Calculate The Sum Of The Following Fractions:${ 4 \frac{5}{6} + 5 \frac{7}{12} }$

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Introduction

Fractions are a fundamental concept in mathematics, and calculating the sum of fractions is a crucial skill to master. In this article, we will explore the process of calculating the sum of two fractions, 456+57124 \frac{5}{6} + 5 \frac{7}{12}, and provide a step-by-step guide on how to do it.

Understanding Fractions

Fractions are a way of representing a part of a whole. They consist of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts in the whole.

For example, the fraction 12\frac{1}{2} represents one half of a whole. The numerator is 1, and the denominator is 2.

Converting Mixed Numbers to Improper Fractions

Before we can calculate the sum of the fractions, we need to convert the mixed numbers to improper fractions. A mixed number is a combination of a whole number and a fraction.

To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and add the numerator. Then, we write the result as the new numerator, and keep the same denominator.

For example, to convert the mixed number 4564 \frac{5}{6} to an improper fraction, we multiply 4 by 6 and add 5:

4×6=244 \times 6 = 24 24+5=2924 + 5 = 29

So, the improper fraction is 296\frac{29}{6}.

Similarly, to convert the mixed number 57125 \frac{7}{12} to an improper fraction, we multiply 5 by 12 and add 7:

5×12=605 \times 12 = 60 60+7=6760 + 7 = 67

So, the improper fraction is 6712\frac{67}{12}.

Calculating the Sum of Fractions

Now that we have converted the mixed numbers to improper fractions, we can calculate the sum of the fractions.

To add fractions, we need to have the same denominator. In this case, the denominators are 6 and 12. We can find the least common multiple (LCM) of 6 and 12, which is 12.

So, we can rewrite the fractions with a denominator of 12:

296=29×26×2=5812\frac{29}{6} = \frac{29 \times 2}{6 \times 2} = \frac{58}{12} 6712=6712\frac{67}{12} = \frac{67}{12}

Now, we can add the fractions:

5812+6712=58+6712=12512\frac{58}{12} + \frac{67}{12} = \frac{58 + 67}{12} = \frac{125}{12}

Simplifying the Result

The result is an improper fraction, 12512\frac{125}{12}. We can simplify this fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

The GCD of 125 and 12 is 1. So, the simplified fraction is 12512\frac{125}{12}.

Conclusion

Calculating the sum of fractions requires converting mixed numbers to improper fractions and finding the least common multiple of the denominators. We can then add the fractions and simplify the result.

In this article, we have walked through the process of calculating the sum of the fractions 456+57124 \frac{5}{6} + 5 \frac{7}{12}. We have converted the mixed numbers to improper fractions, found the least common multiple of the denominators, added the fractions, and simplified the result.

By following these steps, you can calculate the sum of fractions with ease and become more confident in your math skills.

Example Problems

Here are some example problems to practice calculating the sum of fractions:

  • 325+2353 \frac{2}{5} + 2 \frac{3}{5}
  • 513+3235 \frac{1}{3} + 3 \frac{2}{3}
  • 249+1592 \frac{4}{9} + 1 \frac{5}{9}

Try solving these problems on your own, and then check your answers with the solutions provided below.

Solutions

  • 325+235=1753 \frac{2}{5} + 2 \frac{3}{5} = \frac{17}{5}
  • 513+323=2035 \frac{1}{3} + 3 \frac{2}{3} = \frac{20}{3}
  • 249+159=1992 \frac{4}{9} + 1 \frac{5}{9} = \frac{19}{9}

Tips and Tricks

Here are some tips and tricks to help you calculate the sum of fractions:

  • Always convert mixed numbers to improper fractions before adding them.
  • Find the least common multiple of the denominators to add the fractions.
  • Simplify the result by dividing the numerator and denominator by their greatest common divisor.
  • Practice, practice, practice! The more you practice, the more confident you will become in your math skills.

By following these tips and tricks, you can become a master of calculating the sum of fractions and tackle even the most challenging math problems with ease.

Conclusion

Calculating the sum of fractions is a crucial skill to master in mathematics. By following the steps outlined in this article, you can calculate the sum of fractions with ease and become more confident in your math skills.

Remember to always convert mixed numbers to improper fractions, find the least common multiple of the denominators, add the fractions, and simplify the result. With practice and patience, you can become a master of calculating the sum of fractions and tackle even the most challenging math problems with ease.

Final Answer

The final answer is 12512\boxed{\frac{125}{12}}.

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Introduction

Calculating the sum of fractions can be a challenging task, especially for those who are new to mathematics. In this article, we will answer some of the most frequently asked questions about calculating the sum of fractions.

Q: What is the first step in calculating the sum of fractions?

A: The first step in calculating the sum of fractions is to convert the mixed numbers to improper fractions. This involves multiplying the whole number by the denominator and adding the numerator.

Q: How do I find the least common multiple (LCM) of the denominators?

A: To find the LCM of the denominators, you can list the multiples of each denominator and find the smallest multiple that is common to both. Alternatively, you can use a formula to find the LCM.

Q: Can I add fractions with different denominators?

A: Yes, you can add fractions with different denominators. However, you need to find the least common multiple (LCM) of the denominators before adding the fractions.

Q: How do I simplify the result after adding the fractions?

A: To simplify the result, you need to divide the numerator and denominator by their greatest common divisor (GCD). This will give you the simplest form of the fraction.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction.

Q: Can I use a calculator to calculate the sum of fractions?

A: Yes, you can use a calculator to calculate the sum of fractions. However, it's always a good idea to double-check your answer by hand to make sure it's correct.

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

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

Q: Can I add fractions with negative numbers?

A: Yes, you can add fractions with negative numbers. However, you need to follow the same steps as adding fractions with positive numbers.

Q: What is the difference between adding and subtracting fractions?

A: The main difference between adding and subtracting fractions is that when subtracting fractions, you need to subtract the numerators and keep the same denominator.

Q: Can I use a formula to calculate the sum of fractions?

A: Yes, you can use a formula to calculate the sum of fractions. However, it's always a good idea to understand the steps involved in calculating the sum of fractions.

Q: How do I calculate the sum of fractions with unlike denominators?

A: To calculate the sum of fractions with unlike denominators, you need to find the least common multiple (LCM) of the denominators and then add the fractions.

Q: Can I use a calculator to find the least common multiple (LCM) of the denominators?

A: Yes, you can use a calculator to find the least common multiple (LCM) of the denominators. However, it's always a good idea to double-check your answer by hand to make sure it's correct.

Conclusion

Calculating the sum of fractions can be a challenging task, but with practice and patience, you can become more confident in your math skills. By following the steps outlined in this article, you can answer some of the most frequently asked questions about calculating the sum of fractions.

Final Answer

The final answer is 12512\boxed{\frac{125}{12}}.