math help, please!!!

[Jalojuab4]

hello, i am new to this site and i am desperate to help out my son with some math. i was hoping that someone out there could give me some advice. it is truly simple math i think but just cant remember if there is a systematic way of solving it... the problem is that you must combine six 12's (12, 12, 12, 12, 12, 12), using +, -, x, / to get answers 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 ,27, 28, 29, 30, 31. i have an example of one that we completed below.
12/12/12x12+12+12=25 . Help!!! :/ please advise

 

[mmm4444bot]

This exercise is intended to get your son to practice the Order of Operations.

Grouping symbols can also be used. For example:

(12 + 12 + 12)/12 + 12 + 12 = 27

There is no formula; your son needs to experiment for as much time as he has to spend on it. (2 hrs is probably good enough practice, even if he doesn't get them all)

Does your son understand the Order of Operations, and how he can group operations using parentheses?

Keep on chuggin' .

BTW, there's nothing wrong with trying to "build" an expression for a specific result.

Like, if we need to do one for 18, then we could think, 18 - 12 is 6, so if we can find a way to get five 12s to generate a 6, then we just add that expression to the sixth 12.

How do we get five 12s to generate a 6?

Well, if we get four 12s to generate a 2, then we can divide the fifth 12 to get a 6.

How do we get four 12s to generate a 2? Oh, how about 12/12 + 12/12.

In other words, I used this strategy to "build" the following.

\(\displaystyle 12 \;+\; \frac{12}{\frac{12}{12} + \frac{12}{12}} \;=\; 18\)

It's typed like this: 12 + 12/(12/12 + 12/12)

See how that went down? My point is that we can be smart about it, rather than wildly guessing. Nothin' wrong with wildly guessing a little, either. Being logical saves times, though.

Oh, and here's the advice that you asked for: Have Fun!

 

[Jalojuab4]

Of course "pemdas" (does this seem to be advanced for 4th grade?) you are right though...intent and focus are far better methods than a random shot in the dark.

 

[soroban]

Hello, Jalojuab4!

Welcome aboard!

Here is some help . . .

We must combine six 12's [12, 12, 12, 12, 12, 12], using +, -, x, /
to get answers 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 ,27, 28, 29, 30, 31.

We can find expressions for number that are "near 24".


We know that: .\(\displaystyle 12+12 \,=\,24\)

We can use the other four 12's to make "adjustments" to the 24.

Experiment with four 12's and create some values.


\(\displaystyle \text{Since }\frac{12+12}{12+12} \,=\,1,\:\text{ we can adjust the 24 by 1.}\)

. . . \(\displaystyle \begin{array}{ccc} (12 + 12) -\frac{12+12}{12+12} &=& 23 \\ \\[-3mm] (12+12) + \frac{12+12}{12+12} &=& 25 \end{array}\)


\(\displaystyle \text{Since }\frac{12}{12} + \frac{12}{12} \,=\,2,\:\text{ we can adjust the 24 by 2.}\)

. . . \(\displaystyle \begin{array}{ccc}(12+12) - \frac{12}{12} - \frac{12}{12} &=& 22 \\ \\[-3mm] (12+12) + \frac{12}{12} + \frac{12}{12} &=& 26 \end{array}\)


\(\displaystyle \text{Since }\frac{12+12+12}{12} \,=\,3,\:\text{ we can adjust the 24 by 3.}\)


Get the idea?

 

[Jalojuab4]

Thank you very much, your reply has been very helpful!