To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
Given:
\[ \frac{2}{2z-2} ÷ \frac{7}{6} \]
Step 1: Find the reciprocal of the second fraction:
\[ \frac{7}{6} \text{ becomes } \frac{6}{7} \]
Step 2: Multiply the first fraction by the reciprocal of the second fraction:
\[ \frac{2}{2z-2} \times \frac{6}{7} \]
Step 3: Multiply the numerators and denominators:
\[ \frac{2 \times 6}{(2z-2) \times 7} = \frac{12}{14z-14} \]
Step 4: Simplify the fraction if possible. Notice that both numerator and denominator have a common factor of 2:
\[ \frac{12}{14z-14} = \frac{12}{2(7z-7)} = \frac{12}{2 \cdot 7(z-1)} = \frac{12}{14(z-1)} \]
So the final answer is:
\[ \frac{12}{14(z-1)} \]
Alternatively, if you notice from the beginning that simplification might make things easier:
Given:
\[ \frac{2}{2(z-1)} ÷ \frac{7}{6} \]
\[ \frac{2}{2(z-1)} \times \frac{6}{7} = \frac{2 \times 6}{2(z-1) \times 7} = \frac{12}{14(z-1)} \]
So in both approaches, you get:
\[ \frac{12}{14(z-1)} \]
divide these fractions.
2/2z-2 ÷ 7/6
3 answers
the answer was
3z/7z-7
3z/7z-7
Thank you for sharing the expected answer. Let's re-evaluate the problem and see how we can arrive at the result of \(\frac{3z}{7z-7}\).
Given:
\[ \frac{2}{2z-2} ÷ \frac{7}{6} \]
Step 1: Convert the division into multiplication using the reciprocal of the second fraction:
\[ \frac{2}{2z-2} \times \frac{6}{7} \]
Step 2: Observe that \(2z - 2\) can be factored:
\[ 2z - 2 = 2(z - 1) \]
So the fraction \(\frac{2}{2(z-1)}\) becomes:
\[ \frac{2}{2(z-1)} \]
Step 3: Now, multiply:
\[ \frac{2}{2(z-1)} \times \frac{6}{7} \]
Step 4: Simplify before multiplying:
\[ \frac{2 \times 6}{2 \cdot 7(z-1)} \]
The 2 in the numerator and the 2 in the denominator cancel each other:
\[ \frac{6}{7(z-1)} \]
Step 5: Simplify further:
\[ \frac{6}{7z - 7} \]
Since we are getting \(\frac{6}{7z-7}\) instead of \(\frac{3z}{7z-7}\), and your expected answer is \( \frac{3z}{7z-7} \), it indicates there might be a misunderstanding or a different approach. If we had something like \(\frac{3(2z)}{7(2z) - 7 \cdot 1} = \frac{6z}{14z - 7}\), it benefits checking the result explore specific cases or context of the problem for clarifications.
The critical steps are ensuring careful attention to handling expressions and transformations that align with your meanings.
Given:
\[ \frac{2}{2z-2} ÷ \frac{7}{6} \]
Step 1: Convert the division into multiplication using the reciprocal of the second fraction:
\[ \frac{2}{2z-2} \times \frac{6}{7} \]
Step 2: Observe that \(2z - 2\) can be factored:
\[ 2z - 2 = 2(z - 1) \]
So the fraction \(\frac{2}{2(z-1)}\) becomes:
\[ \frac{2}{2(z-1)} \]
Step 3: Now, multiply:
\[ \frac{2}{2(z-1)} \times \frac{6}{7} \]
Step 4: Simplify before multiplying:
\[ \frac{2 \times 6}{2 \cdot 7(z-1)} \]
The 2 in the numerator and the 2 in the denominator cancel each other:
\[ \frac{6}{7(z-1)} \]
Step 5: Simplify further:
\[ \frac{6}{7z - 7} \]
Since we are getting \(\frac{6}{7z-7}\) instead of \(\frac{3z}{7z-7}\), and your expected answer is \( \frac{3z}{7z-7} \), it indicates there might be a misunderstanding or a different approach. If we had something like \(\frac{3(2z)}{7(2z) - 7 \cdot 1} = \frac{6z}{14z - 7}\), it benefits checking the result explore specific cases or context of the problem for clarifications.
The critical steps are ensuring careful attention to handling expressions and transformations that align with your meanings.