CPhill

Ah....your answer was certainly "easier," Anonymous!!!.......but mine was  pretty interesting, too........if I do say so myself !!!

Looks good, rosala.....you were probably "stressed out" thinking about school when you did this one !!!

I gave you 3 points...... (if I remember correctly)

Thou magic is powerful Morgan Tud, but it hath produced not a single zero......!!!! Twas more crafty when thou employed "not(0)" to obtain like answers as found by thy Humble Servant with the employ of that magical digit. A true trick of conjuring on thy part!!! Thus....thou may find that "not(quadratic)"  be of more power and produce results that edge on - or, possibly, even duplicate - those produced  by the equally powerful  "quadratic! "

For Thou Consideration.......

Your Humble Servant,

Sir CPhill

Actually...in some sense, " ! " represents an "operator"........so I actually "cheated" because I used the "+" operator, too......

But I'm willing to forget about it if you are........

It helps if we can reduce before we multiply

9/60  = 3/20

30/60 = 1/2

16/60 = 4/15

So we have

3/20 * 4/15 * 1/2      note something...I can write this as...

3/15 * 4/20 * 1/2      (verify for yourself that this =  the previous product)   .... and rearranging this, we have....

1/5 * 1/5 * 1/2   =   1/50

See how "cancelling" and "rearranging" makes the multiplication of fractions easier??    (Be careful though, the "rearranging" thing only works with multiplication of fractions....NOT addition)

Remember, zegroes....we have to perform any multiplications/divisions we encounter from left to right before any additions/subtractions.....

So, for 15 + 6/3.....we have to first divide 6 by 3  = 2

Then, 15 + 2 = 17

I see why it's confusing, though......and your answer actually IS correct if the questioner meant (15 + 6)/3

I'll call it a draw and give us BOTH a FG (3 pts.) !!!

Adios.......muchachita !!!!

Que tengas un buen día   !!!

Those are some interesting "properties," rosala

Let's try this, again

2³ = 8    and 3² = 9

So 8 * 9   = 72

You don't know the half of it, zegroes....I spent all afternoon helping a girl with an Algebra 2 Test and a Trig Test...........

In short....I'm fried !!!!

Let's assume that we have an arithmetic series here (I don't know if we do, or not)

An arithmetic series is given by

a_n+1 = a_n + (n-1)d

Where a_n+1 is the term following a₁.....n represents the nth term of the series, and d is the common difference between successive terms

Let's call the first term a₁. And the second term(a₂) is just a₁ + (2-1)d = a₁ + d

So the sum of the first two terms is just

a₁+ (a₁ + d) = 5   or     2a₁ + d = 5    .....call this Equation 1

And the third term (a₃) is just ....  a₁ + (3-1)d =   a₁ + 2d

And the fourth term(a₄) is just.....    a₁ + (4-1)d  = a₁ + 3d

And the sum of these two terms = 12...... so

a₁ + 2d + a₁ + 3d  = 12    or    2a₁ + 5d = 12   ......     call this Equation 2

Now multiplying Equation 1 through by -1 on both sides and adding it to Equation 2, we get

4d = 7      so d = 7/4

And substituting for d in Equation 1, we have

2a₁ + 7/4 = 5

2a₁ = 13/4

a₁ = 13/8   and that's the first term.....Now, lets check our results

a₂ = a₁ + (2-1)(7/4)  = 13/8 +7/4  =  27/8

So    a₁ + a₂= 13/8 + 27/8 = 40/8 = 5  .....and that's OK

And the sum of a₃ and a₄  is given by Equation 2 = 2a₁ + 5d = 12

So we have

2(13/8) + 5(7/4) =

26/8 + 35/4 =

26/8 + 70/8 =

96/8  =   12     .....and that's OK, too

So our series (so far) is just

13/8, 27/8,  41/8,  55/8

And the sum of the 10th and 13th terms is

[a₁ + (9)d] + [a₁ + (12)d] = 2a₁ + 21d =  2(13/8) + 21(7/4) =  26/8 + 294/8 = 320/8 = 40