(a) 5 1 5 − 2 1 10 5 \frac{1}{5} - 2 \frac{1}{10} 5 5 1 ​ − 2 10 1 ​

by ADMIN 69 views

Introduction

Mixed numbers are a combination of a whole number and a fraction. They are used to represent quantities that have both a whole part and a fractional part. In this article, we will focus on solving mixed numbers, specifically the problem of subtracting one mixed number from another. We will use the example of 515−21105 \frac{1}{5} - 2 \frac{1}{10} to illustrate the steps involved.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form abca \frac{b}{c}, where aa is the whole number part, bb is the numerator of the fractional part, and cc is the denominator of the fractional part. For example, 3253 \frac{2}{5} is a mixed number that represents the quantity 33 plus 25\frac{2}{5}.

Subtracting Mixed Numbers

To subtract one mixed number from another, we need to follow a series of steps. 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 part by the denominator and add the numerator. We then write the result as a fraction with the denominator remaining the same.

Step 1: Convert the Mixed Numbers to Improper Fractions

To convert 5155 \frac{1}{5} to an improper fraction, we multiply the whole number part by the denominator and add the numerator:

515=(5×5)+15=2655 \frac{1}{5} = \frac{(5 \times 5) + 1}{5} = \frac{26}{5}

To convert 21102 \frac{1}{10} to an improper fraction, we multiply the whole number part by the denominator and add the numerator:

2110=(2×10)+110=21102 \frac{1}{10} = \frac{(2 \times 10) + 1}{10} = \frac{21}{10}

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

To subtract the two improper fractions, we need to find the least common multiple (LCM) of the denominators. 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: Rewrite the Improper Fractions with the LCM as the Denominator

We rewrite the improper fractions with the LCM (10) as the denominator:

265=26×25×2=5210\frac{26}{5} = \frac{26 \times 2}{5 \times 2} = \frac{52}{10}

2110=21×110×1=2110\frac{21}{10} = \frac{21 \times 1}{10 \times 1} = \frac{21}{10}

Step 4: Subtract the Numerators

Now that the denominators are the same, we can subtract the numerators:

5210−2110=52−2110=3110\frac{52}{10} - \frac{21}{10} = \frac{52 - 21}{10} = \frac{31}{10}

Step 5: Simplify the Result (Optional)

If the result is an improper fraction, we can simplify it by dividing the numerator by the denominator and writing the result as a mixed number. In this case, the result is already a mixed number, so we can leave it as is.

Conclusion

In this article, we have learned how to subtract mixed numbers by converting them to improper fractions, finding the least common multiple (LCM) of the denominators, rewriting the improper fractions with the LCM as the denominator, subtracting the numerators, and simplifying the result (if necessary). We have used the example of 515−21105 \frac{1}{5} - 2 \frac{1}{10} to illustrate the steps involved. With practice, you will become proficient in solving mixed number subtraction problems.

Common Mistakes to Avoid

When subtracting mixed numbers, it is easy to make mistakes. Here are some common mistakes to avoid:

  • Not converting the mixed numbers to improper fractions: Failing to convert the mixed numbers to improper fractions can lead to incorrect results.
  • Not finding the least common multiple (LCM) of the denominators: Failing to find the LCM of the denominators can lead to incorrect results.
  • Not rewriting the improper fractions with the LCM as the denominator: Failing to rewrite the improper fractions with the LCM as the denominator can lead to incorrect results.
  • Not subtracting the numerators: Failing to subtract the numerators can lead to incorrect results.

Practice Problems

To practice subtracting mixed numbers, try the following problems:

  • 325−2353 \frac{2}{5} - 2 \frac{3}{5}
  • 4110−32104 \frac{1}{10} - 3 \frac{2}{10}
  • 534−4145 \frac{3}{4} - 4 \frac{1}{4}

Real-World Applications

Subtracting mixed numbers has many real-world applications. For example:

  • Cooking: When cooking, you may need to subtract mixed numbers to measure out ingredients. For example, if a recipe calls for 2142 \frac{1}{4} cups of flour and you have 3123 \frac{1}{2} cups of flour, you can subtract the two mixed numbers to find out how much flour you have left.
  • Building: When building a structure, you may need to subtract mixed numbers to measure out materials. For example, if a blueprint calls for 5125 \frac{1}{2} feet of lumber and you have 7147 \frac{1}{4} feet of lumber, you can subtract the two mixed numbers to find out how much lumber you have left.
  • Finance: When managing finances, you may need to subtract mixed numbers to calculate interest rates or investment returns. For example, if you have a savings account with a balance of 5155 \frac{1}{5} and you earn an interest rate of 21102 \frac{1}{10} percent, you can subtract the two mixed numbers to find out how much interest you earn.
    Frequently Asked Questions (FAQs) About Subtracting Mixed Numbers ====================================================================

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 abca \frac{b}{c}, where aa is the whole number part, bb is the numerator of the fractional part, and cc is the denominator of the fractional part.

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 part by the denominator and add the numerator. You then write the result as a fraction with the denominator remaining the same.

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

A: The least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into evenly.

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

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Q: Why do I need to find the LCM of the denominators when subtracting mixed numbers?

A: You need to find the LCM of the denominators because it allows you to subtract the numerators directly. If the denominators are different, you would need to find a common denominator, which can be a complex process.

Q: Can I simplify the result of subtracting mixed numbers?

A: Yes, you can simplify the result of subtracting mixed numbers by dividing the numerator by the denominator and writing the result as a mixed number.

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
  • Not finding the least common multiple (LCM) of the denominators
  • Not rewriting the improper fractions with the LCM as the denominator
  • Not subtracting the numerators

Q: How can I practice subtracting mixed numbers?

A: You can practice subtracting mixed numbers by trying the following problems:

  • 325−2353 \frac{2}{5} - 2 \frac{3}{5}
  • 4110−32104 \frac{1}{10} - 3 \frac{2}{10}
  • 534−4145 \frac{3}{4} - 4 \frac{1}{4}

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

A: Some real-world applications of subtracting mixed numbers include:

  • Cooking: When cooking, you may need to subtract mixed numbers to measure out ingredients.
  • Building: When building a structure, you may need to subtract mixed numbers to measure out materials.
  • Finance: When managing finances, you may need to subtract mixed numbers to calculate interest rates or investment returns.

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

A: Yes, you can use a calculator to subtract mixed numbers. However, it's always a good idea to understand the steps involved in subtracting mixed numbers to ensure that you are getting the correct result.

Q: How do I know if I have subtracted mixed numbers correctly?

A: To ensure that you have subtracted mixed numbers correctly, you can:

  • Check your work by plugging in the numbers into a calculator
  • Use a pencil and paper to work out the problem step by step
  • Ask a teacher or tutor for help if you are unsure