| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | To find the greatest common divisor (GCD) of the set \(\left\{\frac{2185}{7}, 718, -274\right\}\), we need to follow these steps: 1. **Convert all numbers to integers**: - \(\frac{2185}{7}\) is already in fractional form. To convert it to an integer, we multiply by 7: \[ \frac{2185}{7} \times 7 = 2185 \] - \(718\) is already an integer. - \(-274\) is already an integer. 2. **Find the GCD of the resulting integers**: - The integers we need to consider are \(2185\), \(718\), and \(-274\). - Since the GCD is always non-negative, we can ignore the negative sign and find the GCD of \(2185\), \(718\), and \(274\). 3. **Calculate the GCD using the Euclidean algorithm**: - First, find the GCD of \(2185\) and \(718\): \[ 2185 \div 718 \approx 3 \quad \text{(remainder } 2185 - 3 \times 718 = 2185 - 2154 = 31\text{)} \] \[ \text{GCD}(2185, 718) = \text{GCD}(718, 31) \] \[ 718 \div 31 \approx 23 \quad \text{(remainder } 718 - 23 \times 31 = 718 - 713 = 5\text{)} \] \[ \text{GCD}(718, 31) = \text{GCD}(31, 5) \] \[ 31 \div 5 \approx 6 \quad \text{(remainder } 31 - 6 \times 5 = 31 - 30 = 1\text{)} \] \[ \text{GCD}(31, 5) = \text{GCD}(5, 1) = 1 \] - Now, find the GCD of \(1\) and \(274\): \[ \text{GCD}(1, 274) = 1 \] Therefore, the greatest common divisor of the set \(\left\{\frac{2185}{7}, 718, -274\right\}\) is \(\boxed{1}\). |
\frac{1}{7} |
| deepseek-r1 | To find the greatest common divisor (GCD) of the numbers \(\left\{\frac{2185}{7}, 718, -274\right\}\), we need to consider the GCD of the numerators and the least common multiple (LCM) of the denominators. 1. **Convert the numbers to fractions with a common denominator**: - \(\frac{2185}{7}\) is already a fraction with denominator 7. - \(718\) can be written as \(\frac{718}{1}\). - \(-274\) can be written as \(\frac{-274}{1}\). 2. **Find the GCD of the numerators**: - The numerators are 2185, 718, and -274. - Using the Euclidean algorithm, we find the GCD of 718 and -274: - \(718 \div 274 = 2\) with remainder 170. - \(274 \div 170 = 1\) with remainder 104. - \(170 \div 104 = 1\) with remainder 66. - \(104 \div 66 = 1\) with remainder 38. - \(66 \div 38 = 1\) with remainder 28. - \(38 \div 28 = 1\) with remainder 10. - \(28 \div 10 = 2\) with remainder 8. - \(10 \div 8 = 1\) with remainder 2. - \(8 \div 2 = 4\) with remainder 0. - GCD(718, -274) = 2. - Next, find GCD(2, 2185). Since 2185 is odd, GCD(2, 2185) = 1. 3. **Find the LCM of the denominators**: - The denominators are 7, 1, and 1. - LCM(7, 1, 1) = 7. 4. **Calculate the GCD of the set**: - The GCD of the numerators is 1. - The LCM of the denominators is 7. - Therefore, the GCD of the set \(\left\{\frac{2185}{7}, 718, -274\right\}\) is \(\frac{1}{7}\). Thus, the greatest common divisor is \(\boxed{\dfrac{1}{7}}\). |
\frac{1}{7} |
