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The dosage for an adult is [tex] \frac{5}{6} [/tex] of a gram of medicine. The child dosage is [tex] \frac{1}{2} [/tex] of the adult dosage. How many grams of the medicine should a child take?

Answer :

Sure! Let's break down the problem step by step:

1. Determine the adult dosage:
The problem states that the dosage for an adult is [tex]\(\frac{5}{6}\)[/tex] of a gram of medicine.
[tex]\[
\text{Adult dosage} = \frac{5}{6} \text{ grams}
\][/tex]

2. Calculate the child dosage:
The child dosage is given as [tex]\(\frac{1}{2}\)[/tex] of the adult dosage. Thus, we need to find half of the adult dosage.

To do this, we multiply the adult dosage by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
\text{Child dosage} = \frac{1}{2} \times \frac{5}{6}
\][/tex]

3. Simplify the multiplication:
First, we multiply the numerators (top numbers) and then the denominators (bottom numbers):
[tex]\[
\text{Child dosage} = \frac{1 \times 5}{2 \times 6} = \frac{5}{12} \text{ grams}
\][/tex]

4. Convert [tex]\(\frac{5}{12}\)[/tex] to a decimal (optional but helps to understand the dosage in a more intuitive way):
[tex]\[
\frac{5}{12} = 0.4166666667 \approx 0.4167 \text{ grams}
\][/tex]

So, the dosage of the medicine that a child should take is approximately [tex]\(0.4167\)[/tex] grams, or more exactly [tex]\(\frac{5}{12}\)[/tex] grams.