Sure, let's go through a step-by-step solution for this problem.
Step 1: Convert the mixed number to an improper fraction
We start with Martin’s initial amount of grapes:
[tex]\[ 12 \frac{3}{5} = 12 + \frac{3}{5} \][/tex]
To convert the mixed number \(12 \frac{3}{5}\) into an improper fraction:
[tex]\[ 12 \frac{3}{5} = \frac{12 \times 5 + 3}{5} = \frac{60 + 3}{5} = \frac{63}{5} \][/tex]
So, Martin bought \( \frac{63}{5} \) pounds of grapes.
Step 2: Determine the fraction of grapes his friend bought
His friend bought \(\frac{3}{8}\) of Martin’s grapes. To find the amount his friend bought, we multiply the fraction of the grapes by the total amount of grapes Martin has:
[tex]\[ \text{Friend's grapes} = \frac{3}{8} \times \frac{63}{5} \][/tex]
Step 3: Perform the multiplication
Multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
[tex]\[ \frac{3 \times 63}{8 \times 5} = \frac{189}{40} \][/tex]
Step 4: Simplify the fraction
Now, we convert the fraction to a decimal to understand how many pounds of grapes Martin's friend bought:
[tex]\[ \frac{189}{40} \approx 4.725 \][/tex]
Therefore, Martin’s friend bought approximately \( 4.725 \) pounds of grapes.
Conclusion:
When Martin bought \(12 \frac{3}{5}\) pounds of grapes, his friend bought about \(4.725\) pounds of those grapes.
So, Martin's friend bought about [tex]\( \boxed{4.725} \)[/tex] pounds of grapes.