| gpto1 | To solve for the greatest common divisor (GCD) of \(\left\{\dfrac{2185}{7},\ 718,\ -274\right\}\), we need to handle the fraction first and ensure all numbers are represented with common denominators. **Step 1: Express all numbers with a common denominator of 7:** - \(\dfrac{2185}{7}\) - \(718 = \dfrac{718 \times 7}{7} = \dfrac{5026}{7}\) - \(-274 = \dfrac{-274 \times 7}{7} = \dfrac{-1918}{7}\) Now, all numbers are fractions with a denominator of 7: \(\dfrac{2185}{7}\), \(\dfrac{5026}{7}\), and \(\dfrac{-1918}{7}\). **Step 2: Find the GCD of the numerators:** Compute the GCD of the numerators \(2185\), \(5026\), and \(-1918\) (we can ignore the sign for the GCD). First, find the GCD of \(2185\) and \(5026\): 1. \(5026 ÷ 2185\) gives a quotient of 2 and a remainder of 656. 2. \(2185 ÷ 656\) gives a quotient of 3 and a remainder of 217. 3. \(656 ÷ 217\) gives a quotient of 3 and a remainder of 5. 4. \(217 ÷ 5\) gives a quotient of 43 and a remainder of 2. 5. \(5 ÷ 2\) gives a quotient of 2 and a remainder of 1. 6. \(2 ÷ 1\) gives a quotient of 2 and a remainder of 0. Thus, the GCD of \(2185\) and \(5026\) is 1. Next, find the GCD of this result with \(1918\): Since the GCD of 1 and any number is 1, the overall GCD of the numerators is 1. **Step 3: Find the LCM of the denominators:** The denominators are all 7, so the least common multiple (LCM) is 7. **Step 4: Compute the GCD of the original set:** The GCD of fractions \(\dfrac{a}{b}\) and \(\dfrac{c}{d}\) is \(\dfrac{\text{GCD}(a,c)}{\text{LCM}(b,d)}\). Therefore, the GCD of our set is \(\dfrac{1}{7}\). **Final Answer:** \(\boxed{\dfrac{1}{7}}\) |
\frac{1}{7} |
| gpt-4o-2024-08-06 | To find the greatest common divisor (GCD) of the set \(\left\{\frac{2185}{7}, 718, -274\right\}\), we first need to simplify the fraction \(\frac{2185}{7}\). First, divide 2185 by 7: \[ 2185 \div 7 = 312.142857\ldots \] Since 2185 is divisible by 7, we perform the division: \[ 2185 \div 7 = 312 \] Thus, \(\frac{2185}{7} = 312\). Now, we need to find the GCD of the integers \(312\), \(718\), and \(-274\). The GCD is unaffected by the sign, so we consider the positive values: \(312\), \(718\), and \(274\). We will use the Euclidean algorithm to find the GCD. 1. **Find \(\gcd(312, 718)\):** - Divide 718 by 312: \[ 718 \div 312 = 2 \quad \text{remainder: } 718 - 2 \times 312 = 94 \] - Now, find \(\gcd(312, 94)\): \[ 312 \div 94 = 3 \quad \text{remainder: } 312 - 3 \times 94 = 30 \] - Now, find \(\gcd(94, 30)\): \[ 94 \div 30 = 3 \quad \text{remainder: } 94 - 3 \times 30 = 4 \] - Now, find \(\gcd(30, 4)\): \[ 30 \div 4 = 7 \quad \text{remainder: } 30 - 7 \times 4 = 2 \] - Now, find \(\gcd(4, 2)\): \[ 4 \div 2 = 2 \quad \text{remainder: } 4 - 2 \times 2 = 0 \] - Since the remainder is 0, \(\gcd(4, 2) = 2\). Therefore, \(\gcd(312, 718) = 2\). 2. **Find \(\gcd(2, 274)\):** - Since 274 is even, it is divisible by 2: \[ 274 \div 2 = 137 \quad \text{remainder: } 0 \] Therefore, \(\gcd(2, 274) = 2\). Thus, the greatest common divisor of \(\left\{\frac{2185}{7}, 718, -274\right\}\) is \(\boxed{2}\). |
\frac{1}{7} |
| DeepSeek-Coder-V2-Lite-Instruct | To find the greatest common divisor (GCD) of the numbers \(\left\{\frac{2185}{7}, 718, -274\right\}\), we first need to convert all the numbers to integers. 1. Convert \(\frac{2185}{7}\) to an integer: \[ \frac{2185}{7} = 312.142857 \approx 312 \] So, \(\frac{2185}{7} = 312\). 