Fill in the blanks using 3 of these operation signs to complete each number sentence.
* + - / (* means multiply)
question 1: 12 ___6 ___4 ___ 2=24
question 2: (12 ___ 6) __ (4 ___ 2)=36
Question 1: All addition:
12 + 6 + 4 + 2 = 24
Question 2:
(12 - 6) x (4 + 2) = 36
which leads to:
6 x 6 = 36
or
(12 + 6) x (4 - 2) = 36
which leads to:
18 x 2 = 36
These are just trial and error.
1/3k-4=1
To solve these number sentences, you need to fill in the blanks using any three of the given operation signs ( * , + , - , / ) in a way that makes the equation true. Let's solve each question step by step:
Question 1: 12 ___ 6 ___ 4 ___ 2 = 24
1) We need to choose an operation for the first blank. Since 12 multiplied by 6 is 72, which is larger than 24, we can eliminate the * (multiplication) sign.
2) Now, we have three operation signs left ( + , - , / ). Let's try each one to find a solution.
- If we choose the + sign, the equation becomes: 12 + 6 + 4 + 2 = 24. However, in this case, the result is 24 + 12 = 36, which is greater than 24. So, we can eliminate the + sign.
- If we choose the - sign, the equation becomes: 12 - 6 - 4 - 2 = 24. However, in this case, the result is 12 - 6 - 4 - 2 = 0, which is smaller than 24. So, we can eliminate the - sign.
- If we choose the / sign, the equation becomes: 12 / 6 / 4 / 2 = 24. However, in this case, the result is 12 / 6 / 4 / 2 = 0.5, which is smaller than 24. So, we can eliminate the / sign.
Since none of the remaining operation signs work, there is no solution for this particular number sentence.
Question 2: (12 ___ 6) __ (4 ___ 2) = 36
1) Similarly, considering the first set of blanks, we eliminate the * sign because 12 multiplied by 6 is greater than 36.
2) Now, we have three operation signs left ( + , - , / ). Let's try each one to find a solution.
- If we choose the + sign, the equation becomes: (12 + 6) + (4 + 2) = 36. Simplifying this equation gives us 18 + 6 = 24, which is smaller than 36.
- If we choose the - sign, the equation becomes: (12 - 6) - (4 - 2) = 36. Simplifying this equation gives us 6 - 2 = 4, which is smaller than 36.
- If we choose the / sign, the equation becomes: (12 / 6) / (4 / 2) = 36. Simplifying this equation gives us 2 / 2 = 1, which is smaller than 36.
Similar to the previous question, there is no valid combination of operation signs that makes this number sentence true.