Estimating with Compatible Fractions

On another day, Martin bought \( 12 \frac{3}{5} \) pounds of grapes for a picnic. His friend bought \( \frac{3}{8} \) of that amount. Use compatible fractions to estimate how many pounds of grapes Martin's friend bought.

[tex]\[ 12 \frac{3}{5} \times \frac{3}{8} \rightarrow \][/tex]

Martin's friend bought about [tex]\(\square\)[/tex] pounds of grapes.



Answer :

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.