Subtract $6 \frac{2}{5} - 1 \frac{1}{4}$. Simplify The Answer And Write As A Mixed Number.A. $7 \frac{13}{20}$B. \$\frac{3}{20}$[/tex\]C. $5 \frac{3}{20}$D. $5 \frac{1}{20}$

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Introduction

Mixed numbers are a combination of a whole number and a fraction. They are commonly used in mathematics to represent quantities that have both a whole and a part. In this article, we will focus on subtracting mixed numbers, specifically the problem of subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$. We will simplify the answer and write it as a mixed number.

Understanding Mixed Numbers

Before we proceed with the subtraction, let's take a closer look at mixed numbers. A mixed number is a combination of a whole number and a fraction. It is written in the form of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

For example, $3 \frac{2}{5}$ is a mixed number where $3$ is the whole number, $2$ is the numerator, and $5$ is the denominator.

Subtracting Mixed Numbers

To subtract mixed numbers, we need to follow a specific procedure. Here are the steps:

  1. Convert the mixed numbers to improper fractions: To subtract 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.
  2. Find a common denominator: Once we have converted the mixed numbers to improper fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two fractions.
  3. Subtract the numerators: Once we have found the common denominator, we can subtract the numerators. The numerator of the first fraction is the product of the whole number and the denominator, plus the numerator.
  4. Simplify the result: After subtracting the numerators, we need to simplify the result. If the result is an improper fraction, we can convert it back to a mixed number.

Subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$

Now that we have understood the procedure for subtracting mixed numbers, let's apply it to the problem of subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$.

Step 1: Convert the mixed numbers to improper fractions

To convert the mixed numbers to improper fractions, we need to multiply the whole number by the denominator and add the numerator.

625=(6×5)+25=30+25=3256 \frac{2}{5} = \frac{(6 \times 5) + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5}

114=(1×4)+14=4+14=541 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}

Step 2: Find a common denominator

To find a common denominator, we need to find the least common multiple (LCM) of the denominators of the two fractions.

The LCM of $5$ and $4$ is $20$.

Step 3: Subtract the numerators

Once we have found the common denominator, we can subtract the numerators.

325−54=(32×4)−(5×5)20=128−2520=10320\frac{32}{5} - \frac{5}{4} = \frac{(32 \times 4) - (5 \times 5)}{20} = \frac{128 - 25}{20} = \frac{103}{20}

Step 4: Simplify the result

After subtracting the numerators, we need to simplify the result. Since the result is an improper fraction, we can convert it back to a mixed number.

10320=5320\frac{103}{20} = 5 \frac{3}{20}

Conclusion

In this article, we have learned how to subtract mixed numbers. We have applied the procedure to the problem of subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$ and simplified the answer to a mixed number. The correct answer is $5 \frac{3}{20}$.

Frequently Asked Questions

  • What is a mixed number? A mixed number is a combination of a whole number and a fraction.
  • How do I subtract mixed numbers? To subtract mixed numbers, you need to convert them to improper fractions, find a common denominator, subtract the numerators, and simplify the result.
  • What is the correct answer to the problem of subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$? The correct answer is $5 \frac{3}{20}$.

References

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Introduction

Mixed numbers are a combination of a whole number and a fraction. They are commonly used in mathematics to represent quantities that have both a whole and a part. In this article, we will focus on the topic of subtracting mixed numbers, specifically answering frequently asked questions about the process.

Q&A

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 of $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you need to follow these steps:

  1. Convert the mixed numbers to improper fractions.
  2. Find a common denominator.
  3. Subtract the numerators.
  4. Simplify the result.

Q: What is the correct order of operations when subtracting mixed numbers?

A: The correct order of operations is:

  1. Convert the mixed numbers to improper fractions.
  2. Find a common denominator.
  3. Subtract the numerators.
  4. Simplify the result.

Q: How do I find a common denominator when subtracting mixed numbers?

A: To find a common denominator, you need to find the least common multiple (LCM) of the denominators of the two fractions.

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

A: The least common multiple (LCM) is the smallest multiple that is common to two or more numbers.

Q: How do I simplify the result when subtracting mixed numbers?

A: To simplify the result, you need to convert the improper fraction back to a mixed number.

Q: What is the correct answer to the problem of subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$?

A: The correct answer is $5 \frac{3}{20}$.

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

A: Yes, you can use a calculator to subtract mixed numbers. However, it is recommended to follow the steps outlined above to ensure accuracy.

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 a common denominator.
  • Not subtracting the numerators correctly.
  • Not simplifying the result correctly.

Conclusion

In this article, we have answered frequently asked questions about subtracting mixed numbers. We have provided step-by-step instructions on how to subtract mixed numbers and have highlighted common mistakes to avoid.

Frequently Asked Questions

  • What is a mixed number?
  • How do I subtract mixed numbers?
  • What is the correct order of operations when subtracting mixed numbers?
  • How do I find a common denominator when subtracting mixed numbers?
  • What is the least common multiple (LCM)?
  • How do I simplify the result when subtracting mixed numbers?
  • What is the correct answer to the problem of subtracting $6 \frac{2}{5} - 1 \frac{1}{4}$?
  • Can I use a calculator to subtract mixed numbers?
  • What are some common mistakes to avoid when subtracting mixed numbers?

References

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