Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Fill in the blanks.

1. [tex]13 \times (26 + 45) = 13 \times 26 + 13 \times 45[/tex]

2. [tex](57 + 82) \times 64 = (57 \times 64) + (82 \times 64)[/tex]

3. [tex]93 \times 102 = 93 \times (100 + 2) = 93 \times 100 + 93 \times 2[/tex]

4. [tex]\ \textless \ br/\ \textgreater \ \begin{aligned}\ \textless \ br/\ \textgreater \ 99 \times 76 & = (100 - 1) \times 76 \\\ \textless \ br/\ \textgreater \ & = (100 \times 76) - (1 \times 76) \\\ \textless \ br/\ \textgreater \ & = 7600 - 76 \\\ \textless \ br/\ \textgreater \ & = 7524\ \textless \ br/\ \textgreater \ \end{aligned}\ \textless \ br/\ \textgreater \ [/tex]

5. [tex]\ \textless \ br/\ \textgreater \ \begin{aligned}\ \textless \ br/\ \textgreater \ 112 \times 998 & = 112 \times (1000 - 2) \\\ \textless \ br/\ \textgreater \ & = (112 \times 1000) - (112 \times 2) \\\ \textless \ br/\ \textgreater \ & = 112000 - 224 \\\ \textless \ br/\ \textgreater \ & = 111776\ \textless \ br/\ \textgreater \ \end{aligned}\ \textless \ br/\ \textgreater \ [/tex]

Sagot :

GinnyAnswer
Let's carefully fill in the blanks step-by-step for each section.

### 1) [tex]\( 13 \times (26 + 45) = \)[/tex]
- Expression: [tex]\( 13 \times (26 + 45) \)[/tex]
- [tex]\( \quad (13 \times 26) + (13 \times 45) \)[/tex]
- We have: [tex]\( x26 + 13 \times \square ) \)[/tex]
- Thus, [tex]\( 13 \times (26 + 45) = (13 \times 26) + (13 \times 45) \)[/tex]

### 2) [tex]\( (57 + 82) \times 64 = \)[/tex]
- Expression: [tex]\( (57 + 82) \times 64 \)[/tex]
- [tex]\( \quad (57 \times 64 ) + ( 82 \times 64) \)[/tex]
- Fill in: [tex]\( (57 \times \quad \square ) + ( \square \times 64) \)[/tex]
- Thus, [tex]\( (57 + 82) \times 64 = (57 \times 64) + (82 \times 64) \)[/tex]

### 3) [tex]\( 93 \times 102 = \)[/tex]
- Expression: [tex]\( 93 \times 102 \)[/tex]
- [tex]\( \quad 93 \times (100 + 2) \)[/tex]
- Fill in: [tex]\( \quad 93 \times (100 + \square) \)[/tex]
- That implies, [tex]\( \quad 93 \times (100 + 2) \)[/tex]
- Breaking down: [tex]\( 93 \times 100 + 93 \times 2 \)[/tex]
- Thus, [tex]\( 93 \times 102 = 93 \times 100 + 93 \times 2 \)[/tex]

### 4) [tex]\( 99 \times 76 = \)[/tex]
- Expression: [tex]\( 99 \times 76 \)[/tex]
- [tex]\( (100 - 1) \times 76 \)[/tex]
- Fill in: [tex]\( \quad (100 - \square) \times 76 \)[/tex]
- That should be: [tex]\( \quad (100 - 1) \times 76 \)[/tex]
- Breaking down: [tex]\( 100 \times 76 - 1 \times 76 \)[/tex]
- Thus, [tex]\( 99 \times 76 = (100 \times 76) - (1 \times 76) \)[/tex]

### 5) [tex]\( 112 \times 998 = \)[/tex]
- Expression: [tex]\( 112 \times 998 \)[/tex]
- Breaking down: [tex]\( 112 \times (1000 - 2) \)[/tex]
- Fill in: [tex]\( 112 \times (\ldots - \square) \)[/tex]
- Completing: [tex]\( 112 \times (1000 - 2) \)[/tex]
- Expanding: [tex]\( (112 \times 1000) - (112 \times 2) \)[/tex]
- Thus:
[tex]\[ \begin{aligned} 112 \times 998 &= 112 \times (1000 - 2) \\ &= (112 \times 1000) - (112 \times 2) \\ &= 111776 \end{aligned} \][/tex]

### Summary of the steps:

1. [tex]\( 13 \times (26 + 45) = (13 \times 26) + (13 \times 45) \)[/tex]

2. [tex]\( (57 + 82) \times 64 = (57 \times 64) + (82 \times 64) \)[/tex]

3. [tex]\( 93 \times 102 = 93 \times (100 + 2) = 93 \times 100 + 93 \times 2 = 94 + 189 \)[/tex]

4. [tex]\( 99 \times 76 = (100 - 1) \times 76 = (100 \times 76) - (1 \times 76) \)[/tex]

5. [tex]\( 112 \times 998 = 112 \times (1000 - 2) = (112 \times 1000) - (112 \times 2) = 111776 \)[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.