Sure, let's address each equation step-by-step to find the number that should be placed in the blank:
### Equation 1: [tex]\( \boxed{} + (-3) = 12 \)[/tex]
To solve for the blank, we need to find the number that, when added to [tex]\(-3\)[/tex], equals 12. Let's denote the blank as [tex]\(x\)[/tex].
[tex]\[ x + (-3) = 12 \][/tex]
To isolate [tex]\(x\)[/tex], add 3 to both sides of the equation:
[tex]\[ x = 12 + 3 \][/tex]
[tex]\[ x = 15 \][/tex]
So, the blank should be 15.
### Equation 2: [tex]\( \boxed{} - (-7) = -1 \)[/tex]
To solve for the blank, we need to find the number that, when subtracted by [tex]\(-7\)[/tex], equals [tex]\(-1\)[/tex]. Let's denote the blank as [tex]\(y\)[/tex].
[tex]\[ y - (-7) = -1 \][/tex]
This simplifies to:
[tex]\[ y + 7 = -1 \][/tex]
To isolate [tex]\(y\)[/tex], subtract 7 from both sides of the equation:
[tex]\[ y = -1 - 7 \][/tex]
[tex]\[ y = -8 \][/tex]
So, the blank should be [tex]\(-8\)[/tex].
### Equation 3: [tex]\( \boxed{} - (-72) = -64 \)[/tex]
To solve for the blank, we need to find the number that, when subtracted by [tex]\(-72\)[/tex], equals [tex]\(-64\)[/tex]. Let's denote the blank as [tex]\(z\)[/tex].
[tex]\[ z - (-72) = -64 \][/tex]
This simplifies to:
[tex]\[ z + 72 = -64 \][/tex]
To isolate [tex]\(z\)[/tex], subtract 72 from both sides of the equation:
[tex]\[ z = -64 - 72 \][/tex]
[tex]\[ z = 8 \][/tex]
So, the blank should be 8.
### Equation 4: [tex]\( \boxed{} \times (-5) = 15 \)[/tex]
To solve for the blank, we need to find the number that, when multiplied by [tex]\(-5\)[/tex], equals 15. Let's denote the blank as [tex]\(w\)[/tex].
[tex]\[ w \times -5 = 15 \][/tex]
To isolate [tex]\(w\)[/tex], divide both sides of the equation by [tex]\(-5\)[/tex]:
[tex]\[ w = \frac{15}{-5} \][/tex]
[tex]\[ w = -3 \][/tex]
So, the blank should be [tex]\(-3\)[/tex].
### Conclusion
To summarize, the blanks should be filled with the following numbers:
1. [tex]\( \boxed{15} \)[/tex]
2. [tex]\( \boxed{-8} \)[/tex]
3. [tex]\( \boxed{8} \)[/tex]
4. [tex]\( \boxed{-3} \)[/tex]
And there you go! These are the values that fill in the blanks to make each equation correct.
