Calculate The Result Of The Subtraction:$\[ \begin{array}{r} 4 \frac{1}{5} \\ -2 \frac{3}{10} \\ \hline \end{array} \\]

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Introduction

When it comes to subtracting mixed numbers, many of us struggle to find the correct result. Mixed numbers are a combination of a whole number and a fraction, and they can be tricky to work with. However, with a clear understanding of the concept and a step-by-step approach, you can master the art of subtracting mixed numbers. In this article, we will explore the concept of mixed numbers, how to subtract them, and provide a detailed example to help you understand the process.

What are Mixed Numbers?

A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as 4 1/5 or 2 3/10. Mixed numbers can be used to represent a wide range of values, from simple fractions to complex decimals.

Subtracting Mixed Numbers: A Step-by-Step Approach

To subtract mixed numbers, you need to follow a specific step-by-step approach. Here's how to do it:

Step 1: Convert the Mixed Numbers to Improper Fractions

The first step in subtracting mixed numbers is 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, you need to multiply the whole number by the denominator and add the numerator.

For example, let's say you want to subtract 4 1/5 from 2 3/10. To convert the mixed numbers to improper fractions, you would follow these steps:

  • Convert 4 1/5 to an improper fraction: 4 x 5 + 1 = 21/5
  • Convert 2 3/10 to an improper fraction: 2 x 10 + 3 = 23/10

Step 2: Find the Least Common Multiple (LCM) of the Denominators

The next step is to find the least common multiple (LCM) of the denominators of the two improper fractions. The LCM is the smallest number that both denominators can divide into evenly.

In this case, the denominators are 5 and 10. The LCM of 5 and 10 is 10.

Step 3: Convert the Improper Fractions to Have the Same Denominator

Now that you have the LCM, you need to convert the improper fractions to have the same denominator. To do this, you need to multiply the numerator and denominator of each fraction by the necessary factor to get the LCM as the denominator.

For example, let's say you want to subtract 21/5 from 23/10. To convert the fractions to have the same denominator, you would follow these steps:

  • Multiply 21/5 by 2/2 to get 42/10
  • Multiply 23/10 by 1/1 to get 23/10

Step 4: Subtract the Numerators

Now that the fractions have the same denominator, you can subtract the numerators. To do this, you need to subtract the numerator of the second fraction from the numerator of the first fraction.

In this case, the numerators are 42 and 23. Subtracting 23 from 42 gives you 19.

Step 5: Write the Result as a Mixed Number

The final step is to write the result as a mixed number. To do this, you need to divide the numerator by the denominator and write the result as a whole number and a fraction.

In this case, the numerator is 19 and the denominator is 10. Dividing 19 by 10 gives you 1 with a remainder of 9. Therefore, the result is 1 9/10.

Conclusion

Subtracting mixed numbers can be a challenging task, but with a clear understanding of the concept and a step-by-step approach, you can master the art of subtracting fractions and whole numbers. By following the steps outlined in this article, you can confidently subtract mixed numbers and get the correct result.

Example Problem

Let's say you want to subtract 4 1/5 from 2 3/10. To do this, you would follow the steps outlined in this article:

  • Convert the mixed numbers to improper fractions: 4 1/5 = 21/5 and 2 3/10 = 23/10
  • Find the LCM of the denominators: 10
  • Convert the improper fractions to have the same denominator: 42/10 and 23/10
  • Subtract the numerators: 42 - 23 = 19
  • Write the result as a mixed number: 1 9/10

Therefore, the result of subtracting 4 1/5 from 2 3/10 is 1 9/10.

Tips and Tricks

Here are some tips and tricks to help you master the art of subtracting mixed numbers:

  • Make sure to convert the mixed numbers to improper fractions before subtracting.
  • Find the LCM of the denominators before converting the improper fractions to have the same denominator.
  • Subtract the numerators carefully to avoid making mistakes.
  • Write the result as a mixed number to make it easier to understand.

By following these tips and tricks, you can confidently subtract mixed numbers and get the correct result.

Common Mistakes to Avoid

Here are some common mistakes to avoid when subtracting mixed numbers:

  • Not converting the mixed numbers to improper fractions before subtracting.
  • Not finding the LCM of the denominators before converting the improper fractions to have the same denominator.
  • Subtracting the numerators incorrectly.
  • Not writing the result as a mixed number.

By avoiding these common mistakes, you can ensure that you get the correct result when subtracting mixed numbers.

Conclusion

Q: What is the first step in subtracting mixed numbers?

A: The first step in subtracting mixed numbers is to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to 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 need to multiply the whole number by the denominator and add the numerator. For example, to convert 4 1/5 to an improper fraction, you would multiply 4 by 5 and add 1, which gives you 21/5.

Q: What is the least common multiple (LCM) and why is it important?

A: The least common multiple (LCM) is the smallest number that both denominators can divide into evenly. It is important because it allows you to convert the improper fractions to have the same denominator, making it easier to subtract the numerators.

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

A: To find the LCM of two numbers, you need to list the multiples of each number and find the smallest number that appears in both lists. For example, to find the LCM of 5 and 10, you would list the multiples of 5 (5, 10, 15, 20, ...) and the multiples of 10 (10, 20, 30, 40, ...). The smallest number that appears in both lists is 10.

Q: What is the next step after finding the LCM?

A: After finding the LCM, you need to convert the improper fractions to have the same denominator. To do this, you need to multiply the numerator and denominator of each fraction by the necessary factor to get the LCM as the denominator.

Q: How do I subtract the numerators?

A: To subtract the numerators, you need to subtract the numerator of the second fraction from the numerator of the first fraction. For example, if you have 42/10 and 23/10, you would subtract 23 from 42, which gives you 19.

Q: What is the final step in subtracting mixed numbers?

A: The final step in subtracting mixed numbers is to write the result as a mixed number. To do this, you need to divide the numerator by the denominator and write the result as a whole number and a fraction.

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

A: Some common mistakes to avoid when subtracting mixed numbers include not converting the mixed numbers to improper fractions before subtracting, not finding the LCM of the denominators before converting the improper fractions to have the same denominator, subtracting the numerators incorrectly, and not writing the result as a mixed number.

Q: How can I practice subtracting mixed numbers?

A: You can practice subtracting mixed numbers by working through examples and exercises. You can also use online resources and math games to make practicing more fun and engaging.

Q: What are some real-world applications of subtracting mixed numbers?

A: Subtracting mixed numbers has many real-world applications, including cooking, building, and finance. For example, if you are cooking a recipe that calls for 2 3/4 cups of flour and you only have 1 1/2 cups of flour, you would need to subtract the mixed numbers to find out how much more flour you need.

Q: Can I use a calculator to subtract mixed numbers?

A: Yes, you can use a calculator to subtract mixed numbers. However, it is still important to understand the concept and be able to do it manually. Using a calculator can help you check your work and ensure that you are getting the correct result.

Q: How can I apply subtracting mixed numbers to my everyday life?

A: You can apply subtracting mixed numbers to your everyday life by using it to solve real-world problems. For example, if you are planning a trip and you need to subtract the cost of a hotel room from the total cost of the trip, you would need to subtract mixed numbers to find out how much you will save.