2. The numbers are now \(312, 718, -274\). Next, we find the GCD of these integers. We can use the Euclidean algorithm for this purpose. ### Step-by-Step Calculation: 1. **Find the GCD of \(312\) and \(718\):** - Apply the Euclidean algorithm: \[ \text{GCD}(312, 718) = \text{GCD}(312, 718 \mod 312) \] \[ 718 \mod 312 = 718 - 2 \times 312 = 718 - 624 = 94 \] \[ \text{GCD}(312, 94) = \text{GCD}(94, 312 \mod 94) \] \[ 312 \mod 94 = 312 - 3 \times 94 = 312 - 282 = 30 \] \[ \text{GCD}(94, 30) = \text{GCD}(30, 94 \mod 30) \] \[ 94 \mod 30 = 94 - 3 \times 30 = 94 - 90 = 4 \] \[ \text{GCD}(30, 4) = \text{GCD}(4, 30 \mod 4) \] \[ 30 \mod 4 = 30 - 7 \times 4 = 30 - 28 = 2 \] \[ \text{GCD}(4, 2) = \text{GCD}(2, 4 \mod 2) \] \[ 4 \mod 2 = 0 \] \[ \text{GCD}(2, 0) = 2 \] 2. **Find the GCD of the result \(2\) and \(-274\):** - Since the GCD is invariant under the sign of the numbers, we can consider the absolute values: \[ \text{GCD}(2, 274) = \text{GCD}(2, 274) \] - The Euclidean algorithm for \(2\) and \(274\): \[ \text{GCD}(2, 274) = \text{GCD}(2, 274 \mod 2) \] \[ 274 \mod 2 = 0 \] \[ \text{GCD}(2, 0) = 2 \] Thus, the greatest common divisor of \(\left\{\frac{2185}{7}, 718, -274\right\}\) is \(\boxed{2}\). |
\frac{1}{7} |
| Meta-Llama-3.1-405B-Instruct-Turbo | ## Step 1: To find the greatest common divisor (GCD) of the given set of numbers, we first need to simplify the fraction $\frac{2185}{7}$ to obtain an integer. ## Step 2: Dividing $2185$ by $7$ gives us a quotient of $312$ with a remainder of $1$. Therefore, we can express $\frac{2185}{7}$ as $312\frac{1}{7}$. ## Step 3: Since we're looking for the GCD, which is an integer, we can disregard the fractional part and consider the integer part, which is $312$. ## Step 4: Now, we need to find the GCD of the set $\{312, 718, -274\}$. To do this, we can use the Euclidean algorithm. ## Step 5: First, we find the GCD of $312$ and $718$. We can express $718$ as $312 \times 2 + 94$. Then, we find the GCD of $312$ and $94$, which can be expressed as $312 = 94 \times 3 + 30$. ## Step 6: Continuing this process, we find the GCD of $94$ and $30$, which is $4$. ## Step 7: Now, we need to find the GCD of $4$ and $-274$. Since $4$ is a factor of $-274$, the GCD is simply $4$. ## Step 8: Therefore, the greatest common divisor of the given set of numbers is $\boxed{4}$. The final answer is: $\boxed{4}$ |
\frac{1}{7} |
| Meta-Llama-3.1-70B-Instruct-Turbo | ## Step 1: First, let's find the prime factorization of each number in the set. To find the greatest common divisor (GCD), we need to find the prime factorization of each number. The numbers are 2185/7, 718, and -274. ## Step 2: Find the prime factorization of 2185/7. First, let's simplify 2185/7. 2185 divided by 7 is 312.25, but since we are looking for the GCD, we will consider the numerator 2185. The prime factorization of 2185 is 5 * 19 * 23. ## Step 3: Find the prime factorization of 718. The prime factorization of 718 is 2 * 359. ## Step 4: Find the prime factorization of -274. The prime factorization of 274 is 2 * 137. Since the number is negative, we consider the absolute value. ## Step 5: Now, let's find the common factors among the three numbers. Comparing the prime factorizations, we see that there are no common prime factors among the three numbers. ## Step 6: Since there are no common prime factors, the greatest common divisor is 1. When there are no common prime factors, the GCD is always 1. The final answer is: $\boxed{1}$ |
\frac{1}{7} |
