Shade The Model To Help You Find The Product.$2 \times \frac{7}{8}$Write The Product As A Mixed Number.

Feb 27, 2025 by ADMIN 104 views

**Simplifying Fractions and Writing Products as Mixed Numbers**

Understanding the Problem

When dealing with fractions, it's essential to understand how to simplify them and write products as mixed numbers. In this article, we will explore how to shade a model to help us find the product of two fractions and then write the result as a mixed number.

Shading the Model

To begin, let's consider the problem $2 \times \frac{7}{8}$ . We can represent this product using a model, such as a rectangular array or a grid. The model will help us visualize the product and make it easier to calculate.

Step 1: Draw the Model

Draw a rectangular array with 2 rows and 8 columns. This will represent the product of 2 and $\frac{7}{8}$ .

Step 2: Shade the Model

Shade 7 out of the 8 columns in each row. This will represent the fraction $\frac{7}{8}$ .

Step 3: Count the Shaded Columns

Count the total number of shaded columns in the entire array. Since there are 2 rows, and each row has 7 shaded columns, the total number of shaded columns is 2 x 7 = 14.

Step 4: Write the Product as a Mixed Number

Now that we have counted the total number of shaded columns, we can write the product as a mixed number. A mixed number is a combination of a whole number and a fraction. In this case, the whole number part is 1 (since 8 x 1 = 8), and the fraction part is $\frac{6}{8}$ (since 14 - 8 = 6).

Therefore, the product $2 \times \frac{7}{8}$ can be written as a mixed number: 1 $\frac{6}{8}$ .

Simplifying the Fraction

We can simplify the fraction $\frac{6}{8}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. This gives us $\frac{3}{4}$ .

Therefore, the product $2 \times \frac{7}{8}$ can be written as a simplified mixed number: 1 $\frac{3}{4}$ .

Conclusion

In this article, we learned how to shade a model to help us find the product of two fractions and then write the result as a mixed number. We used a rectangular array to represent the product and shaded 7 out of 8 columns in each row to represent the fraction $\frac{7}{8}$ . We then counted the total number of shaded columns and wrote the product as a mixed number. Finally, we simplified the fraction by dividing both the numerator and the denominator by their greatest common divisor.

Key Takeaways

To simplify fractions, divide both the numerator and the denominator by their greatest common divisor.
To write products as mixed numbers, count the total number of shaded columns in the model and write the result as a combination of a whole number and a fraction.
Shading a model can help us visualize the product and make it easier to calculate.

Practice Problems

Simplify the fraction $\frac{9}{12}$ .
Write the product $3 \times \frac{5}{6}$ as a mixed number.
Shade a model to represent the product $4 \times \frac{3}{5}$ and write the result as a mixed number.

Answer Key

$\frac{3}{4}$
1 $\frac{5}{6}$
1 $\frac{2}{5}$

Additional Resources

For more practice problems and resources, visit the following websites:

Khan Academy: Fractions and Mixed Numbers
Mathway: Fractions and Mixed Numbers
IXL: Fractions and Mixed Numbers
Frequently Asked Questions (FAQs) about Simplifying Fractions and Writing Products as Mixed Numbers =============================================================================================

Q: What is a fraction?

A: A fraction is a way to represent a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, $\frac{1}{2}$ represents one half of a whole.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, 1 $\frac{3}{4}$ represents one whole and three quarters.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify $\frac{6}{8}$ , divide both numbers by 2 to get $\frac{3}{4}$ .

Q: How do I write a product as a mixed number?

A: To write a product as a mixed number, count the total number of shaded columns in the model and write the result as a combination of a whole number and a fraction. For example, to write the product $2 \times \frac{7}{8}$ as a mixed number, count the total number of shaded columns (14) and write the result as 1 $\frac{6}{8}$ .

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction without leaving a remainder. For example, the GCD of 6 and 8 is 2.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, list the factors of each number and find the largest factor they have in common. For example, the factors of 6 are 1, 2, 3, and 6, and the factors of 8 are 1, 2, 4, and 8. The largest factor they have in common is 2.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way to represent a part of a whole, while a decimal is a way to represent a number as a sum of powers of 10. For example, $\frac{1}{2}$ is equal to 0.5.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert $\frac{1}{2}$ to a decimal, divide 1 by 2 to get 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, express the decimal as a sum of powers of 10 and then simplify the resulting fraction. For example, to convert 0.5 to a fraction, express it as $\frac{5}{10}$ and then simplify to $\frac{1}{2}$ .

Q: What are some common mistakes to avoid when simplifying fractions and writing products as mixed numbers?

A: Some common mistakes to avoid include:

Not simplifying fractions enough
Not writing products as mixed numbers correctly
Not counting the total number of shaded columns correctly
Not finding the greatest common divisor correctly

Q: How can I practice simplifying fractions and writing products as mixed numbers?

A: You can practice simplifying fractions and writing products as mixed numbers by:

Using online resources such as Khan Academy, Mathway, and IXL
Working with a tutor or teacher
Practicing with worksheets and exercises
Using real-world examples and applications

Q: What are some real-world applications of simplifying fractions and writing products as mixed numbers?

A: Some real-world applications of simplifying fractions and writing products as mixed numbers include:

Cooking and measuring ingredients
Building and construction
Finance and accounting
Science and engineering

Conclusion

In this article, we have answered some frequently asked questions about simplifying fractions and writing products as mixed numbers. We have covered topics such as what a fraction and a mixed number are, how to simplify a fraction, how to write a product as a mixed number, and how to find the greatest common divisor. We have also provided some common mistakes to avoid and some real-world applications of simplifying fractions and writing products as mixed numbers.