Solve 24/7*15+5/8*35+13/7+298/5

$$2 \frac{ 4 }{ 7 } \times 15+ \frac{ 5 }{ 8 } \times 35+1 \frac{ 3 }{ 7 } +29 \frac{ 8 }{ 5 }$$

Evaluate

$$\frac{3699}{40}=92.475$$

Solution Steps

Multiply 2 and 7 to get 14.

$$\frac{14+4}{7}\times 15+\frac{5}{8}\times 35+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Add 14 and 4 to get 18.

$$\frac{18}{7}\times 15+\frac{5}{8}\times 35+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Express \frac{18}{7}\times 15 as a single fraction.

$$\frac{18\times 15}{7}+\frac{5}{8}\times 35+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Multiply 18 and 15 to get 270.

$$\frac{270}{7}+\frac{5}{8}\times 35+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Express \frac{5}{8}\times 35 as a single fraction.

$$\frac{270}{7}+\frac{5\times 35}{8}+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Multiply 5 and 35 to get 175.

$$\frac{270}{7}+\frac{175}{8}+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Least common multiple of 7 and 8 is 56. Convert \frac{270}{7} and \frac{175}{8} to fractions with denominator 56.

$$\frac{2160}{56}+\frac{1225}{56}+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Since \frac{2160}{56} and \frac{1225}{56} have the same denominator, add them by adding their numerators.

$$\frac{2160+1225}{56}+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Add 2160 and 1225 to get 3385.

$$\frac{3385}{56}+\frac{1\times 7+3}{7}+\frac{29\times 5+8}{5}$$

Multiply 1 and 7 to get 7.

$$\frac{3385}{56}+\frac{7+3}{7}+\frac{29\times 5+8}{5}$$

Add 7 and 3 to get 10.

$$\frac{3385}{56}+\frac{10}{7}+\frac{29\times 5+8}{5}$$

Least common multiple of 56 and 7 is 56. Convert \frac{3385}{56} and \frac{10}{7} to fractions with denominator 56.

$$\frac{3385}{56}+\frac{80}{56}+\frac{29\times 5+8}{5}$$

Since \frac{3385}{56} and \frac{80}{56} have the same denominator, add them by adding their numerators.

$$\frac{3385+80}{56}+\frac{29\times 5+8}{5}$$

Add 3385 and 80 to get 3465.

$$\frac{3465}{56}+\frac{29\times 5+8}{5}$$

Reduce the fraction \frac{3465}{56} to lowest terms by extracting and canceling out 7.

$$\frac{495}{8}+\frac{29\times 5+8}{5}$$

Multiply 29 and 5 to get 145.

$$\frac{495}{8}+\frac{145+8}{5}$$

Add 145 and 8 to get 153.

$$\frac{495}{8}+\frac{153}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{495}{8} and \frac{153}{5} to fractions with denominator 40.

$$\frac{2475}{40}+\frac{1224}{40}$$

Since \frac{2475}{40} and \frac{1224}{40} have the same denominator, add them by adding their numerators.

$$\frac{2475+1224}{40}$$

Add 2475 and 1224 to get 3699.

$$\frac{3699}{40}$$

Factor

$$\frac{3 ^ {3} \cdot 137}{2 ^ {3} \cdot 5} = 92\frac{19}{40} = 92.475$$