Questions: Consider the division expression (7 frac12 div 2). Select all multiplication equations that correspond to this division expression. a. (2 cdot ?=7 frac12) b. (7 frac12 cdot ?=2)

$Consider the division expression (7 frac12 div 2). Select all multiplication equations that correspond to this division expression. a. (2 cdot ?=7 frac12) b. (7 frac12 cdot ?=2)$

Transcript text: 2. Consider the division expression $7 \frac{1}{2} \div 2$. Select all multiplication equations that correspond to this division expression. a. $2 \cdot ?=7 \frac{1}{2}$ b. $7 \frac{1}{2} \cdot ?=2$

Solution

Solution Steps

Step 1: Convert Mixed Number to Improper Fraction

First, convert the mixed number $7 \frac{1}{2}$ into an improper fraction.

\[ 7 \frac{1}{2} = \frac{15}{2} \]

Step 2: Understand the Division Expression

The division expression $7 \frac{1}{2} \div 2$ can be rewritten using the improper fraction:

\[ \frac{15}{2} \div 2 = \frac{15}{2} \times \frac{1}{2} = \frac{15}{4} \]

Step 3: Translate Division to Multiplication

The division expression $7 \frac{1}{2} \div 2$ can be translated into a multiplication equation by finding a number that, when multiplied by 2, gives $7 \frac{1}{2}$.

For option (a): $2 \cdot ? = 7 \frac{1}{2}$

This is correct because if we let $x = \frac{15}{4}$, then:

\[ 2 \cdot \frac{15}{4} = \frac{30}{4} = \frac{15}{2} = 7 \frac{1}{2} \]
For option (b): $7 \frac{1}{2} \cdot ? = 2$

This is incorrect because multiplying $7 \frac{1}{2}$ by any positive number greater than zero will not result in 2.