(+9/5)+(+7/8)+(+1/10)​

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The Mysterious World of Fractions: A Step-by-Step Guide to Solving (+9/5)+(+7/8)+(+1/10)

In the world of mathematics, fractions are a fundamental concept that can be both fascinating and intimidating. When dealing with fractions, it's essential to understand the rules of addition, subtraction, multiplication, and division. In this article, we will delve into the world of fractions and explore the step-by-step process of solving the equation (+9/5)+(+7/8)+(+1/10).

Before we dive into the solution, let's take a moment to understand what fractions are. A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction 3/4 represents three equal parts of a whole, with four parts in total.

When adding fractions, there are a few rules to keep in mind:

  • Like denominators: If the denominators are the same, we can simply add the numerators. For example, 1/4 + 2/4 = 3/4.
  • Unlike denominators: If the denominators are different, we need to find a common denominator. For example, 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
  • Adding fractions with different signs: When adding fractions with different signs, we need to subtract the absolute values of the fractions. For example, 2/3 - 1/3 = 1/3.

Now that we have a solid understanding of fractions and the rules of addition, let's tackle the equation (+9/5)+(+7/8)+(+1/10).

Step 1: Find a Common Denominator

To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 5, 8, and 10 is 40.

Step 2: Convert Each Fraction

We need to convert each fraction to have a denominator of 40.

  • (+9/5) = (+9 * 8)/40 = (+72)/40
  • (+7/8) = (+7 * 5)/40 = (+35)/40
  • (+1/10) = (+1 * 4)/40 = (+4)/40

Step 3: Add the Fractions

Now that we have the same denominator for each fraction, we can add them together.

(+72)/40 + (+35)/40 + (+4)/40 = (+111)/40

In conclusion, solving the equation (+9/5)+(+7/8)+(+1/10) requires a step-by-step approach. We need to find a common denominator, convert each fraction, and then add them together. By following these steps, we can arrive at the solution: (+111)/40.

Fractions are used in a variety of real-world applications, including:

  • Cooking: Recipes often require fractions of ingredients, such as 1/4 cup of sugar or 3/4 teaspoon of salt.
  • Building: Architects and builders use fractions to measure and calculate the dimensions of buildings and structures.
  • Science: Scientists use fractions to measure and calculate the results of experiments and observations.

When working with fractions, it's essential to avoid common mistakes, such as:

  • Adding fractions without finding a common denominator: This can lead to incorrect results.
  • Subtracting fractions without finding a common denominator: This can also lead to incorrect results.
  • Not simplifying fractions: Failing to simplify fractions can make them more difficult to work with.

Here are some tips and tricks for working with fractions:

  • Use a common denominator: When adding or subtracting fractions, it's essential to find a common denominator.
  • Simplify fractions: Simplifying fractions can make them easier to work with.
  • Use visual aids: Visual aids, such as diagrams and charts, can help to illustrate the concept of fractions.

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 as the separator between the whole number and the fractional part. For example, the fraction 3/4 can be expressed as the decimal 0.75.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly. Once you have the common denominator, you can convert each fraction to have that denominator and then add them together.

Q: Can I subtract fractions with different denominators?

A: Yes, you can subtract fractions with different denominators. The process is the same as adding fractions: find a common denominator, convert each fraction to have that denominator, and then subtract them.

Q: How do I multiply fractions?

A: To multiply fractions, you simply multiply the numerators together and the denominators together. For example, (2/3) × (4/5) = (2 × 4)/(3 × 5) = 8/15.

Q: Can I divide fractions?

A: Yes, you can divide fractions. To divide fractions, you invert the second fraction (i.e., flip the numerator and denominator) and then multiply. For example, (2/3) ÷ (4/5) = (2/3) × (5/4) = (2 × 5)/(3 × 4) = 10/12.

Q: How do I simplify fractions?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, the fraction 12/16 can be simplified by dividing both numbers by 4, resulting in 3/4.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) of two or more numbers is the smallest number that all of the numbers can divide into evenly. For example, the LCM of 4 and 6 is 12.

Q: How do I find the LCM of two or more numbers?

A: There are several ways to find the LCM of two or more numbers. One way is to list the multiples of each number and find the smallest number that appears in all of the lists. Another way is to use the prime factorization method, which involves breaking down each number into its prime factors and then multiplying the highest power of each prime factor together.

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

A: The greatest common divisor (GCD) of two or more numbers is the largest number that all of the numbers can divide into evenly. For example, the GCD of 12 and 16 is 4.

Q: How do I find the GCD of two or more numbers?

A: There are several ways to find the GCD of two or more numbers. One way is to list the factors of each number and find the largest number that appears in all of the lists. Another way is to use the prime factorization method, which involves breaking down each number into its prime factors and then multiplying the lowest power of each prime factor together.

Q: Can I use a calculator to solve equations involving fractions?

A: Yes, you can use a calculator to solve equations involving fractions. However, it's essential to understand the underlying math and be able to check your work to ensure that the calculator is giving you the correct answer.

Q: How do I check my work when solving equations involving fractions?

A: To check your work, you can plug your answer back into the original equation and see if it's true. You can also use a calculator to check your work and make sure that you're getting the correct answer.

In conclusion, fractions and equations can be challenging to work with, but with practice and patience, you can become proficient in solving them. Remember to always find a common denominator when adding or subtracting fractions, and to simplify fractions by dividing both numbers by the greatest common divisor. If you have any more questions or need further clarification, don't hesitate to ask.