Divide.$\[ 16 \div 1 \frac{16}{17} \\]$\[ 16 \div 1 \frac{16}{17} = \square \\](Type An Integer, Proper Fraction, Or Mixed Number.)

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Understanding the Problem

When dealing with division problems involving mixed numbers, it's essential to understand the concept of dividing by a mixed number. A mixed number is a combination of a whole number and a proper fraction. In this case, we have 1 16/17 as the divisor. To divide 16 by 1 16/17, we need to follow a specific procedure.

Converting the Mixed Number to an Improper Fraction

To make the division process easier, we can convert the mixed number 1 16/17 to an improper fraction. To do this, we multiply the whole number part (1) by the denominator (17) and then add the numerator (16). This gives us:

1 × 17 = 17 17 + 16 = 33

So, the mixed number 1 16/17 is equivalent to the improper fraction 33/17.

Dividing 16 by the Improper Fraction

Now that we have the mixed number converted to an improper fraction, we can proceed with the division. To divide 16 by 33/17, we can multiply 16 by the reciprocal of 33/17, which is 17/33.

16 × 17/33 = 272/33

Simplifying the Result

To simplify the result, we can divide both the numerator (272) and the denominator (33) by their greatest common divisor (GCD). The GCD of 272 and 33 is 1, so the result remains the same.

272 ÷ 1 = 272 33 ÷ 1 = 33

Therefore, the result of dividing 16 by 1 16/17 is 272/33.

Conclusion

In conclusion, when dividing by a mixed number, it's essential to convert the mixed number to an improper fraction first. Then, we can proceed with the division by multiplying the dividend by the reciprocal of the divisor. In this case, the result of dividing 16 by 1 16/17 is 272/33.

Final Answer

The final answer is: 272/33\boxed{272/33}

Frequently Asked Questions

Q: What is the concept of dividing by a mixed number?

A: Dividing by a mixed number involves converting the mixed number to an improper fraction and then proceeding with the division. This is because mixed numbers can be more challenging to work with in division problems.

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 part by the denominator and then add the numerator. This gives you the new numerator, and the denominator remains the same.

Q: What is the reciprocal of a fraction?

A: The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 3/4 is 4/3.

Q: How do I multiply a fraction by its reciprocal?

A: When you multiply a fraction by its reciprocal, the result is always 1. This is because the numerator and the denominator are swapped, and the product of the numerator and the denominator is always 1.

Q: Why do I need to multiply the dividend by the reciprocal of the divisor?

A: Multiplying the dividend by the reciprocal of the divisor is a way to simplify the division problem. By doing this, you are essentially multiplying the dividend by 1, which does not change the value of the dividend.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. In the context of this problem, the GCD of 272 and 33 is 1, which means that the result of the division cannot be simplified further.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

Q: What is the final answer to the problem 16 ÷ 1 16/17?

A: The final answer to the problem 16 ÷ 1 16/17 is 272/33.

Additional Tips and Tricks

  • When working with mixed numbers, it's essential to convert them to improper fractions to make the division process easier.
  • Multiplying a fraction by its reciprocal is a way to simplify the division problem.
  • The greatest common divisor (GCD) is a crucial concept in simplifying fractions.
  • To simplify a fraction, you need to find the GCD of the numerator and the denominator and divide both numbers by the GCD.

Conclusion

In conclusion, dividing by a mixed number involves converting the mixed number to an improper fraction and then proceeding with the division. By following the steps outlined in this article, you can simplify the division problem and arrive at the final answer. Remember to convert mixed numbers to improper fractions, multiply the dividend by the reciprocal of the divisor, and simplify the fraction by finding the greatest common divisor (GCD).