Sure, let's fill in the blanks step-by-step, explaining each part clearly:
### a. [tex]\(77 + \_\_\_\_\_ = 103 + 77\)[/tex]
To make the equation true, the blank must be equal to 103.
So:
[tex]\[ 77 + 103 = 103 + 77 \][/tex]
### b. [tex]\(56 + (937 + 44) = 937 + (\_\_\_\_\_)\)[/tex]
Using the associative property of addition, the blank must be 44.
So:
[tex]\[ 56 + (937 + 44) = 937 + (56 + 44) \][/tex]
### c. [tex]\(88 + 0 = \_\_\_\_\_\)[/tex]
Using the identity property of addition, the blank must be 88.
So:
[tex]\[ 88 + 0 = 88 \][/tex]
### d. [tex]\(872 + \_\_\_\_\_ = 872\)[/tex]
Using the identity property of addition, the blank must be 0.
So:
[tex]\[ 872 + 0 = 872 \][/tex]
### e. [tex]\(77 + 998 = 998 + \_\_\_\_\_\)[/tex]
Using the commutative property of addition, the blank must be 77.
So:
[tex]\[ 77 + 998 = 998 + 77 \][/tex]
### f. [tex]\(183 \times \_\_\_\_\_ = 183\)[/tex]
Using the identity property of multiplication, the blank must be 1.
So:
[tex]\[ 183 \times 1 = 183 \][/tex]
### g. [tex]\(75 \times 42 = 42 \times \_\_\_\_\_\)[/tex]
Using the commutative property of multiplication, the blank must be 75.
So:
[tex]\[ 75 \times 42 = 42 \times 75 \][/tex]
### h. [tex]\(394 \times 65 \times 72 = 394 \times 72 \times \_\_\_\_\_\)[/tex]
Using the associative property of multiplication, the blank must be 65.
So:
[tex]\[ 394 \times 65 \times 72 = 394 \times 72 \times 65 \][/tex]
### i. [tex]\(2 \times 179 \times 50 = 179 \times \_\_\_\_\_\)[/tex]
To make the equation true, you need:
[tex]\[ 179 \times (2 \times 50) \][/tex]
So the blank must be:
[tex]\[ 2 \times 50 = 100 \][/tex]
Thus:
[tex]\[ 2 \times 179 \times 50 = 179 \times 100 \][/tex]
### j. [tex]\(\_\_\_\_\_\div 972 = 1\)[/tex]
To make the division true, the blank must be 972.
So:
[tex]\[ 972 \div 972 = 1 \][/tex]
Putting it all together:
[tex]\[
\begin{aligned}
\text{a. } & 77 + \text{103} = 103 + 77 \\
\text{b. } & 56 + (937 + 44) = 937 + (56 + 44) \\
\text{c. } & 88 + 0 = 88 \\
\text{d. } & 872 + 0 = 872 \\
\text{e. } & 77 + 998 = 998 + 77 \\
\text{f. } & 183 \times \text{1} = 183 \\
\text{g. } & 75 \times 42 = 42 \times 75 \\
\text{h. } & 394 \times 65 \times 72 = 394 \times 72 \times 65 \\
\text{i. } & 2 \times 179 \times 50 = 179 \times 100 \\
\text{j. } & 972 \div 972 = 1 \\
\end{aligned}
\][/tex]
