Question

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thursday 2-12-26
what is the value of $\frac{2}{3} \times \frac{3}{4}$? divide the figure into the correct number of equal parts. then shade the correct parts.

Explanation:

Step1: Multiply numerators, denominators

$\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4}$

Step2: Simplify the fraction

$\frac{6}{12} = \frac{1}{2}$

Step3: Divide the rectangle

Divide the rectangle into 4 equal vertical parts (to represent $\frac{3}{4}$), then divide those into 3 equal horizontal sections (to represent $\frac{2}{3}$), creating 12 small equal rectangles total.

Step4: Shade the correct parts

Shade 6 of the 12 small rectangles (which equals $\frac{1}{2}$ of the whole rectangle; this can also be seen as shading 2 out of the 3 horizontal sections, each covering 3 vertical parts, so $2 \times 3 = 6$ shaded parts).

Answer:

The value of $\frac{2}{3} \times \frac{3}{4}$ is $\frac{1}{2}$. The rectangle should be divided into 12 equal small rectangles, with 6 of them shaded (or equivalently, half the rectangle shaded).