$\frac{2}{3}+\frac{4}{5}$ is-

Q: $\frac{2}{3}+\frac{4}{5}$ is-

To solve the problem of adding the fractions $\frac{2}{3}$ and $\frac{4}{5}$, we need to find a common denominator. The denominators here are 3 and 5, and their least common multiple (LCM) is 15. 1. **Convert each fraction to have the common denominator of 15:** - For $\frac{2}{3}$, multiply both the numerator and the denominator by 5: \[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \] - For $\frac{4}{5}$, multiply both the numerator and the denominator by 3: \[ \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \] 2. **Add the two fractions:** \[ \frac{10}{15} + \frac{12}{15} = \frac{10 + 12}{15} = \frac{22}{15} \] 3. **Convert the improper fraction $\frac{22}{15}$ to a mixed number:** - Divide 22 by 15, which gives 1 as the whole number and a remainder of 7. - Therefore, $\frac{22}{15}$ can be expressed as the mixed number $1\frac{7}{15}$. Thus, the correct answer is Option 3: $1\frac{7}{15}$. **Explanation of why other options are incorrect:** 1. **Option 1: $\frac{6}{8}$** - $\frac{6}{8}$ simplifies to $\frac{3}{4}$, which is not equivalent to the sum $\frac{22}{15}$. 2. **Option 2: $1\frac{6}{15}$** - $1\frac{6}{15}$ simplifies to $1\frac{2}{5}$, which is not equal to $1\frac{7}{15}$. 3. **Option 4: $\frac{8}{15}$** - $\frac{8}{15}$ is less than 1 and does not match the sum $\frac{22}{15}$, which is greater than 1. Therefore, the only correct answer that matches the sum of $\frac{2}{3} + \frac{4}{5}$ is Option 3: $1\frac{7}{15}$.

Question

Accepted Answer

To solve the problem of adding the fractions $\frac{2}{3}$ and $\frac{4}{5}$, we need to find a common denominator. The denominators here are 3 and 5, and their least common multiple (LCM) is 15.

1. **Convert each fraction to have the common denominator of 15:**

- For $\frac{2}{3}$, multiply both the numerator and the denominator by 5:
     $$
     \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
     $$

- For $\frac{4}{5}$, multiply both the numerator and the denominator by 3:
     $$
     \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
     $$

2. **Add the two fractions:**

$$
   \frac{10}{15} + \frac{12}{15} = \frac{10 + 12}{15} = \frac{22}{15}
   $$

3. **Convert the improper fraction $\frac{22}{15}$ to a mixed number:**

- Divide 22 by 15, which gives 1 as the whole number and a remainder of 7.
   - Therefore, $\frac{22}{15}$ can be expressed as the mixed number $1\frac{7}{15}$.

Thus, the correct answer is Option 3: $1\frac{7}{15}$.

**Explanation of why other options are incorrect:**

1. **Option 1: $\frac{6}{8}$**

- $\frac{6}{8}$ simplifies to $\frac{3}{4}$, which is not equivalent to the sum $\frac{22}{15}$.

2. **Option 2: $1\frac{6}{15}$**

- $1\frac{6}{15}$ simplifies to $1\frac{2}{5}$, which is not equal to $1\frac{7}{15}$.

3. **Option 4: $\frac{8}{15}$**

- $\frac{8}{15}$ is less than 1 and does not match the sum $\frac{22}{15}$, which is greater than 1.

Therefore, the only correct answer that matches the sum of $\frac{2}{3} + \frac{4}{5}$ is Option 3: $1\frac{7}{15}$.