Question
Roberto has a 7/9 yard piece of yarn for a project. How many whole, equal 1/5 yard pieces can he cut from his yarn?
Answers
GPT-4o mini
To find out how many whole pieces of \( \frac{1}{5} \) yard can be cut from \( \frac{7}{9} \) yard, we can divide \( \frac{7}{9} \) by \( \frac{1}{5} \).
The division of fractions can be done by multiplying by the reciprocal. So we compute:
\[
\frac{7}{9} \div \frac{1}{5} = \frac{7}{9} \times \frac{5}{1} = \frac{7 \times 5}{9 \times 1} = \frac{35}{9}
\]
Next, we need to determine how many whole pieces there are in \( \frac{35}{9} \). To find this, we can perform the division:
\[
35 \div 9 = 3 \quad \text{(since } 9 \times 3 = 27 \text{)}
\]
This means that \( \frac{35}{9} \) is equal to \( 3 \) with a remainder. We can find the remainder more precisely:
\[
35 - 27 = 8
\]
Thus, \( \frac{35}{9} = 3 + \frac{8}{9} \).
Therefore, Roberto can cut **3 whole pieces** of \( \frac{1}{5} \) yard from his \( \frac{7}{9} \) yard of yarn.
\[
\boxed{3}
\]
The division of fractions can be done by multiplying by the reciprocal. So we compute:
\[
\frac{7}{9} \div \frac{1}{5} = \frac{7}{9} \times \frac{5}{1} = \frac{7 \times 5}{9 \times 1} = \frac{35}{9}
\]
Next, we need to determine how many whole pieces there are in \( \frac{35}{9} \). To find this, we can perform the division:
\[
35 \div 9 = 3 \quad \text{(since } 9 \times 3 = 27 \text{)}
\]
This means that \( \frac{35}{9} \) is equal to \( 3 \) with a remainder. We can find the remainder more precisely:
\[
35 - 27 = 8
\]
Thus, \( \frac{35}{9} = 3 + \frac{8}{9} \).
Therefore, Roberto can cut **3 whole pieces** of \( \frac{1}{5} \) yard from his \( \frac{7}{9} \) yard of yarn.
\[
\boxed{3}
\]