Answer :
To solve the problem of finding which expression is equivalent to [tex]\(5.8 \div 1.15\)[/tex], let's go through each of the given options and determine which one yields the same result.
The original expression is [tex]\(5.8 \div 1.15\)[/tex].
Now, let's examine each option:
1. Option 1: [tex]\(0.58 \div 115\)[/tex]
- Evaluate [tex]\(0.58 \div 115\)[/tex]. This expression results in a very small value, nowhere near the value of the original expression.
2. Option 2: [tex]\(5.8 \div 115\)[/tex]
- Evaluate [tex]\(5.8 \div 115\)[/tex]. This is also a much smaller number than the result of the original expression.
3. Option 3: [tex]\(58 \div 115\)[/tex]
- Evaluate [tex]\(58 \div 115\)[/tex]. This value is approximately 0.504, which is smaller than the original expression.
4. Option 4: [tex]\(580 \div 115\)[/tex]
- Evaluate [tex]\(580 \div 115\)[/tex]. This result is approximately 5.043, which matches the original expression.
From this evaluation, we can see that the expression [tex]\(580 \div 115\)[/tex] is equivalent to [tex]\(5.8 \div 1.15\)[/tex]. Therefore, the correct answer is the fourth option: [tex]\(580 \div 115\)[/tex].
The original expression is [tex]\(5.8 \div 1.15\)[/tex].
Now, let's examine each option:
1. Option 1: [tex]\(0.58 \div 115\)[/tex]
- Evaluate [tex]\(0.58 \div 115\)[/tex]. This expression results in a very small value, nowhere near the value of the original expression.
2. Option 2: [tex]\(5.8 \div 115\)[/tex]
- Evaluate [tex]\(5.8 \div 115\)[/tex]. This is also a much smaller number than the result of the original expression.
3. Option 3: [tex]\(58 \div 115\)[/tex]
- Evaluate [tex]\(58 \div 115\)[/tex]. This value is approximately 0.504, which is smaller than the original expression.
4. Option 4: [tex]\(580 \div 115\)[/tex]
- Evaluate [tex]\(580 \div 115\)[/tex]. This result is approximately 5.043, which matches the original expression.
From this evaluation, we can see that the expression [tex]\(580 \div 115\)[/tex] is equivalent to [tex]\(5.8 \div 1.15\)[/tex]. Therefore, the correct answer is the fourth option: [tex]\(580 \div 115\)[/tex].
