The Sharp Mathematics Contest #2 (My Entry)

Hi guys, this is my first entry in this contest, I'm not a native english speaker so I'll do my best giving a clear explanation, these are the questions:

a) 2 ÷ 1/4 = 2 x 4

the left side of the equation is telling us that we have two units like this ones:

then it says that every unit must be divided by 4 like this:

now we have 8 new units that we'll call "prime units", that's the answer for this part of the equation, working with the right side of the equation we can notice that the first square (1) have little squares (1', 2', 3', 4'), so, if every square contains 4 pieces and we have two squares, we just need to multiply 2 times 4 to get the answer: 8 prime units.

b) 6 ÷ 2/3 = 6 x 3/2

The left side of the equation is telling us that we have 6 units like this ones:

The number two (2) that is over the three (3) in the fraction is telling us that we need to created a new unit formed by two squares, with the quantity of squares that we have we can form three groups of two squares.

Lets call this new units A, B and C

the number three that appears in the fraction (2/3) is telling us we need to divide every new unit by three

Now appears a new unit that we will call "prime unit" and we have 9 of these, that's the answer for this part of the equation. In the right side of the equation we can see 6 x 3/2, that is because every original unit (1, 2, 3, 4, 5 and 6) contains 3/2 (1.5) of the prime units, we can see this here

so, if every original unit contains 3/2 (1.5) of the prime units, we just need to multiply 6 times 3/2 to get the answer: 9 prime units.

c) 9 ÷ 3/2 = 9 x 2/3

The last one, the left side of the equation is telling us we have 9 units like this ones:

the three that is over the two in the fraction (3/2) is telling that we need to create a new unit formed by three original units, just like this

We are going to call this units A, B and C. Then, the two that appears in the fraction (3/2) is indicate us that A, B and C must be divided by 2, like this

That's how we get six primes units, this is the answer for this part of the equation. The right part of the equation is 9 x 2/3, this is because every original unit (1, 2, 3, 4, 5, 6, 7, 8 and 9) contains 2/3 (0.66) of the prime units, we can see this here:

so, if every original unit contains 2/3 (0.66) of the prime units and we have 9 original units, we just need to multiply 9 times 2/3 to get the answer: six primes units.

Well, this was my first entry in this contest and I hope you liked it, you can leave a comment if you don't understand or if something is wrong with the explanation. I hope more contest like this one in the future, take care my friends and don't forget to follow me :P