missing operation

[kdp]

is there a trick to solving for missing operations?
My problem is 14 7 63 3 3 9 =10
What sign goes in between the numbers?

 

[fcabanski]

The trick on this type of problem is often to go left to right, ignoring order of operations (as if there are ()).

What divided by 9, for example, = 10? 90. If you add up all the preceding numbers, they equal 90.

(14+7+63+3+3)/ 9 =10

 

[John Marsh]

14 7 63 3 3 9 = 10
14 + 7 + 63 + 3 + 3 / 9 = 10
21 + 63 + 3 + 3 / 9 = 10
84 + 3 + 3 / 9 = 10
87 + 3 / 9 = 10
90 / 9 = 10
10 = 10


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[lookagain]

14 7 63 3 3 9 = 10

14 + 7 + 63 + 3 + 3 / 9 = 10

21 + 63 + 3 + 3 / 9 = 10

84 + 3 + 3 / 9 = 10

87 + 3 / 9 = 10

90 / 9 = 10

10 = 10
​

That's wrong!

Grouping symbols are required:

14 7 63 3 3 9 = 10

(14 + 7 + 63 + 3 + 3)/9 = 10

(21 + 63 + 3 + 3)/9 = 10

(84 + 3 + 3)/9 = 10

(87 + 3)/9 = 10

90/9 = 10

10 = 10

 

[fcabanski]

That's wrong!

Grouping symbols are required:

14 7 63 3 3 9 = 10

(14 + 7 + 63 + 3 + 3)/9 = 10

(21 + 63 + 3 + 3)/9 = 10

(84 + 3 + 3)/9 = 10

(87 + 3)/9 = 10

90/9 = 10

10 = 10

For some odd reason, with this type of problem, the authors/books/teachers sometimes ignore order of operations. But you're right, the grouping symbols, which I used in the first response, are needed. Why people keep repeating the correct response is beyond me.

 

[Quaid]

is there a trick to solving for missing operations?

No. I think that you're supposed to use trial-and-error, while making educated guesses. So, experiment!

(With the instructions as posted, I do not agree that we should ignore the Order of Operations.)

This type of exercise tests your knowledge of the Order of Operations, so make sure that you understand the Order of Operations beforehand. The trial-and-error part gives you practice.

:idea: With these types of exercises, it really helps to have the multiplication table memorized.

14 7 63 3 3 9 = 10

First, I notice that 7 ÷ 63 equals 1/9 (because I have memorized the multiplication table).

I also notice that 3 × 3 equals 9, so I know that I can form 1 by multiplying 1/9 × 9.

And 1 + 9 equals 10!

What about the 14? Not a problem, as 14 minus 7 is still 7. Therefore, an alternate solution is:

(14 - 7) ÷ 63 × 3 × 3 + 9 = 10

We need the grouping symbols above because we want to do the subtraction before doing the division. In other words, we need the grouping symbols because we want to change the Order of Operations.