Simplify The Expression:${ 3 \frac{2}{5} + 1 \frac{9}{10} }$

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Introduction

When dealing with mixed numbers, it's essential to understand how to add and subtract them. A mixed number is a combination of a whole number and a fraction. In this article, we will focus on simplifying the expression $3 \frac{2}{5} + 1 \frac{9}{10}$, which involves adding two mixed numbers.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It's 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, $3 \frac{2}{5}$ is a mixed number where $3$ is the whole number, $2$ is the numerator, and $5$ is the denominator.

Adding Mixed Numbers

To add mixed numbers, we need to follow a specific procedure. The first step is to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. The result is then written as a fraction with the same denominator.

Converting Mixed Numbers to Improper Fractions

Let's convert the mixed numbers $3 \frac{2}{5}$ and $1 \frac{9}{10}$ to improper fractions.

Converting $3 \frac{2}{5}$ to an Improper Fraction

To convert $3 \frac{2}{5}$ to an improper fraction, we multiply the whole number $3$ by the denominator $5$ and add the numerator $2$. The result is $15 + 2 = 17$. The improper fraction is then written as $\frac{17}{5}$.

Converting $1 \frac{9}{10}$ to an Improper Fraction

To convert $1 \frac{9}{10}$ to an improper fraction, we multiply the whole number $1$ by the denominator $10$ and add the numerator $9$. The result is $10 + 9 = 19$. The improper fraction is then written as $\frac{19}{10}$.

Adding Improper Fractions

Now that we have converted the mixed numbers to improper fractions, we can add them. To add improper fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators. In this case, the LCM of $5$ and $10$ is $10$.

Finding the Common Denominator

The common denominator is $10$. We can rewrite the improper fractions with the common denominator.

Rewriting $\frac{17}{5}$ with the Common Denominator

To rewrite $\frac{17}{5}$ with the common denominator $10$, we multiply the numerator and denominator by $2$. The result is $\frac{34}{10}$.

Rewriting $\frac{19}{10}$ with the Common Denominator

$\frac{19}{10}$ already has the common denominator $10$, so we don't need to rewrite it.

Adding the Improper Fractions

Now that we have rewritten the improper fractions with the common denominator, we can add them.

$\frac{34}{10} + \frac{19}{10} = \frac{53}{10}$

Simplifying the Result

The result $\frac{53}{10}$ is an improper fraction. We can simplify it by dividing the numerator by the denominator.

$\frac{53}{10} = 5 \frac{3}{10}$

Conclusion

In this article, we simplified the expression $3 \frac{2}{5} + 1 \frac{9}{10}$ by converting the mixed numbers to improper fractions, finding the common denominator, adding the improper fractions, and simplifying the result. The final answer is $5 \frac{3}{10}$.

Frequently Asked Questions

• Q: What is a mixed number? A: A mixed number is a combination of a whole number and a fraction.
• Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.
• Q: How do I add mixed numbers? A: To add mixed numbers, convert them to improper fractions, find the common denominator, add the improper fractions, and simplify the result.

Final Answer

The final answer is $5 \frac{3}{10}$.

Introduction

Mixed numbers can be a bit tricky to work with, but with practice and patience, you can become a pro at adding, subtracting, multiplying, and dividing them. In this article, we'll answer some of the most frequently asked questions about mixed numbers.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It's written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

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

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. The result is then written as a fraction with the same denominator.

Example

To convert $3 \frac{2}{5}$ to an improper fraction, multiply the whole number $3$ by the denominator $5$ and add the numerator $2$. The result is $15 + 2 = 17$. The improper fraction is then written as $\frac{17}{5}$.

Q: How do I add mixed numbers?

A: To add mixed numbers, convert them to improper fractions, find the common denominator, add the improper fractions, and simplify the result.

Example

To add $3 \frac{2}{5}$ and $1 \frac{9}{10}$, convert them to improper fractions, find the common denominator, add the improper fractions, and simplify the result.

Q: What is the common denominator?

A: The common denominator is the least common multiple (LCM) of the denominators. In the case of $3 \frac{2}{5}$ and $1 \frac{9}{10}$, the LCM of $5$ and $10$ is $10$.

Q: How do I find the common denominator?

A: To find the common denominator, list the multiples of each denominator and find the smallest multiple that is common to both.

Example

To find the common denominator of $5$ and $10$, list the multiples of each denominator:

Multiples of $5$: $5, 10, 15, 20, 25, 30, ...$ Multiples of $10$: $10, 20, 30, 40, 50, 60, ...$

The smallest multiple that is common to both is $10$, so the common denominator is $10$.

Q: How do I add improper fractions?

A: To add improper fractions, add the numerators and keep the common denominator.

Example

To add $\frac{17}{5}$ and $\frac{19}{10}$, add the numerators and keep the common denominator:

$\frac{17}{5} + \frac{19}{10} = \frac{34}{10} + \frac{19}{10} = \frac{53}{10}$

Q: How do I simplify a mixed number?

A: To simplify a mixed number, divide the numerator by the denominator and write the result as a whole number and a fraction.

Example

To simplify $\frac{53}{10}$, divide the numerator by the denominator:

$\frac{53}{10} = 5 \frac{3}{10}$

Q: What are some common mistakes to avoid when working with mixed numbers?

A: Some common mistakes to avoid when working with mixed numbers include:

• Not converting mixed numbers to improper fractions before adding or subtracting
• Not finding the common denominator before adding or subtracting improper fractions
• Not simplifying the result after adding or subtracting mixed numbers

Q: How can I practice working with mixed numbers?

A: You can practice working with mixed numbers by:

• Using online resources and worksheets to practice adding, subtracting, multiplying, and dividing mixed numbers
• Working with a partner or tutor to practice mixed number problems
• Creating your own mixed number problems to solve

Conclusion

Mixed numbers can be a bit tricky to work with, but with practice and patience, you can become a pro at adding, subtracting, multiplying, and dividing them. Remember to convert mixed numbers to improper fractions before adding or subtracting, find the common denominator before adding or subtracting improper fractions, and simplify the result after adding or subtracting mixed numbers. With these tips and tricks, you'll be well on your way to mastering mixed numbers!