Rewrite The Following Mixed Numbers As Improper Fractions:1. $2 \frac{1}{2}$2. $-3 \frac{2}{3}$3. $7 \frac{1}{4}$4. $-5 \frac{91}{100}$5. $6 \frac{5}{7}$6. $-8 \frac{3}{4}$7. $100

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Understanding Mixed Numbers and Improper Fractions

In mathematics, mixed numbers and improper fractions are two ways to express a number that is greater than a whole number. A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator. In this article, we will focus on rewriting mixed numbers as improper fractions.

Rewriting Mixed Numbers as Improper Fractions: A Step-by-Step Guide

1. 2122 \frac{1}{2}

To rewrite the mixed number 2122 \frac{1}{2} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

212=2×2+1=52 \frac{1}{2} = 2 \times 2 + 1 = 5

So, the improper fraction is 52\frac{5}{2}.

2. −323-3 \frac{2}{3}

To rewrite the mixed number −323-3 \frac{2}{3} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

−323=−3×3+2=−7-3 \frac{2}{3} = -3 \times 3 + 2 = -7

So, the improper fraction is −73\frac{-7}{3}.

3. 7147 \frac{1}{4}

To rewrite the mixed number 7147 \frac{1}{4} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

714=7×4+1=297 \frac{1}{4} = 7 \times 4 + 1 = 29

So, the improper fraction is 294\frac{29}{4}.

4. −591100-5 \frac{91}{100}

To rewrite the mixed number −591100-5 \frac{91}{100} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

−591100=−5×100+91=−509-5 \frac{91}{100} = -5 \times 100 + 91 = -509

So, the improper fraction is −509100\frac{-509}{100}.

5. 6576 \frac{5}{7}

To rewrite the mixed number 6576 \frac{5}{7} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

657=6×7+5=476 \frac{5}{7} = 6 \times 7 + 5 = 47

So, the improper fraction is 477\frac{47}{7}.

6. −834-8 \frac{3}{4}

To rewrite the mixed number −834-8 \frac{3}{4} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

−834=−8×4+3=−31-8 \frac{3}{4} = -8 \times 4 + 3 = -31

So, the improper fraction is −314\frac{-31}{4}.

7. 10012100 \frac{1}{2}

To rewrite the mixed number 10012100 \frac{1}{2} as an improper fraction, we need to multiply the whole number by the denominator and then add the numerator.

10012=100×2+1=201100 \frac{1}{2} = 100 \times 2 + 1 = 201

So, the improper fraction is 2012\frac{201}{2}.

Conclusion

Rewriting mixed numbers as improper fractions is an essential skill in mathematics. By following the steps outlined in this article, you can easily convert mixed numbers to improper fractions. Remember to multiply the whole number by the denominator and then add the numerator to get the improper fraction. With practice, you will become proficient in rewriting mixed numbers as improper fractions.

Tips and Tricks

  • When rewriting mixed numbers as improper fractions, make sure to multiply the whole number by the denominator and then add the numerator.
  • Use a calculator to check your answers if you are unsure.
  • Practice rewriting mixed numbers as improper fractions to become proficient in this skill.
  • Remember that improper fractions can be simplified by dividing the numerator and denominator by their greatest common divisor (GCD).

Common Mistakes to Avoid

  • Not multiplying the whole number by the denominator before adding the numerator.
  • Not adding the numerator to the product of the whole number and the denominator.
  • Not simplifying the improper fraction by dividing the numerator and denominator by their GCD.

Real-World Applications

Rewriting mixed numbers as improper fractions has many real-world applications. For example:

  • In cooking, you may need to convert a mixed number of cups to an improper fraction to measure ingredients accurately.
  • In construction, you may need to convert a mixed number of feet to an improper fraction to measure distances accurately.
  • In finance, you may need to convert a mixed number of dollars to an improper fraction to calculate interest rates accurately.

Frequently Asked Questions

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I rewrite a mixed number as an improper fraction?

A: To rewrite a mixed number as an improper fraction, you need to multiply the whole number by the denominator and then add the numerator.

Q: What is the formula for rewriting a mixed number as an improper fraction?

A: The formula is: (whole number × denominator) + numerator = improper fraction

Q: Can I simplify an improper fraction?

A: Yes, you can simplify an improper fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Q: How do I simplify an improper fraction?

A: To simplify an improper fraction, you need to find the GCD of the numerator and denominator and divide both numbers by the GCD.

Q: What is the GCD of two numbers?

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.

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

A: You can find the GCD of two numbers by listing the factors of each number and finding the largest common factor.

Q: Can I convert an improper fraction to a mixed number?

A: Yes, you can convert an improper fraction to a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction.

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

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and write the remainder as a fraction.

Q: What is the formula for converting an improper fraction to a mixed number?

A: The formula is: (numerator ÷ denominator) = whole number + (remainder ÷ denominator)

Q: Can I use a calculator to convert mixed numbers to improper fractions?

A: Yes, you can use a calculator to convert mixed numbers to improper fractions.

Q: How do I use a calculator to convert a mixed number to an improper fraction?

A: To use a calculator to convert a mixed number to an improper fraction, you need to enter the mixed number in the calculator and select the "mixed to improper" function.

Q: Can I use a calculator to convert improper fractions to mixed numbers?

A: Yes, you can use a calculator to convert improper fractions to mixed numbers.

Q: How do I use a calculator to convert an improper fraction to a mixed number?

A: To use a calculator to convert an improper fraction to a mixed number, you need to enter the improper fraction in the calculator and select the "improper to mixed" function.

Common Mistakes to Avoid

  • Not multiplying the whole number by the denominator before adding the numerator.
  • Not adding the numerator to the product of the whole number and the denominator.
  • Not simplifying the improper fraction by dividing the numerator and denominator by their GCD.
  • Not using a calculator to check your answers.
  • Not practicing rewriting mixed numbers as improper fractions.

Real-World Applications

Rewriting mixed numbers as improper fractions has many real-world applications. For example:

  • In cooking, you may need to convert a mixed number of cups to an improper fraction to measure ingredients accurately.
  • In construction, you may need to convert a mixed number of feet to an improper fraction to measure distances accurately.
  • In finance, you may need to convert a mixed number of dollars to an improper fraction to calculate interest rates accurately.

By mastering the skill of rewriting mixed numbers as improper fractions, you can apply it to a wide range of real-world situations.

Conclusion

Rewriting mixed numbers as improper fractions is an essential skill in mathematics. By following the steps outlined in this article, you can easily convert mixed numbers to improper fractions. Remember to multiply the whole number by the denominator and then add the numerator to get the improper fraction. With practice, you will become proficient in rewriting mixed numbers as improper fractions.