4. Draw an area model to find $$ 3 \frac{5}{8} imes 4 \frac{2}{3} $$

Question

4. Draw an area model to find $$ 3 \frac{5}{8} 	imes 4 \frac{2}{3} $$

UpStudy AI · Accepted Answer

First, we need to convert the mixed numbers $$ 3 \frac{5}{8} $$ and $$ 4 \frac{2}{3} $$ into improper fractions.

For $$ 3 \frac{5}{8} $$:
$$
3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8}
$$

For $$ 4 \frac{2}{3} $$:
$$
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
$$
We will represent the multiplication $$ \frac{29}{8} \times \frac{14}{3} $$ using an area model.

1. Draw a rectangle.
2. Divide the rectangle into two sections horizontally, representing $$ \frac{29}{8} $$ (which can be split into $$ 29 $$ parts of width $$ \frac{1}{8} $$).
3. Divide the rectangle into three sections vertically, representing $$ \frac{14}{3} $$ (which can be split into $$ 14 $$ parts of height $$ \frac{1}{3} $$).

The area of the rectangle will represent the product of the two fractions.
Now, we can calculate the product of the two improper fractions:
$$
\frac{29}{8} \times \frac{14}{3} = \frac{29 \times 14}{8 \times 3}
$$
Now, we will perform the multiplication:
$$
29 \times 14 = 406
$$
$$
8 \times 3 = 24
$$
Thus, we have:
$$
\frac{406}{24}
$$
Next, we simplify $$ \frac{406}{24} $$. We can find the greatest common divisor (GCD) of $$ 406 $$ and $$ 24 $$ to simplify the fraction.

The GCD of $$ 406 $$ and $$ 24 $$ is $$ 2 $$:
$$
\frac{406 \div 2}{24 \div 2} = \frac{203}{12}
$$
The product $$ 3 \frac{5}{8} \times 4 \frac{2}{3} $$ is $$ \frac{203}{12} $$ or $$ 16 \frac{11}{12} $$ when converted back to a mixed number.

Draw an area model to find

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