Calculate The Sum:$\[ 4 \frac{4}{5} + 12 \frac{3}{4} = \\]$\[ \square \\] $\[ \square \\] $\[ \square \\] $\[ \square \\] ResetNext

Mastering Mixed Numbers: A Step-by-Step Guide to Calculating the Sum of Fractions

In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that are not whole, but can be expressed as a combination of a whole number and a fraction of that number. In this article, we will explore how to calculate the sum of mixed numbers, using the example of $4 \frac{4}{5} + 12 \frac{3}{4}$.

Understanding 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, $4 \frac{4}{5}$ is a mixed number, where $4$ is the whole number, $4$ is the numerator, and $5$ is the denominator.

Adding Mixed Numbers: A Step-by-Step Guide

To add mixed numbers, we need to follow a series of steps. Here's a step-by-step guide on how to add $4 \frac{4}{5} + 12 \frac{3}{4}$:

Step 1: Convert the Mixed Numbers to Improper Fractions

To add mixed numbers, we need to convert them 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. Then, we write the result as a fraction with the same denominator.

For $4 \frac{4}{5}$, we multiply $4$ by $5$ to get $20$, and add $4$ to get $24$. So, $4 \frac{4}{5} = \frac{24}{5}$.

For $12 \frac{3}{4}$, we multiply $12$ by $4$ to get $48$, and add $3$ to get $51$. So, $12 \frac{3}{4} = \frac{51}{4}$.

Step 2: Find a Common Denominator

To add fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the fractions. In this case, the denominators are $5$ and $4$. The LCM of $5$ and $4$ is $20$.

Step 3: Convert the Fractions to Have the Common Denominator

To convert the fractions to have the common denominator, we multiply the numerator and denominator of each fraction by the necessary factor. For $\frac{24}{5}$, we multiply the numerator and denominator by $4$ to get $\frac{96}{20}$. For $\frac{51}{4}$, we multiply the numerator and denominator by $5$ to get $\frac{255}{20}$.

Step 4: Add the Fractions

Now that the fractions have the same denominator, we can add them. To add fractions, we add the numerators and keep the denominator the same. So, $\frac{96}{20} + \frac{255}{20} = \frac{351}{20}$.

Step 5: Convert the Result to a Mixed Number

To convert the result to a mixed number, we divide the numerator by the denominator and write the result as a whole number and a fraction. So, $\frac{351}{20} = 17 \frac{11}{20}$.

Conclusion

In this article, we explored how to calculate the sum of mixed numbers using the example of $4 \frac{4}{5} + 12 \frac{3}{4}$. We followed a series of steps to convert the mixed numbers to improper fractions, find a common denominator, convert the fractions to have the common denominator, add the fractions, and finally convert the result to a mixed number. By following these steps, we can add mixed numbers with ease and accuracy.

Tips and Tricks

• When adding mixed numbers, it's essential to convert them to improper fractions first.
• To find a common denominator, you can use the LCM of the denominators.
• When converting fractions to have a common denominator, make sure to multiply the numerator and denominator by the necessary factor.
• When adding fractions, add the numerators and keep the denominator the same.
• When converting the result to a mixed number, divide the numerator by the denominator and write the result as a whole number and a fraction.

Practice Problems

• $3 \frac{2}{3} + 2 \frac{1}{4} = \square$
• $5 \frac{3}{5} + 8 \frac{2}{3} = \square$
• $2 \frac{1}{2} + 4 \frac{3}{4} = \square$

Answer Key

• $3 \frac{2}{3} + 2 \frac{1}{4} = 5 \frac{13}{12}$
• $5 \frac{3}{5} + 8 \frac{2}{3} = 13 \frac{38}{15}$
• $2 \frac{1}{2} + 4 \frac{3}{4} = 6 \frac{13}{4}$
  Mastering Mixed Numbers: A Q&A Guide

In our previous article, we explored how to calculate the sum of mixed numbers using the example of $4 \frac{4}{5} + 12 \frac{3}{4}$. We followed a series of steps to convert the mixed numbers to improper fractions, find a common denominator, convert the fractions to have the common denominator, add the fractions, and finally convert the result to a mixed number. In this article, we will answer some frequently asked questions about mixed numbers and provide additional tips and tricks to help you master this concept.

Q: What is a mixed number?

A: 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.

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

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. Then, you write the result as a fraction with the same denominator.

For example, to convert $4 \frac{4}{5}$ to an improper fraction, you multiply $4$ by $5$ to get $20$, and add $4$ to get $24$. So, $4 \frac{4}{5} = \frac{24}{5}$.

Q: How do I find a common denominator?

A: To find a common denominator, you need to find the least common multiple (LCM) of the denominators of the fractions. The LCM is the smallest number that both denominators can divide into evenly.

For example, to find the common denominator of $5$ and $4$, you can list the multiples of each number:

Multiples of $5$: $5, 10, 15, 20, 25, ...$ Multiples of $4$: $4, 8, 12, 16, 20, ...$

The first number that appears in both lists is $20$, so the common denominator is $20$.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator and convert each fraction to have that common denominator. Then, you can add the fractions.

For example, to add $\frac{24}{5}$ and $\frac{51}{4}$, you need to find a common denominator, which is $20$. Then, you convert each fraction to have the common denominator:

$\frac{24}{5} = \frac{96}{20}$ $\frac{51}{4} = \frac{255}{20}$

Now, you can add the fractions:

$\frac{96}{20} + \frac{255}{20} = \frac{351}{20}$

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

A: To convert an improper fraction to a mixed number, you divide the numerator by the denominator and write the result as a whole number and a fraction.

For example, to convert $\frac{351}{20}$ to a mixed number, you divide $351$ by $20$ to get $17$ with a remainder of $11$. So, $\frac{351}{20} = 17 \frac{11}{20}$.

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 them
• Not finding a common denominator when adding or subtracting fractions with different denominators
• Not converting fractions to have the common denominator before adding or subtracting them
• Not converting improper fractions to mixed numbers when the result is a whole number and a fraction

Conclusion

In this article, we answered some frequently asked questions about mixed numbers and provided additional tips and tricks to help you master this concept. By following these steps and avoiding common mistakes, you can become proficient in working with mixed numbers and solve problems with ease and accuracy.

Practice Problems

• $3 \frac{2}{3} + 2 \frac{1}{4} = \square$
• $5 \frac{3}{5} + 8 \frac{2}{3} = \square$
• $2 \frac{1}{2} + 4 \frac{3}{4} = \square$

Answer Key

• $3 \frac{2}{3} + 2 \frac{1}{4} = 5 \frac{13}{12}$
• $5 \frac{3}{5} + 8 \frac{2}{3} = 13 \frac{38}{15}$
• $2 \frac{1}{2} + 4 \frac{3}{4} = 6 \frac{13}{4}$