(a) 1 6 ÷ 5 = \frac{1}{6} \div 5 = 6 1 ​ ÷ 5 =

by ADMIN 47 views

Introduction

When dealing with fractions and division, it's essential to understand the concept of dividing by a whole number. In this case, we're asked to find the result of 16\frac{1}{6} divided by 5. To approach this problem, we need to recall the rules of dividing fractions, which involve inverting the second fraction and then multiplying.

Dividing Fractions

To divide a fraction by a whole number, we can use the following rule:

ab÷c=ab×1c\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}

In this case, we have 16\frac{1}{6} as the dividend and 5 as the divisor. We can rewrite the division as a multiplication by inverting the divisor:

16÷5=16×15\frac{1}{6} \div 5 = \frac{1}{6} \times \frac{1}{5}

Multiplying Fractions

Now that we have the division rewritten as a multiplication, we can proceed to multiply the fractions. When multiplying fractions, we simply multiply the numerators and denominators separately:

16×15=1×16×5\frac{1}{6} \times \frac{1}{5} = \frac{1 \times 1}{6 \times 5}

Simplifying the Result

After multiplying the fractions, we get a new fraction with a numerator of 1 and a denominator of 30. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case. However, we can simplify the fraction by dividing both the numerator and denominator by 1.

130\frac{1}{30}

Conclusion

In conclusion, the result of 16\frac{1}{6} divided by 5 is 130\frac{1}{30}. This is a fundamental concept in mathematics, and understanding how to divide fractions is crucial for solving various problems in algebra, geometry, and other branches of mathematics.

Real-World Applications

Dividing fractions has numerous real-world applications, such as:

  • Cooking: When a recipe calls for a certain amount of an ingredient, and you need to scale it up or down, you'll need to divide fractions to get the correct amount.
  • Science: In chemistry and physics, dividing fractions is essential for calculating concentrations, rates, and other quantities.
  • Finance: When investing or managing finances, dividing fractions can help you calculate interest rates, returns on investment, and other financial metrics.

Tips and Tricks

Here are some tips and tricks to help you master dividing fractions:

  • Always remember to invert the second fraction when dividing.
  • Use the rule ab÷c=ab×1c\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c} to rewrite division as multiplication.
  • Simplify the result by dividing both the numerator and denominator by their GCD.
  • Practice, practice, practice! Dividing fractions is a skill that requires practice to develop muscle memory.

Common Mistakes

Here are some common mistakes to avoid when dividing fractions:

  • Forgetting to invert the second fraction.
  • Not simplifying the result.
  • Not using the correct rule for dividing fractions.
  • Not practicing enough to develop muscle memory.

Conclusion

In conclusion, dividing fractions is a fundamental concept in mathematics that has numerous real-world applications. By understanding how to divide fractions, you'll be able to solve various problems in algebra, geometry, and other branches of mathematics. Remember to always invert the second fraction, use the correct rule, and simplify the result to get the correct answer. With practice and patience, you'll become a master of dividing fractions in no time!

Introduction

Dividing fractions can be a challenging concept, but with practice and patience, you'll become a master of it in no time! In this article, we'll answer some frequently asked questions about dividing fractions to help you better understand the concept.

Q: What is the rule for dividing fractions?

A: The rule for dividing fractions is:

ab÷c=ab×1c\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}

This means that when you divide a fraction by a whole number, you can rewrite it as a multiplication by inverting the second fraction.

Q: Why do I need to invert the second fraction?

A: Inverting the second fraction is necessary because it allows you to multiply the fractions together. When you divide a fraction by a whole number, you're essentially asking how many times the whole number fits into the fraction. Inverting the second fraction helps you to find this answer.

Q: How do I simplify the result of dividing fractions?

A: To simplify the result of dividing fractions, you need to divide both the numerator and denominator by their greatest common divisor (GCD). If the GCD is 1, then the fraction is already simplified.

Q: What if the GCD is not 1?

A: If the GCD is not 1, then you need to divide both the numerator and denominator by the GCD to simplify the fraction. For example, if you have the fraction 1218\frac{12}{18}, the GCD is 6. To simplify the fraction, you would divide both the numerator and denominator by 6, resulting in 23\frac{2}{3}.

Q: Can I divide a fraction by a fraction?

A: Yes, you can divide a fraction by a fraction. To do this, you need to invert the second fraction and then multiply the fractions together. For example, if you have the fraction 12\frac{1}{2} divided by 34\frac{3}{4}, you would invert the second fraction and multiply the fractions together:

12÷34=12×43=46=23\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3}

Q: What if I have a negative fraction?

A: If you have a negative fraction, you can simply multiply the fraction by -1 to make it positive. For example, if you have the fraction −12-\frac{1}{2}, you can multiply it by -1 to get 12\frac{1}{2}.

Q: Can I divide a fraction by a decimal?

A: Yes, you can divide a fraction by a decimal. To do this, you need to convert the decimal to a fraction and then divide the fractions together. For example, if you have the fraction 12\frac{1}{2} divided by 0.5, you would convert the decimal to a fraction and then divide the fractions together:

12÷0.5=12÷12=12×21=1\frac{1}{2} \div 0.5 = \frac{1}{2} \div \frac{1}{2} = \frac{1}{2} \times \frac{2}{1} = 1

Q: What if I have a mixed number?

A: If you have a mixed number, you can convert it to an improper fraction and then divide the fractions together. For example, if you have the mixed number 2122\frac{1}{2}, you can convert it to an improper fraction and then divide the fractions together:

212=522\frac{1}{2} = \frac{5}{2}

52÷3=52×13=56\frac{5}{2} \div 3 = \frac{5}{2} \times \frac{1}{3} = \frac{5}{6}

Conclusion

Dividing fractions can be a challenging concept, but with practice and patience, you'll become a master of it in no time! Remember to always invert the second fraction, use the correct rule, and simplify the result to get the correct answer. With these tips and tricks, you'll be able to solve various problems in algebra, geometry, and other branches of mathematics.