Bot GPT 4-o mini To write the division \( 7 \frac{1}{2} \div \frac{5}{4} \) as a multiplication expression, you can use the reciprocal of the divisor. Here’s how to do it step by step:
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Convert \( 7 \frac{1}{2} \) to an improper fraction:
\[ 7 \frac{1}{2} = 7 \times 2 + 1 = 14 + 1 = 15 \text{ and keep 2 as the denominator} = \frac{15}{2} \] -
Write the division as multiplication by the reciprocal:
\[ 7 \frac{1}{2} \div \frac{5}{4} = \frac{15}{2} \times \frac{4}{5} \]
Thus, you can express the division \( 7 \frac{1}{2} \div \frac{5}{4} \) as:
\[ \frac{15}{2} \times \frac{4}{5} \]
Next, carry out the multiplication:
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Multiply the fractions:
\[ \frac{15 \times 4}{2 \times 5} = \frac{60}{10} \] -
Simplify the result:
\[ \frac{60}{10} = 6 \]
So, \( 7 \frac{1}{2} \div \frac{5}{4} = 6 \).
Now we can summarize the information in a table for the recipe:
\[ \begin{array}{|c|c|} \hline \text{Chocolate Chips (cups)} & \text{Pecans (cups)} \ \hline \frac{5}{4} & 6 \ \hline \end{array} \]
Thus, to maintain the same ratio of chocolate chips to pecans, you would use 6 cups of pecans when you use 1 cup of chocolate chips.
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