Maths Funpack Activity A

Activity A1: Math Magician

The answer here is always 1:

1. Choose a number from 1 to 10
2. Double the number
3. Add 2 to the result
4. Divide that number by 2
5. Subtract the original number from the answer in step 4
6. The answer is always 1

How is this possible? (Hint: Algebra)

Let a represent a number from 1 to 10.

{[2(a)]+2} = (2a+2)

0.5(2a+2) - a = (a+1) - a =1

Activity A2: Number Magic Trick

The answer here is always 37:

1. Choose any number 1 through 9 and multiply it by 3
2. Repeat the original number three times, so it becomes a 3-digit number
3. Divide the answer in step 2 by the answer in step 1
4. Now, divide the answer by 15
5. The answer is always 37

How is this possible? (Hint: Algebra)

Let a represent a number from 1 through 9.

"Repeat the original number three times, so it becomes a 3-digit number"
E.g. if the number 4 is chosen, it would be 444. FInd the relationship between 4 & 444.

111(4) = 444

So, 

[(3a)/(111a)] /15 = 37

[0.02702702702702703..]/15 = 37

English Funpack