Question

you can lay 9 paper clips of the same length end to end to make a length of $7\frac{1}{2}$ inches. what is the length of each paper clip?write a multiplication expression to represent this problem.$7\frac{1}{2} \div 9 = 7\frac{1}{2} \cdot \frac{\square}{\square}$

Explanation:

Step1: Convert division to multiplication

Dividing by a number is multiplying by its reciprocal. So $7\frac{1}{2} \div 9 = 7\frac{1}{2} \times \frac{1}{9}$

Step2: Identify the missing fraction

From the conversion, the missing numerator is 1 and denominator is 9.

Answer:

The multiplication expression is $7\frac{1}{2} \times \frac{1}{9}$, so the missing values are $\frac{1}{9}$.
The length of each paper clip is $\frac{15}{18} = \frac{5}{6}$ inches.

To break down the length calculation:

Step1: Convert mixed number to improper fraction

$7\frac{1}{2} = \frac{15}{2}$

Step2: Multiply by reciprocal

$\frac{15}{2} \times \frac{1}{9} = \frac{15}{18}$

Step3: Simplify the fraction

$\frac{15}{18} = \frac{5}{6}$

Final length of each paper clip: $\frac{5}{6}$ inches
Multiplication expression: $7\frac{1}{2} \times \frac{1}{9}$