You will find that you always get 5, whatever number you start with. This gives the letter E. Did you choose an elephant?

Activity Symbol Activity: How Does This Trick Work?

To see how this trick works, read through the instructions from before. Because you could have thought of any number, replace this unknown number by a thought bubble like this:

This is a picture of a small cloud.
Hint symbol

Comment

Keep the thought bubble as part of the new number that you get at each stage.

Answer Symbol

Answer

This shows that the numerical answer is always 5—it does not depend on which number was chosen first. So the letter of the alphabet chosen is E. There are not many animals with names beginning with E and most people do think of an elephant first, but you might be unlucky if someone chooses an emu or an eel!

Rather than using a cloud to represent the number and explaining the trick pictorially, you could write down expressions for the answer at each stage and use either a word (for example, number) or a letter (for example, n) to represent the number. Write out the trick again, expressing it with the unknown number n.

Answer Symbol

Answer

  
Think of a number:
n
Add 5:
n prefix plus of five
Double it:
n prefix plus of five postfix plus n equation left hand side prefix plus of five equals right hand side two postfix multiplication n prefix plus of 10
Subtract 8:
two multiplication n equation left hand side prefix plus of 10 minus eight equals right hand side two postfix multiplication n prefix plus of two
Divide by 2:
equation left hand side open two postfix multiplication n prefix division of two close plus open two division two close equals right hand side n prefix plus of one
Subtract your number:
n prefix plus of one postfix minus n equals one
Add 4:
one plus four equals five

9.4.2 Spreadsheet Formulas

9.5.1 Another Number Trick