Backwards swimmer - Snapple Real fact #41

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Shrimp can only swim backward.

Shrimp do not have fins to move in the water so they pull in their abdomen toward their body quickly. This motion propels them through the water but because of their configuration it means they are moving backwards.

Credits: Wikianswers

Exponential fractions (1)

Geometric series

Unknown negative integer

Questions

Elementary Algebra as I know it

Primary school exam papers all have a select set of questions to differentiate between those who are better than the others. From my knowledge, the 2 topics: "Algebra" and "Simultaneous Equations" are the solutions for some of these problems. These 2 topics can even be applied to normal everyday maths questions to help solve them more easily. However, these 2 topics are not taught in primary school. Hence, i will try my best to create a simple guide to algebra for primary school students to understand.


Algebra
Algebra is the use of letters (any letter to your liking) to denote unknowns, say an amount of sugar (i.e -- x kg of sugar). Before learning to apply algebra to solve your problem sums, you have got to understand how algebra interacts with mathematical signs and numbers.

1) Letters of the same kind can be added/subtracted together.
- x + x = 2x
- 3a + 4a = 7a
- 10r - 4r = 6r
- 3b + 4b - b = 6b

2) 2 different kind of letters cannot be added/subtracted together

- ( a + b) will still remain as ( a + b)
- x + 4y = x +4y
- 2a + 4a - 3b + 5b - a = 5a + 2b


3) Letters in algebra can be multiplied by any number or letter.

- 3 x b = 3b
- 3a x 6b = 18ab
- 2a x 4y = 8ay


4) Letters of the same kind in algebra can be divided by each other
- 6a / 2a = 3
- 9b / 3 = 3b
- 2 / 4c = (1/4)c --> one quarter of c
- d / d = 1 ( same logic as 2 / 2 or any number divided by itself)


5) Letters of the same kind in algebra cannot be divided by another different letter.
- a / b = a / b
- c / d = c / d

However..
Letters of the 2 different kind with numbers attached to it can still be divided.

- 6a / 2b = 3a/ b
- 2c / 10d = c / 5d


These are how algebraic letters interact with multiplication signs and numbers. For more enquiries, feel free to post at the tagboard to ask questions.




*extra - a x a = a^2 ( a to the power of 2 or as some may prefer to call it, a-squared)

3x3 Magic Square solution

Surely you've come across magic squares. Here's a 3 x 3 magic square. It's really easy to solve and remember.

2 9 4
7 5 3
6 1 8


Here's how i remember the order of the numbers in an empty box:
The even numbers 2, 4, 6, 8 take up each corner of the box with 5 in the middle of the box. The odd numbers take up the remainder empty spots.
Keeping in mind that each row/column/diagonal adds up to 15, it should be pretty easy to figure out which spots the odd numbers belong to since we've already filled up 5/9 of the box.


Perhaps you're wondering why each side should add up to 15. Adding up all the numbers from 1 to 9 will give a result of 45. Since the additions involves 3 numbers, divide 45 by 3 and you get 15. 15 is therefore the average sum of the 3 numbers you add up. This rule can also be applied to other magic squares.