2. draw a model for each expression and solve. a. 6 × 3/4

Answer

Explanation:

Step1: Understand the Expression

The expression is (6\times\frac{3}{4}). This means we are finding (\frac{3}{4}) of 6, or adding (\frac{3}{4}) six times.

Step2: Model the Multiplication (Optional Visual)

For a visual model, we can represent 6 as 6 whole units (e.g., 6 rectangles).
To find (\frac{3}{4}) of each unit, divide each rectangle into 4 equal parts and shade 3 parts of each.
Since we have 6 rectangles, we will have (6\times3 = 18) shaded parts, and each whole is divided into 4 parts, so total parts are (6\times4=24). But we can also simplify the multiplication directly.

Step3: Perform the Calculation

Using the rule for multiplying a whole number by a fraction: (a\times\frac{b}{c}=\frac{a\times b}{c}) (where (a = 6), (b = 3), (c = 4)). So, (6\times\frac{3}{4}=\frac{6\times3}{4}=\frac{18}{4}). Simplify (\frac{18}{4}) by dividing numerator and denominator by their greatest common divisor, which is 2. (\frac{18\div2}{4\div2}=\frac{9}{2}=4\frac{1}{2}).

Answer:

(4\frac{1}{2}) (or (\frac{9}{2}))