| Qwen2-72B-Instruct | To find the greatest common divisor (GCD) of the given numbers, we first need to convert them into integers by multiplying each number by the denominator if it's a fraction. In this case, we have: - The first number is $\frac{2185}{7}$, so when converted to an integer, it becomes $2185$. - The second number is $718$, which is already an integer. - The third number is $-274$, which is also an integer. Now, we need to find the GCD of $2185$, $718$, and $-274$. Since the GCD is always positive, we can ignore the negative sign for $-274$ and treat it as $274$ for our calculations. Let's start by finding the GCD of the first two numbers, $2185$ and $718$: 1. Use the Euclidean algorithm to find the GCD of $2185$ and $718$: - $2185 = 718 \times 3 + 33$ - $718 = 33 \times 21 + 25$ - $33 = 25 \times 1 + 8$ - $25 = 8 \times 3 + 1$ - $8 = 1 \times 8 + 0$ So, the GCD of $2185$ and $718$ is $1$. Next, let's find the GCD of $1$ and $274$: Since any number's GCD with $1$ is $1$, the GCD of $1$ and $274$ is also $1$. Therefore, the greatest common divisor of $\left\{\frac{2185}{7},718,-274\right\}$ is $\boxed{1}$. |
\frac{1}{7} |
| baichuan4 | To find the greatest common divisor (GCD) of the set $\left\{\frac{2185}{7},718,-274\right\}$, we first need to simplify the fractions and find the absolute values of the numbers, since the GCD is always positive. First, let's simplify $\frac{2185}{7}$: $$ \frac{2185}{7} = 312 $$ Now, we have the set $\{312, 718, -274\}$. We can ignore the negative sign for the purpose of finding the GCD, so we consider the set $\{312, 718, 274\}$ instead. Next, we use the Euclidean algorithm to find the GCD of these numbers. The Euclidean algorithm is based on the principle that the GCD of two numbers also divides their difference. 1. Find the GCD of $718$ and $312$: $$ 718 - 312 = 406 $$ 2. Find the GCD of $406$ and $312$: $$ 406 - 312 = 94 $$ 3. Find the GCD of $94$ and $312$: $$ 312 - 94 \times 3 = 312 - 282 = 30 $$ 4. Find the GCD of $30$ and $94$: $$ 94 - 30 \times 3 = 94 - 90 = 4 $$ 5. Find the GCD of $4$ and $30$: $$ 30 - 4 \times 7 = 30 - 28 = 2 $$ 6. Find the GCD of $2$ and $4$: $$ 4 - 2 \times 2 = 4 - 4 = 0 $$ Since the last non-zero remainder is $2$, this means that $2$ is the GCD of $718$ and $312$. Now, we need to verify that $2$ also divides $274$: $$ 274 \div 2 = 137 $$ Since $274$ is divisible by $2$, we can conclude that the GCD of the set $\{312, 718, 274\}$ is $2$. Therefore, the greatest common divisor of the set $\left\{\frac{2185}{7},718,-274\right\}$ is: $$ \boxed{2} $$ |
\frac{1}{7} |
| doubao | First simplify $\frac{2185}{7}=312\frac{1}{7}$. The greatest common divisor of 312 and 718: $312=2\times2\times2\times3\times13$ $718=2\times359$ So the greatest common divisor of 312 and 718 is 2. The greatest common divisor of 2 and -274 is 2. So the greatest common divisor of $\{\frac{2185}{7},718,-274\}$ is 2. $\boxed{2}$. |
\frac{1}{7} |
| gpto1 | To solve for the greatest common divisor (GCD) of \(\left\{\dfrac{2185}{7},\ 718,\ -274\right\}\), we need to handle the fraction first and ensure all numbers are represented with common denominators. **Step 1: Express all numbers with a common denominator of 7:** - \(\dfrac{2185}{7}\) - \(718 = \dfrac{718 \times 7}{7} = \dfrac{5026}{7}\) - \(-274 = \dfrac{-274 \times 7}{7} = \dfrac{-1918}{7}\) Now, all numbers are fractions with a denominator of 7: \(\dfrac{2185}{7}\), \(\dfrac{5026}{7}\), and \(\dfrac{-1918}{7}\). **Step 2: Find the GCD of the numerators:** Compute the GCD of the numerators \(2185\), \(5026\), and \(-1918\) (we can ignore the sign for the GCD). First, find the GCD of \(2185\) and \(5026\): 1. \(5026 ÷ 2185\) gives a quotient of 2 and a remainder of 656. 