Divide. 2(5)/(6)÷2(3)/(7)= _____

Write as Fraction: Write the division problem as a fraction. 2(5/6) ÷ 2(3/7) can be written as (2 * 5/6) / (2 * 3/7).Simplify Expression: Simplify the expression by multiplying the numerators and denominators inside the parentheses. (2 * 5/6) / (2 * 3/7) = (10/6) / (6/7).Multiply by Reciprocal: When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. (10/6) / (6/7) = (10/6) * (7/6).Multiply Numerators: Multiply the numerators and the denominators. (10/6) * (7/6) = (10 * 7) / (6 * 6) = 70 / 36.Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of 70 and 36, which is 2. 70 / 36 can be simplified by dividing both the numerator and the denominator by 2. 70 / 2 = 35 and 36 / 2 = 18, so the simplified fraction is 35/18.Check for Further Simplification: Check if the fraction can be simplified further. The numbers 35 and 18 do not have any common divisors other than 1, so the fraction is already in its simplest form.

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Q. Divide.

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2 \frac{5}{6} \div 2 \frac{3}{7}= \_\_\_\_\_

Write as Fraction: Write the division problem as a fraction. $\newline$ $2\left(\frac{5}{6}\right) \div 2\left(\frac{3}{7}\right)$ can be written as $\left(2 \times \frac{5}{6}\right) / \left(2 \times \frac{3}{7}\right)$ .
Simplify Expression: Simplify the expression by multiplying the numerators and denominators inside the parentheses. $\newline$ $(2 \times 5/6) / (2 \times 3/7) = (10/6) / (6/7)$ .
Multiply by Reciprocal: When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. $\newline$ $(\frac{10}{6}) / (\frac{6}{7}) = (\frac{10}{6}) \times (\frac{7}{6})$ .
Multiply Numerators: Multiply the numerators and the denominators. $\newline$ $(\frac{10}{6}) \times (\frac{7}{6}) = (\frac{10 \times 7}{6 \times 6}) = \frac{70}{36}$ .
Simplify Fraction: Simplify the fraction by finding the greatest common divisor (GCD) of $70$ and $36$ , which is $2$ . $\frac{70}{36}$ can be simplified by dividing both the numerator and the denominator by $2$ . $\frac{70}{2} = 35$ and $\frac{36}{2} = 18$ , so the simplified fraction is $\frac{35}{18}$ .
Check for Further Simplification: Check if the fraction can be simplified further. $\newline$ The numbers $35$ and $18$ do not have any common divisors other than $1$ , so the fraction is already in its simplest form.