What Is The Fraction $\frac{10}{7}$ As A Mixed Number?

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Introduction

In mathematics, fractions and mixed numbers are two types of numbers that are used to represent parts of a whole. A fraction is a number that represents a part of a whole, and it is written in the form $\frac{a}{b}$, where $a$ is the numerator and $b$ is the denominator. A mixed number, on the other hand, is a number that is written as a combination of a whole number and a fraction. In this article, we will explore how to convert the fraction $\frac{10}{7}$ into a mixed number.

What is a Mixed Number?

A mixed number is a number that is written as a combination of a whole number and a fraction. It is written in the form $a\frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction part, and $c$ is the denominator of the fraction part. For example, $3\frac{4}{7}$ is a mixed number that represents $3$ whole units and $\frac{4}{7}$ of a unit.

Converting a Fraction to a Mixed Number

To convert a fraction to a mixed number, we need to divide the numerator by the denominator. The whole number part of the mixed number is the quotient of the division, and the fraction part is the remainder divided by the denominator. In the case of the fraction $\frac{10}{7}$, we can divide the numerator by the denominator to get the quotient and the remainder.

Calculating the Quotient and the Remainder

To calculate the quotient and the remainder, we can use long division or synthetic division. Let's use long division to divide $10$ by $7$.

  ____________________
7 | 10
  -7
  ----
  3

As we can see from the long division, the quotient is $1$ and the remainder is $3$. Therefore, the mixed number equivalent of the fraction $\frac{10}{7}$ is $1\frac{3}{7}$.

Verifying the Mixed Number

To verify that the mixed number $1\frac{3}{7}$ is equivalent to the fraction $\frac{10}{7}$, we can convert the mixed number back to a fraction. We can do this by multiplying the whole number part by the denominator and adding the numerator of the fraction part.

$$1\frac{3}{7} = 1 \times 7 + \frac{3}{7} = 7 + \frac{3}{7} = \frac{49}{7} + \frac{3}{7} = \frac{52}{7}$$

As we can see, the mixed number $1\frac{3}{7}$ is equivalent to the fraction $\frac{52}{7}$, which is the same as the original fraction $\frac{10}{7}$.

Conclusion

In conclusion, we have seen how to convert the fraction $\frac{10}{7}$ into a mixed number. We used long division to calculate the quotient and the remainder, and we verified that the mixed number $1\frac{3}{7}$ is equivalent to the fraction $\frac{10}{7}$. This demonstrates the importance of being able to convert fractions to mixed numbers, as it allows us to represent numbers in different forms and to perform calculations more easily.

Applications of Mixed Numbers

Mixed numbers have many applications in mathematics and real-life situations. For example, in architecture, mixed numbers are used to represent the height of buildings and the width of rooms. In engineering, mixed numbers are used to represent the length of pipes and the width of beams. In finance, mixed numbers are used to represent the interest rates on loans and the amount of money owed.

Real-Life Examples of Mixed Numbers

Here are some real-life examples of mixed numbers:

• A recipe for baking a cake calls for $2\frac{1}{4}$ cups of flour.
• A carpenter needs to cut a piece of wood that is $3\frac{1}{2}$ feet long.
• A doctor prescribes a patient to take $1\frac{1}{2}$ tablets of medication three times a day.

Conclusion

In conclusion, mixed numbers are an important concept in mathematics that has many applications in real-life situations. We have seen how to convert the fraction $\frac{10}{7}$ into a mixed number, and we have explored the importance of being able to convert fractions to mixed numbers. We have also seen some real-life examples of mixed numbers and their applications in mathematics and real-life situations.

Final Thoughts

Mixed numbers are a powerful tool in mathematics that can be used to represent numbers in different forms and to perform calculations more easily. They have many applications in mathematics and real-life situations, and they are an important concept to understand. By being able to convert fractions to mixed numbers, we can better understand the world around us and make more informed decisions.

