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.
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.
