Simplify The Expression: $\frac 7}{9} - \frac{5}{18} =$10. Simplify The Expression $5 \frac{1 {6} - 2 \frac{7}{8} =$

Understanding Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. They are used to represent a value that is part of a whole. For example, $5 \frac{1}{6}$ represents a value that is 5 whole units and $\frac{1}{6}$ of a unit. Mixed numbers can be converted to improper fractions, which are fractions with a larger numerator than denominator.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same. For example, to convert $5 \frac{1}{6}$ to an improper fraction, we multiply 5 by 6 and add 1, resulting in $\frac{31}{6}$.

Simplifying the Expression: $5 \frac{1}{6} - 2 \frac{7}{8}$

To simplify the expression $5 \frac{1}{6} - 2 \frac{7}{8}$, we need to convert both mixed numbers to improper fractions. We can do this by following the steps outlined above.

Converting $5 \frac{1}{6}$ to an Improper Fraction

To convert $5 \frac{1}{6}$ to an improper fraction, we multiply 5 by 6 and add 1, resulting in $\frac{31}{6}$.

Converting $2 \frac{7}{8}$ to an Improper Fraction

To convert $2 \frac{7}{8}$ to an improper fraction, we multiply 2 by 8 and add 7, resulting in $\frac{23}{8}$.

Finding a Common Denominator

Now that we have both mixed numbers converted to improper fractions, we need to find a common denominator. The least common multiple (LCM) of 6 and 8 is 24. We can rewrite both fractions with a denominator of 24.

Rewriting $\frac{31}{6}$ with a Denominator of 24

To rewrite $\frac{31}{6}$ with a denominator of 24, we multiply the numerator and denominator by 4, resulting in $\frac{124}{24}$.

Rewriting $\frac{23}{8}$ with a Denominator of 24

To rewrite $\frac{23}{8}$ with a denominator of 24, we multiply the numerator and denominator by 3, resulting in $\frac{69}{24}$.

Subtracting the Fractions

Now that we have both fractions with a common denominator, we can subtract them. We subtract the numerators and keep the denominator the same.

Subtracting $\frac{124}{24}$ and $\frac{69}{24}$

To subtract $\frac{124}{24}$ and $\frac{69}{24}$, we subtract 124 from 69, resulting in $\frac{55}{24}$.

Converting the Result to a Mixed Number

To convert the improper fraction $\frac{55}{24}$ to a mixed number, we divide the numerator by the denominator and write the remainder as the new numerator.

Converting $\frac{55}{24}$ to a Mixed Number

To convert $\frac{55}{24}$ to a mixed number, we divide 55 by 24, resulting in 2 with a remainder of 11. The mixed number is $2 \frac{11}{24}$.

Conclusion

In conclusion, to simplify the expression $5 \frac{1}{6} - 2 \frac{7}{8}$, we need to convert both mixed numbers to improper fractions, find a common denominator, subtract the fractions, and then convert the result to a mixed number. The final answer is $2 \frac{11}{24}$.

Key Takeaways

• Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator and adding the numerator.
• To subtract fractions with different denominators, we need to find a common denominator and then subtract the numerators.
• To convert an improper fraction to a mixed number, we divide the numerator by the denominator and write the remainder as the new numerator.

Practice Problems

• Simplify the expression $3 \frac{2}{5} - 1 \frac{3}{4}$.
• Simplify the expression $4 \frac{1}{2} - 2 \frac{1}{3}$.

Real-World Applications

Mixed numbers and improper fractions are used in a variety of real-world applications, including cooking, building, and finance. For example, a recipe may call for 2 cups of flour and $\frac{1}{4}$ cup of sugar. A builder may need to measure 3 feet of wood and $\frac{1}{2}$ foot of nails. A financial analyst may need to calculate the interest on a loan of $5,000 and $\frac{1}{4}$ of a percent.

Common Mistakes

• Failing to convert mixed numbers to improper fractions before subtracting.
• Failing to find a common denominator before subtracting fractions.
• Failing to convert the result to a mixed number after subtracting fractions.

Tips and Tricks

• Use a calculator to find the least common multiple (LCM) of two numbers.
• Use a chart or table to help you keep track of the numerators and denominators.
• Practice, practice, practice! The more you practice, the more comfortable you will become with simplifying mixed numbers and subtracting fractions.
  

Understanding Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. They are used to represent a value that is part of a whole. For example, $5 \frac{1}{6}$ represents a value that is 5 whole units and $\frac{1}{6}$ of a unit.

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 with a larger numerator than denominator.

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 by the denominator and add the numerator. The result is the new numerator, and the denominator remains 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: You can use a calculator to find the LCM of two numbers, or you can use a chart or table to help you keep track of the multiples of each number.

Q: What is the difference between subtracting fractions and subtracting mixed numbers?

A: Subtracting fractions involves finding a common denominator and then subtracting the numerators. Subtracting mixed numbers involves converting the mixed numbers to improper fractions, finding a common denominator, and then subtracting the numerators.

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

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

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

A: Some common mistakes to avoid include failing to convert mixed numbers to improper fractions before subtracting, failing to find a common denominator before subtracting fractions, and failing to convert the result to a mixed number after subtracting fractions.

Q: How can I practice simplifying mixed numbers and subtracting fractions?

A: You can practice simplifying mixed numbers and subtracting fractions by working through example problems, using online resources, and taking practice quizzes.

Q: What are some real-world applications of mixed numbers and improper fractions?

A: Mixed numbers and improper fractions are used in a variety of real-world applications, including cooking, building, and finance. For example, a recipe may call for 2 cups of flour and $\frac{1}{4}$ cup of sugar, a builder may need to measure 3 feet of wood and $\frac{1}{2}$ foot of nails, and a financial analyst may need to calculate the interest on a loan of $5,000 and $\frac{1}{4}$ of a percent.

Q: How can I use technology to help me simplify mixed numbers and subtract fractions?

A: You can use a calculator to find the least common multiple (LCM) of two numbers, or you can use online resources such as math websites and apps to help you simplify mixed numbers and subtract fractions.

Q: What are some tips and tricks for simplifying mixed numbers and subtracting fractions?

A: Some tips and tricks for simplifying mixed numbers and subtracting fractions include using a chart or table to help you keep track of the numerators and denominators, practicing regularly, and using technology to help you find the LCM of two numbers.

Conclusion

Simplifying mixed numbers and subtracting fractions can be challenging, but with practice and patience, you can become more confident and proficient in these skills. Remember to convert mixed numbers to improper fractions, find a common denominator, and then subtract the numerators. Don't forget to convert the result to a mixed number after subtracting fractions. With these tips and tricks, you'll be well on your way to mastering the art of simplifying mixed numbers and subtracting fractions.