2. \(2185 ÷ 656\) gives a quotient of 3 and a remainder of 217. 3. \(656 ÷ 217\) gives a quotient of 3 and a remainder of 5. 4. \(217 ÷ 5\) gives a quotient of 43 and a remainder of 2. 5. \(5 ÷ 2\) gives a quotient of 2 and a remainder of 1. 6. \(2 ÷ 1\) gives a quotient of 2 and a remainder of 0. Thus, the GCD of \(2185\) and \(5026\) is 1. Next, find the GCD of this result with \(1918\): Since the GCD of 1 and any number is 1, the overall GCD of the numerators is 1. **Step 3: Find the LCM of the denominators:** The denominators are all 7, so the least common multiple (LCM) is 7. **Step 4: Compute the GCD of the original set:** The GCD of fractions \(\dfrac{a}{b}\) and \(\dfrac{c}{d}\) is \(\dfrac{\text{GCD}(a,c)}{\text{LCM}(b,d)}\). Therefore, the GCD of our set is \(\dfrac{1}{7}\). **Final Answer:** \(\boxed{\dfrac{1}{7}}\) |
\frac{1}{7} |
| kimi | To find the greatest common divisor (GCD) of the numbers \(\left\{\frac{2185}{7}, 718, -274\right\}\), we first simplify \(\frac{2185}{7}\): \[ \frac{2185}{7} = 312.142857 \approx 312 \quad (\text{since GCD is defined for integers}) \] So, we need to find the GCD of \(\{312, 718, -274\}\). The GCD of a set of numbers is the largest positive integer that divides all of them without leaving a remainder. We can use the Euclidean algorithm to find the GCD of these numbers. First, we find the GCD of 312 and 718. The Euclidean algorithm states that \(\gcd(a, b) = \gcd(b, a \mod b)\). So, we compute: \[ 718 \div 312 = 2 \quad \text{with a remainder of} \quad 718 - 2 \cdot 312 = 94 \] Thus, \(\gcd(718, 312) = \gcd(312, 94)\). Next, we compute: \[ 312 \div 94 = 3 \quad \text{with a remainder of} \quad 312 - 3 \cdot 94 = 30 \] So, \(\gcd(312, 94) = \gcd(94, 30)\). Next, we compute: \[ 94 \div 30 = 3 \quad \text{with a remainder of} \quad 94 - 3 \cdot 30 = 4 \] So, \(\gcd(94, 30) = \gcd(30, 4)\). Next, we compute: \[ 30 \div 4 = 7 \quad \text{with a remainder of} \quad 30 - 7 \cdot 4 = 2 \] So, \(\gcd(30, 4) = \gcd(4, 2)\). Next, we compute: \[ 4 \div 2 = 2 \quad \text{with a remainder of} \quad 4 - 2 \cdot 2 = 0 \] So, \(\gcd(4, 2) = 2\). Therefore, \(\gcd(312, 718) = 2\). Next, we find the GCD of 2 and -274. The GCD of two numbers is the same as the GCD of their absolute values, so we need to find \(\gcd(2, 274)\). Since 2 is a divisor of 274, we have: \[ 274 \div 2 = 137 \quad \text{with a remainder of} \quad 274 - 137 \cdot 2 = 0 \] So, \(\gcd(2, 274) = 2\). Therefore, \(\gcd(312, 718, -274) = 2\). The greatest common divisor of \(\left\{\frac{2185}{7}, 718, -274\right\}\) is \(\boxed{2}\). |
\frac{1}{7} |
| minimax | To find the greatest common divisor (GCD) of the set $\left\{\frac{2185}{7}, 718, -274\right\}$, we first need to simplify the set by removing any common factors that are not the greatest. First, let's simplify $\frac{2185}{7}$: $$\frac{2185}{7} = 313$$ Now we have the set $\{313, 718, -274\}$. Next, we need to find the GCD of these three numbers. Since 313 is a prime number, the GCD of any set containing 313 will have to be a divisor of 313. The only divisors of a prime number are 1 and the number itself. Since 313 is not a divisor of 718 or -274, the GCD cannot be 313. Let's check if 718 and -274 have any common factors with 313. Since 313 is prime and does not divide evenly into 718 or -274 (as |
