High School

Which of these expressions is equivalent to [tex]$5.8 \div 1.15$[/tex]?

A. [tex]$0.58 \div 115$[/tex]
B. [tex][tex]$5.8 \div 115$[/tex][/tex]
C. [tex]$58 \div 115$[/tex]
D. [tex]$580 \div 115$[/tex]

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].