Solved on Feb 05, 2024

Find the product of $\frac{5}{6}$ and $\frac{1}{2}$ , then shade the model to solve.

STEP 1

Assumptions
1. We are multiplying two fractions: $\frac{5}{6}$ and $\frac{1}{2}$ .
2. We will use a model to visually represent the multiplication of these fractions.
3. The model consists of a rectangle divided into six equal parts, as indicated by the six rows in the given table.
4. Each part represents $\frac{1}{6}$ of the whole.

STEP 2

To represent the fraction $\frac{5}{6}$ , we need to shade 5 out of the 6 parts of the model. This is because the numerator of the fraction indicates how many parts are being considered.

STEP 3

Shade the model to represent $\frac{5}{6}$ .
\begin{tabular}{|l|l|} \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline & \\ \hline \end{tabular}

STEP 4

Now we need to represent the multiplication by $\frac{1}{2}$ . To do this, we will consider half of the shaded parts. Since we have 5 shaded parts, half of them would be $\frac{5}{2}$ parts. However, since we cannot have a half part in our model, we will need to further divide each row into two equal columns to represent this.

STEP 5

Divide each row of the model into two equal columns, so that each cell now represents $\frac{1}{12}$ of the whole.
\begin{tabular}{|l|l|l|l|} \hline \cellcolor{gray} & \cellcolor{gray} & & \\ \hline \cellcolor{gray} & \cellcolor{gray} & & \\ \hline \cellcolor{gray} & \cellcolor{gray} & & \\ \hline \cellcolor{gray} & \cellcolor{gray} & & \\ \hline \cellcolor{gray} & \cellcolor{gray} & & \\ \hline & & & \\ \hline \end{tabular}

STEP 6

To multiply by $\frac{1}{2}$ , we now shade half of each of the previously shaded rows. This means shading one column out of the two in each of the 5 rows that were shaded to represent $\frac{5}{6}$ .

STEP 7

Shade half of each of the 5 previously shaded rows to represent the multiplication by $\frac{1}{2}$ .
\begin{tabular}{|l|l|l|l|} \hline \cellcolor{gray} & & & \\ \hline \cellcolor{gray} & & & \\ \hline \cellcolor{gray} & & & \\ \hline \cellcolor{gray} & & & \\ \hline \cellcolor{gray} & & & \\ \hline & & & \\ \hline \end{tabular}

STEP 8

Count the number of shaded cells to determine the product of $\frac{5}{6} \times \frac{1}{2}$ . Each shaded cell represents $\frac{1}{12}$ of the whole.

STEP 9

There are 5 shaded cells, each representing $\frac{1}{12}$ . Therefore, the product is $5 \times \frac{1}{12}$ .

STEP 10

Calculate the product.
$\frac{5}{6} \times \frac{1}{2} = 5 \times \frac{1}{12} = \frac{5}{12}$
The product of $\frac{5}{6}$ and $\frac{1}{2}$ is $\frac{5}{12}$ .

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Find the product of $\frac{5}{6}$ and $\frac{1}{2}$ , then shade the model to solve.

STEP 1

STEP 2

To represent the fraction $\frac{5}{6}$ , we need to shade 5 out of the 6 parts of the model. This is because the numerator of the fraction indicates how many parts are being considered.

STEP 3

Shade the model to represent $\frac{5}{6}$ .
\begin{tabular}{|l|l|} \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline & \\ \hline \end{tabular}

STEP 4

STEP 5

STEP 6

To multiply by $\frac{1}{2}$ , we now shade half of each of the previously shaded rows. This means shading one column out of the two in each of the 5 rows that were shaded to represent $\frac{5}{6}$ .

STEP 7

STEP 8

Count the number of shaded cells to determine the product of $\frac{5}{6} \times \frac{1}{2}$ . Each shaded cell represents $\frac{1}{12}$ of the whole.

STEP 9

There are 5 shaded cells, each representing $\frac{1}{12}$ . Therefore, the product is $5 \times \frac{1}{12}$ .

STEP 10

Calculate the product.
$\frac{5}{6} \times \frac{1}{2} = 5 \times \frac{1}{12} = \frac{5}{12}$
The product of $\frac{5}{6}$ and $\frac{1}{2}$ is $\frac{5}{12}$ .

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Find the product of 56\frac{5}{6}65​ and 12\frac{1}{2}21​, then shade the model to solve.

STEP 1

STEP 2

To represent the fraction 56\frac{5}{6}65​, we need to shade 5 out of the 6 parts of the model. This is because the numerator of the fraction indicates how many parts are being considered.

STEP 3

Shade the model to represent 56\frac{5}{6}65​.\begin{tabular}{|l|l|} \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline & \\ \hline \end{tabular}

STEP 4

STEP 5

STEP 6

To multiply by 12\frac{1}{2}21​, we now shade half of each of the previously shaded rows. This means shading one column out of the two in each of the 5 rows that were shaded to represent 56\frac{5}{6}65​.

STEP 7

STEP 8

Count the number of shaded cells to determine the product of 56×12\frac{5}{6} \times \frac{1}{2}65​×21​. Each shaded cell represents 112\frac{1}{12}121​ of the whole.

STEP 9

There are 5 shaded cells, each representing 112\frac{1}{12}121​. Therefore, the product is 5×1125 \times \frac{1}{12}5×121​.

STEP 10

Calculate the product.56×12=5×112=512\frac{5}{6} \times \frac{1}{2} = 5 \times \frac{1}{12} = \frac{5}{12}65​×21​=5×121​=125​The product of 56\frac{5}{6}65​ and 12\frac{1}{2}21​ is 512\frac{5}{12}125​.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the product of $\frac{5}{6}$ and $\frac{1}{2}$ , then shade the model to solve.

To represent the fraction $\frac{5}{6}$ , we need to shade 5 out of the 6 parts of the model. This is because the numerator of the fraction indicates how many parts are being considered.

Shade the model to represent $\frac{5}{6}$ .
\begin{tabular}{|l|l|} \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline \cellcolor{gray} & \\ \hline & \\ \hline \end{tabular}

To multiply by $\frac{1}{2}$ , we now shade half of each of the previously shaded rows. This means shading one column out of the two in each of the 5 rows that were shaded to represent $\frac{5}{6}$ .

Count the number of shaded cells to determine the product of $\frac{5}{6} \times \frac{1}{2}$ . Each shaded cell represents $\frac{1}{12}$ of the whole.

There are 5 shaded cells, each representing $\frac{1}{12}$ . Therefore, the product is $5 \times \frac{1}{12}$ .

Calculate the product.
$\frac{5}{6} \times \frac{1}{2} = 5 \times \frac{1}{12} = \frac{5}{12}$
The product of $\frac{5}{6}$ and $\frac{1}{2}$ is $\frac{5}{12}$ .