# creating an equation help

#### mom

##### New member
What 2 equations can you create that will total 20 and 31 using the numbers -1, 2 -3 and 4?
Each number can only be used once and you can't use absolute value or factorials.

#### mmm4444bot

##### Super Moderator
Staff member

Hi mom:

I'm thinking that this exercise is geared to get your kid to practice using stuff like exponents, grouping symbols, arithmetic with signed numbers, and the proper application of the Order of Operations when evaluating mathematical expressions.

In short, your kid is supposed to use these skills, along with trial-and-error (and reasoning, if possible), to answer the exercise.

So first, make sure that your kid knows how to do arithmetic with signed numbers.

Make sure that your kid understands the Order of Operations and how we change this order by using grouping symbols.

If your kid has been introduced to exponents, make sure the concept is understood.

Get your kid to start trying. The more that they experiment, the more likely they'll experience some sort of epiphany and begin making smarter guesses.

Here's some reasoning:

What happens, if we multiply all of the numbers together ?

(-1)(2)(-3)(4) = 24

Well, to get to 31, we're going to need bigger numbers. That means something might need to be raised to some power.

Let's experiement with that idea.

2^[(-1)(-3)] is 2^3, which is 8. We still have a 4 left to use.

(8)(4) = 32

Darn, so close.

Let's experiment again.

4^[(-1)(-3)] is 4^3, which is 64. We still have a 2 left.

64/2 = 32

Oh, well (heh, heh).

Here's some more reasoning. How might we get bigger factors without using exponents?

Subtracting negative numbers is the same as adding their opposites.

I mean, 4 - (-3) = 4 + 3, which is 7.

We still have -1 and 2, to work with.

7(2) - (-1) = 14 + 1

Nope.

But, do you see that it's trial-and-error here ?

Your kid needs to try stuff.

AND, if your kid has not yet memorized the multiplication table all the way through 12 times 12, start taking care of that NOW.

I mean, if your kid does not realize that 4 times 5 is 20, then your kid is at a disadvantage, because it's VERY easy to make 5 out of the leftovers -1, 2, and -3.

(Easy, that is, if one also knows that 2 plus 3 equals 5, and that one can change -3 to 3 using a factor of -1.)

If I wrote anything that you do not understand, please ask specific questions. I'll make a better effort to explain clearly.

If you would like more help on this exercise, please post your kid's efforts, so that we can see what's happening and correct mistakes.

Cheers ~ Mark

#### mom

##### New member
Hi Mark.
I didn't bother posting the whole story, but my daughter had to use the four numbers above to write an equation for each day of the calendar. She understands all of the operations that you mentioned and has used trial and error thus far. She has completed the majority of the calendar herself and was stumped on 4 of them. I think after working with them for so long it created a mental block. She is now down to the last 2. She is still at it.
Thanks for the help and reasoning.

#### mmm4444bot

##### Super Moderator
Staff member
mmm4444bot said:
4 times 5 is 20

it's VERY easy to make 5 out of the leftovers -1, 2, and -3

2 plus 3 equals 5, and that one can change -3 to 3 using a factor of -1
20 = 20

4[5] = 20

4[2 + 3] = 20

4[2 + (-1)(-3)] = 20

mom said:
I didn't bother posting the whole story

Not many people do, around here.

#### mom

##### New member
Thanks mmm

Here's what my daughter is trying to make happen to get to 31.
Again, working with -1, 2, -3, and 4
(2-(-1)) which gives you 3. She wants to use the answer (3) as an exponent in -3^3 which would give -27. Then she wants to do 4-(-27) to get 31.
I just don't think using the answer 3 as an exponent is a legal move. I know she's close but we need some fresh eyes. And she doesn't know how to write the equation if she uses the 3 an exponent. Last one and she just wants to be done

#### mom

##### New member
Thanks for the help. She figured it out. If anyone is just curious
4-(-3^2-[-1]) = 31. I'm proud of her for sticking with it through the frustration.

#### lookagain

##### Senior Member
mom said:
Thanks for the help. She figured it out. If anyone is just curious
4-(-3^2-[-1]) = 31.
mom,

no, that $$\displaystyle expression$$ is:

4 - (-9 +1) =

4 - (-8) =

4 + 8 =

12

#### mmm4444bot

##### Super Moderator
Staff member
mom said:
4 - (-3^2 - [-1]) = 31

I'm proud of her for sticking with it through the frustration.

So am I. Excellent.
Not that your daughter needs to know (unless she starts typing her math), more grouping symbols are needed, in the equation above.

4 - (-3^2 - [-1]) = 12, not 31

As your daughter can explain to you, we always do exponentiation before multiplication.

-3^2 means (-1)(3^2), which is -9

4 - (-9 - [-1]) = 4 - (-8), which is 12

We could TYPE it this way:

4 - [ (-3)^[2 - (-1)] ]

This shows that the exponent is 2 - (-1), instead of just 2.

This shows that the base is -3, not 3.

Cheer ~ Mark

#### mmm4444bot

##### Super Moderator
Staff member
lookagain said:
mom said:
no, that $$\displaystyle expression$$ is:

12

I like scaring people, too. :twisted:

#### mmm4444bot

##### Super Moderator
Staff member

I think that I made a misstatement.

Your daughter needs to write grouping symbols around the base -3.

Your daughter needs to write grouping symbols around the exponent 2 - (-1).

Maybe she did, but let's be sure.

#### lookagain

##### Senior Member
Re:

mmm4444bot said:
lookagain said:
mom said:
no, that $$\displaystyle expression$$ is:

12

I like scaring people, too. :twisted:

No, I'm not "getting ready for Halloween,"
and I'm not scaring anyone, either.

Moving on:

mom,

you should have more specificity in your original instructions for the problem,
as in allowing exponentiation, using other negative signs, grouping symbols,
and the square root symbol.

I have:

[2 - (-1)]^[-(-3)] + 4 = 31

[-(-3)]^[2 - (-1)] + 4 = 31

4{2^[-(-3)]} - 1 = 31

4/[2^(-3)] - 1 = 31

{4^[-(-3)]}/2 - 1 = 31

-[4(-1)][2 - (-3)] = 20

#### Denis

##### Senior Member
mom said:
What 2 equations can you create that will total 20 and 31 using the numbers -1, 2 -3 and 4?
That's really same as "using numbers 1,2,3,4 since -(-1) = 1 and -(-3) = 3.

Makes it easier to find solutions like 2^4 + 1 + 3 = 20

Add the minus signs: 2^4 -(-1) -(-3) = 20

#### mom

##### New member
Thanks everyone for the help. I am the "mom" and wasn't the best one to help or be asking for help. She got it and they were correct. I posted on here the way I thought it would look clear to view. I didn't realize adding parenthesis completely changed the expresson. She had it set up correctly though. She knows more than I do in that area . Ended up making a mistake finding 17. She used 2 twice. Not bad though.

Thanks again.