References

• [1] "Mathematics for Dummies" by Mark Zegarelli
• [2] "Algebra and Trigonometry" by Michael Sullivan
• [3] "Geometry: Seeing, Doing, Understanding" by Harold R. Jacobs

Further Reading

• [1] "The Art of Mathematics" by Tom M. Apostol
• [2] "Mathematics: A Very Short Introduction" by Timothy Gowers
• [3] "The Joy of Mathematics" by Alfred S. Posamentier
  

Introduction

Mixed numbers are a fundamental concept in mathematics that can be used to represent numbers in different forms and to perform calculations more easily. However, many people may have questions about mixed numbers, such as how to convert fractions to mixed numbers, how to add and subtract mixed numbers, and how to use mixed numbers in real-life situations. In this article, we will answer some of the most frequently asked questions about mixed numbers.

Q: What is a mixed number?

A: A mixed number is a number that is written as a combination of a whole number and a fraction. It is written in the form $a\frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction part, and $c$ is the denominator of the fraction part.

Q: How do I convert a fraction to a mixed number?

A: To convert a fraction to a mixed number, you need to divide the numerator by the denominator. The whole number part of the mixed number is the quotient of the division, and the fraction part is the remainder divided by the denominator.

Q: How do I add and subtract mixed numbers?

A: To add and subtract mixed numbers, you need to follow the same rules as adding and subtracting fractions. You need to find a common denominator and then add or subtract the numerators.

Q: Can I use mixed numbers in real-life situations?

A: Yes, mixed numbers have many applications in real-life situations. For example, in architecture, mixed numbers are used to represent the height of buildings and the width of rooms. In engineering, mixed numbers are used to represent the length of pipes and the width of beams. In finance, mixed numbers are used to represent the interest rates on loans and the amount of money owed.

Q: How do I multiply and divide mixed numbers?

A: To multiply and divide mixed numbers, you need to follow the same rules as multiplying and dividing fractions. You need to multiply or divide the numerators and denominators separately.

Q: Can I use mixed numbers with decimals?

A: Yes, mixed numbers can be used with decimals. For example, $2\frac{1}{2}$ is equivalent to $2.5$.

Q: How do I convert a mixed number to a decimal?

A: To convert a mixed number to a decimal, you need to multiply the whole number part by the denominator and add the numerator. Then, you need to divide the result by the denominator.

Q: Can I use mixed numbers with percentages?

A: Yes, mixed numbers can be used with percentages. For example, $25\frac{1}{2}\%$ is equivalent to $25.5\%$.

Q: How do I convert a mixed number to a percentage?

A: To convert a mixed number to a percentage, you need to multiply the whole number part by the denominator and add the numerator. Then, you need to divide the result by the denominator and multiply by $100\%$.

Q: Can I use mixed numbers with fractions?

A: Yes, mixed numbers can be used with fractions. For example, $2\frac{1}{2} + \frac{1}{4}$ is a valid mathematical expression.

Q: How do I add and subtract mixed numbers with fractions?

A: To add and subtract mixed numbers with fractions, you need to follow the same rules as adding and subtracting fractions. You need to find a common denominator and then add or subtract the numerators.

Q: Can I use mixed numbers with negative numbers?

A: Yes, mixed numbers can be used with negative numbers. For example, $-2\frac{1}{2}$ is a valid mathematical expression.

Q: How do I multiply and divide mixed numbers with negative numbers?

A: To multiply and divide mixed numbers with negative numbers, you need to follow the same rules as multiplying and dividing fractions. You need to multiply or divide the numerators and denominators separately.

Conclusion

In conclusion, mixed numbers are a powerful tool in mathematics that can be used to represent numbers in different forms and to perform calculations more easily. We have answered some of the most frequently asked questions about mixed numbers, including how to convert fractions to mixed numbers, how to add and subtract mixed numbers, and how to use mixed numbers in real-life situations.

Final Thoughts

Mixed numbers are a fundamental concept in mathematics that can be used to represent numbers in different forms and to perform calculations more easily. By understanding mixed numbers, you can better understand the world around you and make more informed decisions.

References

• [1] "Mathematics for Dummies" by Mark Zegarelli
• [2] "Algebra and Trigonometry" by Michael Sullivan
• [3] "Geometry: Seeing, Doing, Understanding" by Harold R. Jacobs

Further Reading

• [1] "The Art of Mathematics" by Tom M. Apostol
• [2] "Mathematics: A Very Short Introduction" by Timothy Gowers
• [3] "The Joy of Mathematics" by Alfred S. Posamentier