Work Out The Following:a) \[$ 4 \frac{1}{3} \times 6 \$\]b) \[$ 2 \frac{3}{5} \times 3 \frac{1}{3} \$\]Note: To Enter A Mixed Number In The Answer Boxes, Please Use The Following Method: - Type The Fractional Part Of The Mixed Number

Introduction

Multiplying mixed numbers can be a challenging task, especially for those who are new to fractions. However, with a clear understanding of the concept and a step-by-step approach, it can be made easier. In this article, we will work out two examples of multiplying mixed numbers: $4 \frac{1}{3} \times 6$ and $2 \frac{3}{5} \times 3 \frac{1}{3}$. We will also provide a discussion on the importance of understanding fractions and mixed numbers in mathematics.

What are Mixed Numbers?

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $4 \frac{1}{3}$ is a mixed number, where $4$ is the whole number and $\frac{1}{3}$ is the fraction.

Multiplying Mixed Numbers: A Step-by-Step Approach

To multiply mixed numbers, we need to follow a step-by-step approach. Here are the steps:

Step 1: Convert the Mixed Numbers to Improper Fractions

The first step is to convert the mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator.

• For $4 \frac{1}{3}$, we multiply $4$ by $3$ and add $1$, which gives us $\frac{13}{3}$.
• For $6$, we can leave it as it is, since it is already an improper fraction.

Step 2: Multiply the Numerators

The next step is to multiply the numerators of the two improper fractions.

• For $\frac{13}{3}$ and $6$, we multiply $13$ by $6$, which gives us $78$.

Step 3: Multiply the Denominators

The next step is to multiply the denominators of the two improper fractions.

• For $\frac{13}{3}$ and $6$, we multiply $3$ by $6$, which gives us $18$.

Step 4: Write the Product as an Improper Fraction

The next step is to write the product as an improper fraction.

• We divide the product of the numerators ($78$) by the product of the denominators ($18$), which gives us $\frac{78}{18}$.

Step 5: Simplify the Improper Fraction

The final step is to simplify the improper fraction.

• We divide the numerator ($78$) by the denominator ($18$), which gives us $4 \frac{2}{3}$.

Example 1: $4 \frac{1}{3} \times 6$

Now that we have understood the step-by-step approach, let's work out the first example: $4 \frac{1}{3} \times 6$.

• We convert the mixed number $4 \frac{1}{3}$ to an improper fraction, which gives us $\frac{13}{3}$.
• We multiply the numerators, which gives us $78$.
• We multiply the denominators, which gives us $18$.
• We write the product as an improper fraction, which gives us $\frac{78}{18}$.
• We simplify the improper fraction, which gives us $4 \frac{2}{3}$.

Example 2: $2 \frac{3}{5} \times 3 \frac{1}{3}$

Now that we have understood the step-by-step approach, let's work out the second example: $2 \frac{3}{5} \times 3 \frac{1}{3}$.

• We convert the mixed numbers $2 \frac{3}{5}$ and $3 \frac{1}{3}$ to improper fractions, which gives us $\frac{13}{5}$ and $\frac{10}{3}$ respectively.
• We multiply the numerators, which gives us $130$.
• We multiply the denominators, which gives us $15$.
• We write the product as an improper fraction, which gives us $\frac{130}{15}$.
• We simplify the improper fraction, which gives us $8 \frac{10}{15}$.

Conclusion

Multiplying mixed numbers can be a challenging task, but with a clear understanding of the concept and a step-by-step approach, it can be made easier. In this article, we have worked out two examples of multiplying mixed numbers: $4 \frac{1}{3} \times 6$ and $2 \frac{3}{5} \times 3 \frac{1}{3}$. We have also provided a discussion on the importance of understanding fractions and mixed numbers in mathematics.

Importance of Understanding Fractions and Mixed Numbers

Understanding fractions and mixed numbers is crucial in mathematics, as it helps us to solve a wide range of problems, from simple arithmetic operations to complex algebraic equations. Fractions and mixed numbers are used in various fields, such as science, engineering, and finance, where precise calculations are required.

In conclusion, multiplying mixed numbers is an essential skill that requires a clear understanding of the concept and a step-by-step approach. By following the steps outlined in this article, you can easily multiply mixed numbers and solve a wide range of problems.

Final Thoughts

Multiplying mixed numbers is a fundamental concept in mathematics that requires a clear understanding of the concept and a step-by-step approach. By following the steps outlined in this article, you can easily multiply mixed numbers and solve a wide range of problems. Remember to convert the mixed numbers to improper fractions, multiply the numerators and denominators, and simplify the improper fraction to get the final answer. With practice and patience, you can become proficient in multiplying mixed numbers and tackle complex problems with confidence.