Question

2 5/13×2 3/5+4 3/7×2 1/3​

Answer 1

Ответ:

16  8/15

Пошаговое объяснение:

Answer 2

To solve this expression, follow these steps:

Step 1: Convert mixed numbers to improper fractions.

• $2 \frac{5}{13}$ can be converted to the improper fraction $\frac{2 \cdot 13 + 5}{13} = \frac{31}{13}$.
• $2 \frac{3}{5}$ can be converted to the improper fraction $\frac{2 \cdot 5 + 3}{5} = \frac{13}{5}$.
• $4 \frac{3}{7}$ can be converted to the improper fraction $\frac{4 \cdot 7 + 3}{7} = \frac{31}{7}$.
• $2 \frac{1}{3}$ can be converted to the improper fraction $\frac{2 \cdot 3 + 1}{3} = \frac{7}{3}$.

Step 2: Perform the multiplications and additions. Now, the expression becomes:

$$\frac{31}{13} \times \frac{13}{5} + \frac{31}{7} \times \frac{7}{3}$$

Simplify each term:

$$\frac{31}{13} \times \frac{13}{5} = \frac{31 \cdot 13}{13 \cdot 5} = \frac{403}{5}$$

$$\frac{31}{7} \times \frac{7}{3} = \frac{31 \cdot 7}{7 \cdot 3} = \frac{217}{3}$$

Step 3: Add the simplified fractions:

$$\frac{403}{5} + \frac{217}{3}$$

To add fractions with different denominators, find a common denominator: The least common multiple (LCM) of 5 and 3 is 15.

Adjust the fractions to have a common denominator of 15:

$$\frac{403 \cdot 3}{5 \cdot 3} + \frac{217 \cdot 5}{3 \cdot 5} = \frac{1209}{15} + \frac{1085}{15}$$

Add the fractions:

$$\frac{1209}{15} + \frac{1085}{15} = \frac{1209 + 1085}{15} = \frac{2294}{15}$$

The final result of the expression is:

$$\frac{2294}{15}$$

This fraction can also be simplified further by finding the greatest common divisor (GCD) of 2294 and 15 and dividing both the numerator and denominator by it.