Answer :
Certainly! Let's go through the problem step-by-step to find out which expression is equivalent to [tex]\(5.8 \div 1.15\)[/tex].
### Step 1: Understand the Original Expression
The original expression we need to evaluate is:
[tex]\[ 5.8 \div 1.15 \][/tex]
When we perform this division, we find that:
[tex]\[ 5.8 \div 1.15 = 5.043478260869565 \][/tex]
### Step 2: Evaluate the Given Expressions
Now let's evaluate each given expression to see which one matches our original:
1. Expression 1:
[tex]\[ 0.58 \div 115 = 0.005043478260869565 \][/tex]
2. Expression 2:
[tex]\[ 5.8 \div 115 = 0.050434782608695654 \][/tex]
3. Expression 3:
[tex]\[ 58 \div 115 = 0.5043478260869565 \][/tex]
4. Expression 4:
[tex]\[ 580 \div 115 = 5.043478260869565 \][/tex]
### Step 3: Compare Each with the Original
Compare each result with the original result [tex]\(5.8 \div 1.15 = 5.043478260869565\)[/tex]:
- Expression 1 (0.58 \div 115): Does not match; result is 0.005043478260869565.
- Expression 2 (5.8 \div 115): Does not match; result is 0.050434782608695654.
- Expression 3 (58 \div 115): Does not match; result is 0.5043478260869565.
- Expression 4 (580 \div 115): Matches; result is 5.043478260869565.
### Conclusion
The expression [tex]\(580 \div 115\)[/tex] is equivalent to [tex]\(5.8 \div 1.15\)[/tex].
Thus, the equivalent expression is:
[tex]\[ 580 \div 115 \][/tex]
### Step 1: Understand the Original Expression
The original expression we need to evaluate is:
[tex]\[ 5.8 \div 1.15 \][/tex]
When we perform this division, we find that:
[tex]\[ 5.8 \div 1.15 = 5.043478260869565 \][/tex]
### Step 2: Evaluate the Given Expressions
Now let's evaluate each given expression to see which one matches our original:
1. Expression 1:
[tex]\[ 0.58 \div 115 = 0.005043478260869565 \][/tex]
2. Expression 2:
[tex]\[ 5.8 \div 115 = 0.050434782608695654 \][/tex]
3. Expression 3:
[tex]\[ 58 \div 115 = 0.5043478260869565 \][/tex]
4. Expression 4:
[tex]\[ 580 \div 115 = 5.043478260869565 \][/tex]
### Step 3: Compare Each with the Original
Compare each result with the original result [tex]\(5.8 \div 1.15 = 5.043478260869565\)[/tex]:
- Expression 1 (0.58 \div 115): Does not match; result is 0.005043478260869565.
- Expression 2 (5.8 \div 115): Does not match; result is 0.050434782608695654.
- Expression 3 (58 \div 115): Does not match; result is 0.5043478260869565.
- Expression 4 (580 \div 115): Matches; result is 5.043478260869565.
### Conclusion
The expression [tex]\(580 \div 115\)[/tex] is equivalent to [tex]\(5.8 \div 1.15\)[/tex].
Thus, the equivalent expression is:
[tex]\[ 580 \div 115 \][/tex]
