Simplify (4ab^(2))/(15)÷(10 a)/(3b). Give your answer as a single fraction in its simplest form

Rewrite division as multiplication: To simplify the given expression, we will first rewrite the division as multiplication by the reciprocal of the second fraction. (4ab^2)/(15) ÷ (10a)/(3b) = (4ab^2)/(15) * (3b)/(10a)Factor out common factors: Next, we will factor out the common factors in the numerator and the denominator. (4 * a * b^2)/(15) * (3 * b)/(10 * a) = (4 * 3 * a * b^2 * b)/(15 * 10 * a)Cancel out common factors: Now, we will cancel out the common factors. The 'a' in the numerator and denominator cancels out, and we can also simplify the numbers. (4 * 3 * b^2 * b)/(15 * 10) = (12 * b^3)/(150)Simplify by dividing: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6. (12/6) * (b^3)/(150/6) = (2 * b^3)/(25)Final simplified answer: The expression is now simplified, and there are no common factors left to cancel out. The final answer is (2b^3)/(25).

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Algebra 2

Add and subtract rational expressions

Full solution

Q. Simplify

\frac{4 a b^{2}}{15} \div \frac{10 a}{3 b}

\newline

Give your answer as a single fraction in its simplest form

Rewrite division as multiplication: To simplify the given expression, we will first rewrite the division as multiplication by the reciprocal of the second fraction. $\newline$ $(4ab^2)/(15) \div (10a)/(3b) = (4ab^2)/(15) \times (3b)/(10a)$
Factor out common factors: Next, we will factor out the common factors in the numerator and the denominator. $\newline$ $(4 \cdot a \cdot b^2)/(15) \cdot (3 \cdot b)/(10 \cdot a) = (4 \cdot 3 \cdot a \cdot b^2 \cdot b)/(15 \cdot 10 \cdot a)$
Cancel out common factors: Now, we will cancel out the common factors. The $a$ in the numerator and denominator cancels out, and we can also simplify the numbers. $(4 \times 3 \times b^2 \times b)/(15 \times 10) = (12 \times b^3)/(150)$
Simplify by dividing: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $6$ . $\newline$ $\frac{12}{6} \times \frac{b^3}{150/6} = \frac{2 \times b^3}{25}$
Final simplified answer: The expression is now simplified, and there are no common factors left to cancel out. $\newline$ The final answer is $(2b^3)/(25)$ .