(a) $7 \div \frac{1}{6} =$
Understanding the Problem
When dealing with division involving fractions, it's essential to remember that division is the same as multiplication by the reciprocal. In this case, we have 7 divided by 1/6. To solve this problem, we need to convert the division into a multiplication problem by taking the reciprocal of the divisor.
The Reciprocal of the Divisor
The reciprocal of a fraction is obtained by swapping its numerator and denominator. In this case, the reciprocal of 1/6 is 6/1, which simplifies to 6.
Multiplying by the Reciprocal
Now that we have the reciprocal of the divisor, we can rewrite the division problem as a multiplication problem. So, 7 divided by 1/6 is equivalent to 7 multiplied by 6.
Solving the Multiplication Problem
To solve the multiplication problem, we simply multiply the two numbers together. 7 multiplied by 6 is equal to 42.
Conclusion
Therefore, the value of 7 divided by 1/6 is 42.
Real-World Applications
Understanding how to divide by fractions is crucial in various real-world applications, such as:
- Cooking: When a recipe calls for a certain amount of an ingredient to be divided among a certain number of people, you may need to divide by fractions to get the correct amount.
- Science: In scientific calculations, you may need to divide by fractions to get accurate results.
- Finance: When dealing with investments or loans, you may need to divide by fractions to calculate interest rates or returns.
Tips and Tricks
Here are some tips and tricks to help you remember how to divide by fractions:
- Reciprocal Rule: Remember that division is the same as multiplication by the reciprocal.
- Swap and Multiply: Swap the numerator and denominator of the divisor and multiply.
- Practice, Practice, Practice: The more you practice dividing by fractions, the more comfortable you'll become with the concept.
Common Mistakes
Here are some common mistakes to avoid when dividing by fractions:
- Forgetting the Reciprocal: Don't forget to take the reciprocal of the divisor.
- Swapping the Wrong Way: Make sure to swap the numerator and denominator of the divisor correctly.
- Not Multiplying: Don't forget to multiply the two numbers together.
Conclusion
Dividing by fractions may seem intimidating at first, but with practice and patience, you'll become proficient in no time. Remember to take the reciprocal of the divisor, swap the numerator and denominator, and multiply. With these tips and tricks, you'll be able to tackle even the most challenging division problems involving fractions.
Final Answer
The final answer is:
Frequently Asked Questions
Q: What is the rule for dividing by fractions?
A: The rule for dividing by fractions is to multiply by the reciprocal of the divisor. In other words, to divide by a fraction, you need to multiply by the reciprocal of that fraction.
Q: How do I find the reciprocal of a fraction?
A: To find the reciprocal of a fraction, you need to swap its numerator and denominator. For example, the reciprocal of 1/6 is 6/1.
Q: Can you give me an example of how to divide by a fraction using the reciprocal rule?
A: Let's say you want to divide 7 by 1/6. To do this, you would multiply 7 by the reciprocal of 1/6, which is 6. So, 7 divided by 1/6 is equal to 7 multiplied by 6, which is 42.
Q: What if I have a fraction with a negative sign?
A: If you have a fraction with a negative sign, you need to take the reciprocal of the absolute value of the fraction. For example, the reciprocal of -1/6 is -6/1.
Q: Can I divide by a fraction that has a variable in the numerator or denominator?
A: Yes, you can divide by a fraction that has a variable in the numerator or denominator. However, you need to follow the same rules as before: multiply by the reciprocal of the divisor.
Q: How do I simplify a fraction after dividing by another fraction?
A: To simplify a fraction after dividing by another fraction, you need to multiply the numerator and denominator by the same value. For example, if you have 7/6 and you want to simplify it, you can multiply both the numerator and denominator by 2 to get 14/12.
Q: Can you give me some examples of real-world applications of dividing by fractions?
A: Here are a few examples:
- Cooking: When a recipe calls for a certain amount of an ingredient to be divided among a certain number of people, you may need to divide by fractions to get the correct amount.
- Science: In scientific calculations, you may need to divide by fractions to get accurate results.
- Finance: When dealing with investments or loans, you may need to divide by fractions to calculate interest rates or returns.
Q: What if I get a negative result when dividing by a fraction?
A: If you get a negative result when dividing by a fraction, it means that the divisor is negative. In this case, you need to take the reciprocal of the absolute value of the divisor and multiply by the numerator.
Q: Can I divide by a fraction that has a zero in the denominator?
A: No, you cannot divide by a fraction that has a zero in the denominator. This is because division by zero is undefined.
Q: How do I know if a fraction is in its simplest form after dividing by another fraction?
A: To check if a fraction is in its simplest form after dividing by another fraction, you need to see if the numerator and denominator have any common factors. If they do, you need to divide both the numerator and denominator by that factor to simplify the fraction.
Q: Can you give me some tips for remembering how to divide by fractions?
A: Here are a few tips:
- Reciprocal Rule: Remember that division is the same as multiplication by the reciprocal.
- Swap and Multiply: Swap the numerator and denominator of the divisor and multiply.
- Practice, Practice, Practice: The more you practice dividing by fractions, the more comfortable you'll become with the concept.
Final Answer
The final answer is: