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

Answer :

We want to find which candidate expression is equivalent to

$$5.8 \div 1.15.$$

A convenient strategy is to eliminate decimals by multiplying both the numerator and the denominator by the same number. Here, multiplying by 100 works well. Doing this, we get:

$$
5.8 \div 1.15 = \frac{5.8}{1.15} = \frac{5.8 \times 100}{1.15 \times 100} = \frac{580}{115}.
$$

Now, comparing with the given expressions:

1. $$0.58 \div 115$$
2. $$5.8 \div 115$$
3. $$58 \div 115$$
4. $$580 \div 115$$

We see that the expression $$\frac{580}{115}$$ is the same as $$580 \div 115.$$

Thus, the candidate expression that is equivalent to $$5.8 \div 1.15$$ is:

$$580 \div 115.$$