Question

a cleaning spray contains \\(\frac{1}{2}\\) cup of vinegar for every 4 teaspoons of lemon oil. one way to find an equivalent ratio is to divide both numbers in a ratio by the same number. how many cups of vinegar are needed for 2 teaspoons of lemon oil? \\(\square\\) c of vinegar is needed for 2 tsp of lemon oil.

Explanation:

Step1: Set up the original ratio

The ratio of vinegar to lemon oil is $\frac{1}{2}$ cup : 4 tsp, or written as a fraction: $\frac{\frac{1}{2}}{4}$

Step2: Simplify using division

We need the lemon oil amount to be 2 tsp, which is dividing 4 by 2. Divide both the numerator and denominator by 2:
$\frac{\frac{1}{2} \div 2}{4 \div 2} = \frac{\frac{1}{4}}{2}$

Answer:

$\frac{1}{4}$ c of vinegar is needed for 2 tsp of lemon oil.