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Which of the following expressions is equivalent to 216 1/3/27 1/3

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5 answers

To simplify the expression \( 216 \frac{1}{3} / 27 \frac{1}{3} \), we first convert both mixed numbers into improper fractions.

  1. Convert \( 216 \frac{1}{3} \):

    • \( 216 \times 3 + 1 = 648 + 1 = 649 \)
    • So, \( 216 \frac{1}{3} = \frac{649}{3} \).

  2. Convert \( 27 \frac{1}{3} \):

    • \( 27 \times 3 + 1 = 81 + 1 = 82 \)
    • So, \( 27 \frac{1}{3} = \frac{82}{3} \).

Now substituting these values back into the expression:

\[ 216 \frac{1}{3} / 27 \frac{1}{3} = \frac{649}{3} / \frac{82}{3} \]

To divide by a fraction, we multiply by its reciprocal:

\[ \frac{649}{3} \times \frac{3}{82} = \frac{649 \times 3}{3 \times 82} \]

The \( 3 \) in the numerator and denominator cancel out:

\[ = \frac{649}{82} \]

Now, to check if this fraction can be simplified further: 649 and 82 have no common factors (since 82 is \( 2 \times 41 \), and \( 649 \) is not divisible by either \( 2 \) or \( 41 \)), so this is in its simplest form.

Thus, the expression \( 216 \frac{1}{3} / 27 \frac{1}{3} \) is equivalent to:

\[ \frac{649}{82} \]

So the final answer is \( \frac{649}{82} \).

wrong try again please

Let's carefully simplify the expression \( 216 \frac{1}{3} / 27 \frac{1}{3} \) step by step.

  1. Convert mixed numbers to improper fractions:

    a. For \( 216 \frac{1}{3} \): \[ 216 \frac{1}{3} = 216 + \frac{1}{3} = \frac{216 \times 3 + 1}{3} = \frac{648 + 1}{3} = \frac{649}{3} \]

    b. For \( 27 \frac{1}{3} \): \[ 27 \frac{1}{3} = 27 + \frac{1}{3} = \frac{27 \times 3 + 1}{3} = \frac{81 + 1}{3} = \frac{82}{3} \]

  2. Set up the division: \[ \frac{649}{3} \div \frac{82}{3} \]

  3. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{649}{3} \times \frac{3}{82} \]

  4. Cancel out the common factors: The \( 3 \) in the numerator and denominator cancels out: \[ = \frac{649}{82} \]

Now, let’s calculate \( 649 \div 82 \):

  • Performing the division, \( 649 \div 82 \approx 7.9 \), and since \( 649 = 7 \times 82 + 53 \), it can be written as: \[ 649 = 7 \times 82 + 53 \quad (\text{Remainder: } 53) \] Thus, \( \frac{649}{82} = 7 \frac{53}{82} \).
  1. Final Answer: Thus the expression \( 216 \frac{1}{3} / 27 \frac{1}{3} = 7 \frac{53}{82} \).

Please check if you are looking for a specific form of the answer or something else. If you have specific choices you'd like me to consider, kindly provide those options.

out of these 4 choices , which is the right one ? or the closest ?

8

18

1/2

2

To solve the expression \( 216 \frac{1}{3} / 27 \frac{1}{3} \), let's break down the numbers:

  1. Convert the mixed numbers to improper fractions:

    • \( 216 \frac{1}{3} = 216 + \frac{1}{3} = \frac{649}{3} \)
    • \( 27 \frac{1}{3} = 27 + \frac{1}{3} = \frac{82}{3} \)

  2. Set up the division: \[ \frac{649/3}{82/3} = \frac{649}{82} \]

  3. Now we can simplify \( \frac{649}{82} \):

    • \( 649 \) divided by \( 82 \) gives approximately \( 7.9 \).
    • We can calculate the exact division: \( 649 \div 82 = 7\) remainder approximately \( 53\).

The answer \( 7.9 \) is closer to 8 in your options.

Conclusion

Among the options given:

  • 8
  • 18
  • \( \frac{1}{2} \)
  • 2

The closest match to \( 7.9 \) is 8.

So the correct choice is 8.