Certainly! Let's break down the solution step-by-step for better understanding.
#### Step 1: Calculate [tex]\( 1,012 \div 11 \)[/tex]
When dividing 1,012 by 11:
[tex]\[ \frac{1012}{11} = 92 \][/tex]
#### Step 2: Verify Given Result
We were given that the result of [tex]\( 1,012 \div 11 \)[/tex] is 82. From our calculation:
[tex]\[ 1,012 \div 11 = 92 \neq 82 \][/tex]
#### Step 3: Calculate [tex]\( 1,344 \div 56 \)[/tex]
When dividing 1,344 by 56:
[tex]\[ \frac{1344}{56} = 24 \][/tex]
#### Step 4: Verify Given Result
We were given that the result of [tex]\( 1,344 \div 56 \)[/tex] is 24. From our calculation:
[tex]\[ 1,344 \div 56 = 24 = 24 \][/tex]
#### Step 5: Given Multiplication [tex]\( 2 \times 11 = 1,012 \)[/tex]
Checking the multiplication:
[tex]\[ 2 \times 11 = 22 \][/tex]
This result indicates that the multiplication statement is incorrect because:
[tex]\[ 22 \neq 1,012 \][/tex]
#### Step 6: Conclusion on Incorrect Answers
From the above steps, we can draw the following conclusions without relying on additional multiplication or division for further verification:
1. The given result [tex]\( 82 \)[/tex] for [tex]\( 1,012 \div 11 \)[/tex] is incorrect as the correct division result is [tex]\( 92 \)[/tex].
2. The statement [tex]\( 2 \times 11 = 1,012 \)[/tex] is incorrect as the correct multiplication result should be [tex]\( 22 \)[/tex].
These discrepancies clearly indicate which given answers are incorrect:
- The given result [tex]\( 82 \)[/tex] for [tex]\( 1,012 \div 11 \)[/tex].
- The multiplication [tex]\( 2 \times 11 = 1,012 \)[/tex].
Therefore, you can know that the answers to two of the problems are incorrect without multiplying, simply by understanding the logical inconsistencies with the given results.
