(e) Calculate:1. $\frac{2}{3}$ Of 12

Mar 1, 2025 by ADMIN 37 views

$(e) Calculate: 1. $\frac{2}{3}$ of 12$

Understanding the Problem

To solve this problem, we need to find $\frac{2}{3}$ of 12, which means we have to multiply 12 by $\frac{2}{3}$ . This operation is a simple multiplication of a fraction by a whole number.

Multiplying a Fraction by a Whole Number

When we multiply a fraction by a whole number, we can multiply the numerator of the fraction by the whole number. In this case, we have $\frac{2}{3}$ and we want to multiply it by 12.

Step-by-Step Solution

To find $\frac{2}{3}$ of 12, we can follow these steps:

Multiply the numerator of the fraction (2) by the whole number (12).
Keep the denominator of the fraction (3) the same.

Performing the Multiplication

Now, let's perform the multiplication:

2 × 12 = 24

So, the numerator of the fraction becomes 24.

Writing the Result as a Fraction

Now that we have the numerator, we can write the result as a fraction:

$\frac{24}{3}$

Simplifying the Fraction

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 24 and 3 is 3.

$\frac{24}{3} = \frac{24 ÷ 3}{3 ÷ 3} = \frac{8}{1}$

Final Answer

Therefore, $\frac{2}{3}$ of 12 is equal to 8.

Conclusion

In this problem, we learned how to multiply a fraction by a whole number. We followed the steps of multiplying the numerator by the whole number and keeping the denominator the same. We then simplified the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor.

Real-World Applications

This concept is useful in real-world applications such as:

Calculating discounts or taxes on a purchase
Finding the area of a shape
Determining the volume of a container

Practice Problems

Try these practice problems to reinforce your understanding:

Find $\frac{3}{4}$ of 16
Calculate $\frac{5}{6}$ of 24
Determine $\frac{2}{5}$ of 15

Additional Resources

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

Khan Academy: Multiplying Fractions
Mathway: Multiplying Fractions

Final Thoughts

Multiplying fractions by whole numbers is a fundamental concept in mathematics. By following the steps outlined in this problem, you can become proficient in solving these types of problems and apply them to real-world situations.

Frequently Asked Questions

Q: What is the difference between multiplying a fraction by a whole number and multiplying two fractions together?

A: When multiplying a fraction by a whole number, we multiply the numerator of the fraction by the whole number and keep the denominator the same. When multiplying two fractions together, we multiply the numerators and denominators separately.

Q: How do I know when to multiply a fraction by a whole number and when to multiply two fractions together?

A: If you are multiplying a fraction by a whole number, you will see a whole number outside of the fraction. If you are multiplying two fractions together, you will see two fractions with no whole numbers in sight.

Q: Can I simplify a fraction after multiplying it by a whole number?

A: Yes, you can simplify a fraction after multiplying it by a whole number. To do this, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What if the GCD of the numerator and denominator is 1? Does that mean the fraction is already simplified?

A: Yes, if the GCD of the numerator and denominator is 1, then the fraction is already simplified and cannot be simplified further.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, you need to convert the decimal to a fraction and then multiply the fractions together.

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

A: To convert a decimal to a fraction, you need to find the place value of the last digit in the decimal and use that as the denominator. For example, if you have the decimal 0.5, you can convert it to the fraction $\frac{5}{10}$ , which can be simplified to $\frac{1}{2}$ .

Q: Can I multiply a fraction by a percentage?

A: Yes, you can multiply a fraction by a percentage. To do this, you need to convert the percentage to a decimal and then multiply the fraction by the decimal.

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

A: To convert a percentage to a decimal, you need to divide the percentage by 100. For example, if you have the percentage 25%, you can convert it to the decimal 0.25.

Q: Can I multiply a fraction by a mixed number?

A: Yes, you can multiply a fraction by a mixed number. To do this, you need to convert the mixed number to an improper fraction and then multiply the fractions together.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. For example, if you have the mixed number 3 $\frac{1}{2}$ , you can convert it to the improper fraction $\frac{7}{2}$ .

Additional Resources

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

Khan Academy: Multiplying Fractions
Mathway: Multiplying Fractions

Final Thoughts

Multiplying fractions by whole numbers, decimals, percentages, and mixed numbers is a fundamental concept in mathematics. By following the steps outlined in this article, you can become proficient in solving these types of problems and apply them to real-world situations.