Integers

Fill in the boxes:

1. [tex]$ 6 \text{ more than } -3 = \square $[/tex]
2. [tex]$ 12 \text{ more than } -60 = \square $[/tex]
3. [tex]$ 18 \text{ less than } 10 = \square $[/tex]
4. [tex]$ -216 \div (-12) = \square $[/tex]
5. [tex]$ (-20) \times (-28) = \square $[/tex]
6. [tex]$ 6 - 8 - 2 = \square $[/tex]
7. Additive inverse of 0 is [tex]$\square$[/tex]
8. [tex]$\square \div (-61) = 0 $[/tex]
9. [tex]$ (-2) \times (-2) \times (-2) = \square $[/tex]
10. [tex]$ 6 + \square = -5 $[/tex]
11. [tex]$ [ (1 - 5) \times 2 ] \times (-4) = (-5) \times [2 \times (-4)] = \square $[/tex]
12. [tex]$ -64 \div \square = 64 $[/tex]
13. [tex]$ -8 \text{ is less than } -3 \text{ by } \square $[/tex]
14. [tex]$ 30 \times (-38) + 30 \times 4 = 30 \times (-38 + 4) = \square $[/tex]
15. [tex]$ (-10) \times (-9) \times (-8) \times (-7) = \square $[/tex]
16. [tex]$ -[-(-37)] = \square $[/tex]

Choose whether the following statements are true or false. Tick [tex]$\Omega$[/tex] in the box:

(Supply the true/false statements for students to answer, if needed.)

Let's carefully solve each part step-by-step.

1. 6 more than [tex]$ -3 $[/tex]:
[tex]\[ -3 + 6 = 3 \][/tex]
So, [tex]$\boxed{3}$[/tex].

3. 18 less than [tex]$ 10 $[/tex]:
[tex]\[ 10 - 18 = -8 \][/tex]
So, [tex]$\boxed{-8}$[/tex].

2. 12 more than [tex]$ -60 $[/tex]:
[tex]\[ -60 + 12 = -48 \][/tex]
So, [tex]$\boxed{-48}$[/tex].

5. [tex]$(-20) \times (-28)$[/tex]:
[tex]\[ -20 \times -28 = 560 \][/tex]
So, [tex]$\boxed{560}$[/tex].

4. [tex]$ -216 \div (-12) $[/tex]:
[tex]\[ \frac{-216}{-12} = 18 \][/tex]
So, [tex]$\boxed{18}$[/tex].

7. Additive inverse of 0:
The additive inverse of 0 is itself, so it is [tex]$ \boxed{0} $[/tex].

6. [tex]$6 - 8 - 2$[/tex]:
[tex]\[ 6 - 8 = -2 \\ -2 - 2 = -4 \][/tex]
So, [tex]$\boxed{-4}$[/tex].

9. [tex]$(-2) \times (-2) \times 2$[/tex]:
[tex]\[ (-2) \times (-2) = 4 \\ 4 \times 2 = 8 \][/tex]
So, [tex]$\boxed{8}$[/tex].

8. [tex]$ \boxed{0} \div (-61) = 0 $[/tex]:
Zero divided by any number is zero.

11.
Here, there is a confusion in the problem statement. However, interpreting what seems asked and equal to:
[tex]\[ (-5) \times (2 \times (-4)) \\ = (-5) \times (-8) \\ = 40 \][/tex]
So, [tex]$\boxed{40}$[/tex].

10. [tex]$ 6 + \text{ } = -5 $[/tex]:
[tex]\[ 6 + x = -5 \\ x = -5 - 6 \\ x = -11 \][/tex]
So, [tex]$\boxed{-11}$[/tex].

12. [tex]$ -64 \div \quad = 64 $[/tex]:
[tex]\[ -64 \div x = 64 \quad \Rightarrow \quad x = -1 \][/tex]
So, [tex]$\boxed{-1}$[/tex].

13. -8 is less than -3 by:
[tex]\[ -8 - (-3) = -8 + 3 = -5 \][/tex]
So, [tex]$\boxed{-5}$[/tex].

14. [tex]$ 30 \times (-38) + 30 \times 4 = 30 \times (-38+4) $[/tex]:
[tex]\[ 30 \times (-38 + 4) = 30 \times (-34) \\ = 30 \times (-34) = -1020 \][/tex]
So, [tex]$\boxed{-1020}$[/tex].

15. [tex]$(-10) \times (-9) \times (-8) \times (-7)$[/tex]:
Start from left and move right:
[tex]\[ (-10) \times (-9) = 90 \\ 90 \times (-8) = -720 \\ -720 \times (-7) = 5040 \][/tex]
So, [tex]$\boxed{5040}$[/tex].

16. [tex]$ -[-(-37)] $[/tex]:
[tex]\[ -[-(-37)] = -37 \][/tex]
So, [tex]$\boxed{-37}$[/tex].