Write Problem: Write down the problem. We need to find the sum of the two fractions (-2)/-3 and (-5)/8.Simplify Fractions: Simplify each fraction if possible. The fraction (-2)/-3 can be simplified because the negative signs cancel each other out, so (-2)/-3 becomes 2/3. The fraction (-5)/8 cannot be simplified further.Find Common Denominator: Find a common denominator for the fractions 2/3 and (-5)/8. The least common denominator (LCD) for 3 and 8 is 24.Convert to Common Denominator: Convert each fraction to an equivalent fraction with the common denominator. For 2/3, we multiply the numerator and the denominator by 8 to get (2*8)/(3*8) = 16/24. For (-5)/8, we multiply the numerator and the denominator by 3 to get (-5*3)/(8*3) = -15/24.Add Fractions: Add the fractions with the common denominator. Now we add 16/24 and -15/24. 16/24 + (-15/24) = (16 - 15)/24 = 1/24.

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

\frac{-2}{-3} + \frac{-5}{8}

Write Problem: Write down the problem. $\newline$ We need to find the sum of the two fractions $\frac{-2}{-3}$ and $\frac{-5}{8}$ .
Simplify Fractions: Simplify each fraction if possible. $\newline$ The fraction $(-2)/-3$ can be simplified because the negative signs cancel each other out, so $(-2)/-3$ becomes $2/3$ . The fraction $(-5)/8$ cannot be simplified further.
Find Common Denominator: Find a common denominator for the fractions $\frac{2}{3}$ and $\frac{-5}{8}$ . The least common denominator (LCD) for $3$ and $8$ is $24$ .
Convert to Common Denominator: Convert each fraction to an equivalent fraction with the common denominator. $\newline$ For $\frac{2}{3}$ , we multiply the numerator and the denominator by $8$ to get $\left(\frac{2\times 8}{3\times 8}\right) = \frac{16}{24}$ . $\newline$ For $\frac{-5}{8}$ , we multiply the numerator and the denominator by $3$ to get $\left(\frac{-5\times 3}{8\times 3}\right) = \frac{-15}{24}$ .
Add Fractions: Add the fractions with the common denominator. $\newline$ Now we add $\frac{16}{24}$ and $-\frac{15}{24}$ . $\newline$ $\frac{16}{24} + (-\frac{15}{24}) = \frac{16 - 15}{24} = \frac{1}{24}.$