\frac{1}{7} |
| wenxinyiyan | 本题考查的是最大公约数的计算。 首先，将给定的分数$\frac{2185}{7}$化为带分数： $\frac{2185}{7}=312\frac{1}{7}$ 接下来，对三个数312$\frac{1}{7}$，718和-274求最大公约数。 由于312$\frac{1}{7}$不是整数，可以先考虑718和-274的最大公约数。 为了找到这两个数的最大公约数，可以使用辗转相除法。 首先，计算718除以-274的余数： $718\div(-274)=2$余$170$ 然后，用-274除以170： $-274\div170=-1$余$-104$ 接着，用170除以-104： $170\div(-104)=-1$余66 再用-104除以66： $-104\div66=-1$余$-38$ 然后，用66除以-38： $66\div(-38)=-1$余28 接着，用-38除以28： $-38\div28=-1$余$-10$ 然后，用28除以-10： $28\div(-10)=-2$余8 再用-10除以8： $-10\div8=-1$余$-2$ 然后，用8除以-2： $8\div(-2)=-4$ 余数为0，说明-2是718和-274的最大公约数。 由于312$\frac{1}{7}$不是整数，它不能和-2有整数倍的关系，所以这三个数的最大公约数仍然是-2。 但是，最大公约数通常定义为正数。 因此，这三个数的最大公约数是2。 所以，最终答案是$\boxed{2}$。 |
\frac{1}{7} |
| zhipu | We start by finding the greatest common divisor (GCD) of the integers $718$ and $-274$. Using the Euclidean algorithm: \[ \text{gcd}(718, -274) = \text{gcd}(718, 274) \] \[ 718 = 2 \cdot 274 + 170 \] \[ 274 = 1 \cdot 170 + 104 \] \[ 170 = 1 \cdot 104 + 66 \] \[ 104 = 1 \cdot 66 + 38 \] \[ 66 = 1 \cdot 38 + 28 \] \[ 38 = 1 \cdot 28 + 10 \] \[ 28 = 2 \cdot 10 + 8 \] \[ 10 = 1 \cdot 8 + 2 \] \[ 8 = 4 \cdot 2 + 0 \] Thus, $\text{gcd}(718, 274) = 2$. Next, we need to find the GCD of this result with $\frac{2185}{7}$. First, simplify $\frac{2185}{7}$: \[ \frac{2185}{7} = 313 \] Now, we find $\text{gcd}(313, 2)$: \[ \text{gcd}(313, 2) \] Since $313$ is an odd number and $2$ is the smallest even number, their GCD is $1$. Thus, the greatest common divisor of the set $\left\{\frac{2185}{7}, 718, -274\right\}$ is $\boxed{1}$. |
\frac{1}{7} |
| deepseek-v3 | To find the greatest common divisor (GCD) of the numbers \(\left\{\frac{2185}{7}, 718, -274\right\}\), follow these steps: 1. **Express All Numbers as Integers or Fractions with the Same Denominator:** - \(\frac{2185}{7}\) is already a fraction. - \(718\) can be written as \(\frac{718 \times 7}{7} = \frac{5026}{7}\). - \(-274\) can be written as \(\frac{-274 \times 7}{7} = \frac{-1918}{7}\). Now, the numbers are: \(\left\{\frac{2185}{7}, \frac{5026}{7}, \frac{-1918}{7}\right\}\). 2. **Find the GCD of the Numerators:** Compute the GCD of \(2185\), \(5026\), and \(1918\) (ignoring the negative sign for GCD). - **GCD of 2185 and 5026:** - \(5026 \div 2185 = 2\) with a remainder of \(5026 - 2 \times 2185 = 656\). - Now, find GCD of \(2185\) and \(656\): - \(2185 \div 656 = 3\) with a remainder of \(2185 - 3 \times 656 = 217\). - Find GCD of \(656\) and \(217\): - \(656 \div 217 = 3\) with a remainder of \(656 - 3 \times 217 = 5\). - Find GCD of \(217\) and \(5\): - \(217 \div 5 = 43\) with a remainder of \(217 - 43 \times 5 = 2\). - Find GCD of \(5\) and \(2\): - \(5 \div 2 = 2\) with a remainder of \(1\). - Find GCD of \(2\) and \(1\): - \(2 \div 1 = 2\) with a remainder of \(0\). - GCD is \(1\). - **GCD of 1 and 1918:** - Since \(1\) is a divisor of all integers, the GCD remains \(1\). 3. **Express the GCD as a Fraction:** The GCD of the numerators is \(1\), and since all fractions have the same denominator \(7\), the overall GCD is: \[ \frac{1}{7} \] \(\boxed{\dfrac{1}{7}}\) |
\frac{1}{7} |