Work Out:a) $\frac{4}{5}$ Of 30b) $\frac{2}{9} \times 45$c) $24 \times \frac{1}{6}$

Introduction

In this article, we will explore the concept of multiplying and dividing fractions and whole numbers. We will work out three different problems that involve these operations. Multiplication and division of fractions and whole numbers are essential skills in mathematics, and understanding these concepts can help you solve a wide range of problems in various fields.

Problem a) $\frac{4}{5}$ of 30

To find $\frac{4}{5}$ of 30, we need to multiply $\frac{4}{5}$ by 30.

$\frac{4}{5} \times 30 = \frac{4 \times 30}{5}$

We can simplify this expression by multiplying the numerator and denominator separately.

$\frac{4 \times 30}{5} = \frac{120}{5}$

Now, we can simplify the fraction by dividing the numerator by the denominator.

$\frac{120}{5} = 24$

Therefore, $\frac{4}{5}$ of 30 is equal to 24.

Problem b) $\frac{2}{9} \times 45$

To find $\frac{2}{9} \times 45$, we need to multiply $\frac{2}{9}$ by 45.

$\frac{2}{9} \times 45 = \frac{2 \times 45}{9}$

We can simplify this expression by multiplying the numerator and denominator separately.

$\frac{2 \times 45}{9} = \frac{90}{9}$

Now, we can simplify the fraction by dividing the numerator by the denominator.

$\frac{90}{9} = 10$

Therefore, $\frac{2}{9} \times 45$ is equal to 10.

Problem c) $24 \times \frac{1}{6}$

To find $24 \times \frac{1}{6}$, we need to multiply 24 by $\frac{1}{6}$.

$24 \times \frac{1}{6} = \frac{24 \times 1}{6}$

We can simplify this expression by multiplying the numerator and denominator separately.

$\frac{24 \times 1}{6} = \frac{24}{6}$

Now, we can simplify the fraction by dividing the numerator by the denominator.

$\frac{24}{6} = 4$

Therefore, $24 \times \frac{1}{6}$ is equal to 4.

Conclusion

In this article, we worked out three different problems that involved multiplication and division of fractions and whole numbers. We learned how to multiply and divide fractions and whole numbers, and we applied these skills to solve the problems. Understanding these concepts can help you solve a wide range of problems in various fields.

Tips and Tricks

• When multiplying fractions, multiply the numerators and denominators separately.
• When dividing fractions, invert the second fraction and multiply.
• When multiplying or dividing fractions and whole numbers, convert the whole number to a fraction with the same denominator as the fraction.
• Simplify fractions by dividing the numerator and denominator by their greatest common divisor.

Real-World Applications

Multiplication and division of fractions and whole numbers have many real-world applications. For example:

• In cooking, you may need to multiply a recipe by a certain fraction to make a larger or smaller batch of food.
• In science, you may need to divide a measurement by a certain fraction to convert it to a different unit.
• In finance, you may need to multiply or divide fractions to calculate interest rates or investment returns.

Practice Problems

Try these practice problems to test your skills:

• $\frac{3}{4} \times 20$
• $\frac{5}{6} \times 30$
• $15 \times \frac{2}{3}$

Answer Key

• $\frac{3}{4} \times 20 = 15$
• $\frac{5}{6} \times 30 = 25$
• $15 \times \frac{2}{3} = 10$

References

• [1] Khan Academy. (n.d.). Multiplication and Division of Fractions. Retrieved from https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions-and-decimals/multiplication-and-division-of-fractions/v/multiplication-and-division-of-fractions
• [2] Math Open Reference. (n.d.). Multiplication and Division of Fractions. Retrieved from https://www.mathopenref.com/fractionsmultiplication.html

Introduction

In our previous article, we explored the concept of multiplying and dividing fractions and whole numbers. We worked out three different problems that involved these operations. In this article, we will answer some frequently asked questions about multiplication and division of fractions and whole numbers.

Q: What is the difference between multiplying and dividing fractions?

A: Multiplying fractions involves multiplying the numerators and denominators separately, while dividing fractions involves inverting the second fraction and multiplying.

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator.

Q: How do I divide fractions?

A: To divide fractions, you need to invert the second fraction and multiply. For example, to divide $\frac{1}{2}$ by $\frac{3}{4}$, you would invert the second fraction and multiply: $\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3}$.

Q: What is the rule for multiplying and dividing fractions with whole numbers?

A: When multiplying or dividing fractions and whole numbers, you need to convert the whole number to a fraction with the same denominator as the fraction.

Q: How do I simplify fractions?

A: To simplify fractions, you need to divide the numerator and denominator by their greatest common divisor (GCD).

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

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a fraction as a number with a point separating the whole number part from the fractional part.

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

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator.

Q: What is the rule for adding and subtracting fractions?

A: To add or subtract fractions, you need to have the same denominator. If the denominators are different, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator.

Q: How do I add or subtract fractions with different denominators?

A: To add or subtract fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator that is greater than the denominator.

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, then write the result as a fraction with the same denominator.

Conclusion

In this article, we answered some frequently asked questions about multiplication and division of fractions and whole numbers. We hope that this article has helped you to better understand these concepts and to feel more confident in your ability to work with fractions and whole numbers.

Practice Problems

Try these practice problems to test your skills:

• $\frac{3}{4} \times 20$
• $\frac{5}{6} \times 30$
• $15 \times \frac{2}{3}$
• $\frac{1}{2} \div \frac{3}{4}$
• $\frac{3}{4} + \frac{1}{6}$

Answer Key

• $\frac{3}{4} \times 20 = 15$
• $\frac{5}{6} \times 30 = 25$
• $15 \times \frac{2}{3} = 10$
• $\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$
• $\frac{3}{4} + \frac{1}{6} = \frac{9}{12} + \frac{2}{12} = \frac{11}{12}$

References

• [1] Khan Academy. (n.d.). Multiplication and Division of Fractions. Retrieved from https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions-and-decimals/multiplication-and-division-of-fractions/v/multiplication-and-division-of-fractions
• [2] Math Open Reference. (n.d.). Multiplication and Division of Fractions. Retrieved from https://www.mathopenref.com/fractionsmultiplication.html