Calculate: $\frac{2}{3} \cdot \frac{9}{10}$

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Understanding the Basics of Multiplying Fractions

Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to obtain a product. In this article, we will focus on calculating the product of two fractions, $\frac{2}{3}$ and $\frac{9}{10}$. To begin with, let's understand the basics of multiplying fractions.

What are Fractions?

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the number on top) and a denominator (the number on the bottom). For example, in the fraction $\frac{2}{3}$, the numerator is 2 and the denominator is 3.

Why Multiply Fractions?

Multiplying fractions is essential in various mathematical operations, such as solving equations, finding areas and volumes of shapes, and working with proportions. In real-life scenarios, multiplying fractions can help us calculate quantities, rates, and ratios.

The Multiplication Rule for Fractions

When multiplying fractions, we simply multiply the numerators together and the denominators together. This is based on the multiplication rule for fractions, which states that:

$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$

where $a$, $b$, $c$, and $d$ are integers.

Calculating $\frac{2}{3} \cdot \frac{9}{10}$

Now that we have understood the basics of multiplying fractions, let's apply this rule to calculate the product of $\frac{2}{3}$ and $\frac{9}{10}$.

$\frac{2}{3} \cdot \frac{9}{10} = \frac{2 \cdot 9}{3 \cdot 10}$

To multiply the numerators, we simply multiply 2 and 9 together, which gives us 18. Similarly, to multiply the denominators, we multiply 3 and 10 together, which gives us 30.

$\frac{2 \cdot 9}{3 \cdot 10} = \frac{18}{30}$

Simplifying the Result

The fraction $\frac{18}{30}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 18 and 30 is 6.

$\frac{18}{30} = \frac{18 \div 6}{30 \div 6} = \frac{3}{5}$

Therefore, the product of $\frac{2}{3}$ and $\frac{9}{10}$ is $\frac{3}{5}$.

Real-World Applications of Multiplying Fractions

Multiplying fractions has numerous real-world applications, such as:

• Cooking and Recipes: When a recipe calls for a certain amount of an ingredient, multiplying fractions can help us scale up or down the quantity.
• Building and Construction: Multiplying fractions can help us calculate the area and volume of shapes, which is essential in building and construction projects.
• Science and Engineering: Multiplying fractions is used to calculate quantities, rates, and ratios in various scientific and engineering applications.

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to obtain a product. By understanding the basics of multiplying fractions and applying the multiplication rule, we can calculate the product of fractions with ease. Whether it's in cooking, building, or science, multiplying fractions has numerous real-world applications that make it an essential skill to possess.

Frequently Asked Questions

• What is the product of $\frac{2}{3}$ and $\frac{9}{10}$?
  • The product of $\frac{2}{3}$ and $\frac{9}{10}$ is $\frac{3}{5}$.
• How do I multiply fractions?
  • To multiply fractions, simply multiply the numerators together and the denominators together.
• What is the greatest common divisor (GCD) of 18 and 30?
  • The GCD of 18 and 30 is 6.

Additional Resources

For more information on multiplying fractions, check out the following resources:

• Math Is Fun: A website that provides interactive math lessons and exercises for students of all ages.
• Khan Academy: A website that offers free online courses and resources for math and other subjects.
• Mathway: A website that provides step-by-step solutions to math problems and exercises.
  

$$

Understanding the Basics of Multiplying Fractions

Multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to obtain a product. In this article, we will focus on calculating the product of two fractions, $\frac{2}{3}$ and $\frac{9}{10}$. To begin with, let's understand the basics of multiplying fractions.

What are Fractions?

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the number on top) and a denominator (the number on the bottom). For example, in the fraction $\frac{2}{3}$, the numerator is 2 and the denominator is 3.

Why Multiply Fractions?

Multiplying fractions is essential in various mathematical operations, such as solving equations, finding areas and volumes of shapes, and working with proportions. In real-life scenarios, multiplying fractions can help us calculate quantities, rates, and ratios.

The Multiplication Rule for Fractions

When multiplying fractions, we simply multiply the numerators together and the denominators together. This is based on the multiplication rule for fractions, which states that:

$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$

where $a$, $b$, $c$, and $d$ are integers.

Calculating $\frac{2}{3} \cdot \frac{9}{10}$

Now that we have understood the basics of multiplying fractions, let's apply this rule to calculate the product of $\frac{2}{3}$ and $\frac{9}{10}$.

$\frac{2}{3} \cdot \frac{9}{10} = \frac{2 \cdot 9}{3 \cdot 10}$

To multiply the numerators, we simply multiply 2 and 9 together, which gives us 18. Similarly, to multiply the denominators, we multiply 3 and 10 together, which gives us 30.

$\frac{2 \cdot 9}{3 \cdot 10} = \frac{18}{30}$

Simplifying the Result

The fraction $\frac{18}{30}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 18 and 30 is 6.

$\frac{18}{30} = \frac{18 \div 6}{30 \div 6} = \frac{3}{5}$

Therefore, the product of $\frac{2}{3}$ and $\frac{9}{10}$ is $\frac{3}{5}$.

Real-World Applications of Multiplying Fractions

Multiplying fractions has numerous real-world applications, such as:

• Cooking and Recipes: When a recipe calls for a certain amount of an ingredient, multiplying fractions can help us scale up or down the quantity.
• Building and Construction: Multiplying fractions can help us calculate the area and volume of shapes, which is essential in building and construction projects.
• Science and Engineering: Multiplying fractions is used to calculate quantities, rates, and ratios in various scientific and engineering applications.

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to obtain a product. By understanding the basics of multiplying fractions and applying the multiplication rule, we can calculate the product of fractions with ease. Whether it's in cooking, building, or science, multiplying fractions has numerous real-world applications that make it an essential skill to possess.

Frequently Asked Questions

Q: What is the product of $\frac{2}{3}$ and $\frac{9}{10}$?

A: The product of $\frac{2}{3}$ and $\frac{9}{10}$ is $\frac{3}{5}$.

Q: How do I multiply fractions?

A: To multiply fractions, simply multiply the numerators together and the denominators together.

Q: What is the greatest common divisor (GCD) of 18 and 30?

A: The GCD of 18 and 30 is 6.

Q: Can I simplify a fraction by dividing both the numerator and the denominator by a number other than their GCD?

A: No, you cannot simplify a fraction by dividing both the numerator and the denominator by a number other than their GCD. This is because the GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.

Q: How do I calculate the area of a rectangle using fractions?

A: To calculate the area of a rectangle using fractions, you need to multiply the length and width of the rectangle. For example, if the length of the rectangle is $\frac{3}{4}$ meters and the width is $\frac{2}{3}$ meters, the area of the rectangle is $\frac{3}{4} \cdot \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$ square meters.

Q: Can I use fractions to calculate the volume of a cube?

A: Yes, you can use fractions to calculate the volume of a cube. To do this, you need to multiply the length of the cube by itself three times. For example, if the length of the cube is $\frac{2}{3}$ meters, the volume of the cube is $\left(\frac{2}{3}\right)^3 = \frac{8}{27}$ cubic meters.

Additional Resources

For more information on multiplying fractions, check out the following resources:

• Math Is Fun: A website that provides interactive math lessons and exercises for students of all ages.
• Khan Academy: A website that offers free online courses and resources for math and other subjects.
• Mathway: A website that provides step-by-step solutions to math problems and exercises.

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that involves multiplying two or more fractions together to obtain a product. By understanding the basics of multiplying fractions and applying the multiplication rule, we can calculate the product of fractions with ease. Whether it's in cooking, building, or science, multiplying fractions has numerous real-world applications that make it an essential skill to possess.