((2)/(5)+(3)/(10))÷(7)/(15)

Add Fractions with Common Denominator: Add the fractions (2/5) and (3/10). To add fractions, they must have a common denominator. The least common denominator (LCD) for 5 and 10 is 10. Convert (2/5) to a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. (2/5) * (2/2) = (4/10) Now add (4/10) and (3/10). (4/10) + (3/10) = (7/10)Divide by Reciprocal: Divide the sum (7/10) by the fraction (7/15). To divide by a fraction, multiply by its reciprocal. The reciprocal of (7/15) is (15/7). (7/10) ÷ (7/15) = (7/10) * (15/7)Simplify Multiplication: Simplify the multiplication of the two fractions. Multiply the numerators together and the denominators together. (7 * 15) / (10 * 7) = 105 / 70Find Greatest Common Divisor: Simplify the fraction 105/70 by finding the greatest common divisor (GCD) of 105 and 70. The GCD of 105 and 70 is 35. Divide both the numerator and the denominator by 35. (105/35) / (70/35) = 3 / 2

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\left(\frac{2}{5}+\frac{3}{10}\right) \div \frac{7}{15}

Add Fractions with Common Denominator: Add the fractions $(\frac{2}{5})$ and $(\frac{3}{10})$ . $\newline$ To add fractions, they must have a common denominator. The least common denominator (LCD) for $5$ and $10$ is $10$ . Convert $(\frac{2}{5})$ to a fraction with a denominator of $10$ by multiplying both the numerator and denominator by $2$ . $\newline$ $(\frac{2}{5}) \times (\frac{2}{2}) = (\frac{4}{10})$ $\newline$ Now add $(\frac{4}{10})$ and $(\frac{3}{10})$ . $\newline$ $(\frac{3}{10})$ $1$
Divide by Reciprocal: Divide the sum $(\frac{7}{10})$ by the fraction $(\frac{7}{15})$ . $\newline$ To divide by a fraction, multiply by its reciprocal. The reciprocal of $(\frac{7}{15})$ is $(\frac{15}{7})$ . $\newline$ $(\frac{7}{10}) \div (\frac{7}{15}) = (\frac{7}{10}) \times (\frac{15}{7})$
Simplify Multiplication: Simplify the multiplication of the two fractions. $\newline$ Multiply the numerators together and the denominators together. $\newline$ $(7 \times 15) / (10 \times 7) = 105 / 70$
Find Greatest Common Divisor: Simplify the fraction $\frac{105}{70}$ by finding the greatest common divisor (GCD) of $105$ and $70$ . The GCD of $105$ and $70$ is $35$ . Divide both the numerator and the denominator by $35$ . $\frac{105}{35}$ / $\frac{70}{35}$ = $\frac{3}{2}$