Solve 4/35*5+18/35*6+12/35*7+1/35*8

$$\frac { 4 } { 35 } \times 5 + \frac { 18 } { 35 } \times 6 + \frac { 12 } { 35 } \times 7 + \frac { 1 } { 35 } \times 8$$

Evaluate

$$\frac{44}{7}\approx 6.285714286$$

Solution Steps

Express \frac{4}{35}\times 5 as a single fraction.

$$\frac{4\times 5}{35}+\frac{18}{35}\times 6+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Multiply 4 and 5 to get 20.

$$\frac{20}{35}+\frac{18}{35}\times 6+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Reduce the fraction \frac{20}{35} to lowest terms by extracting and canceling out 5.

$$\frac{4}{7}+\frac{18}{35}\times 6+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Express \frac{18}{35}\times 6 as a single fraction.

$$\frac{4}{7}+\frac{18\times 6}{35}+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Multiply 18 and 6 to get 108.

$$\frac{4}{7}+\frac{108}{35}+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Least common multiple of 7 and 35 is 35. Convert \frac{4}{7} and \frac{108}{35} to fractions with denominator 35.

$$\frac{20}{35}+\frac{108}{35}+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Since \frac{20}{35} and \frac{108}{35} have the same denominator, add them by adding their numerators.

$$\frac{20+108}{35}+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Add 20 and 108 to get 128.

$$\frac{128}{35}+\frac{12}{35}\times 7+\frac{1}{35}\times 8$$

Express \frac{12}{35}\times 7 as a single fraction.

$$\frac{128}{35}+\frac{12\times 7}{35}+\frac{1}{35}\times 8$$

Multiply 12 and 7 to get 84.

$$\frac{128}{35}+\frac{84}{35}+\frac{1}{35}\times 8$$

Since \frac{128}{35} and \frac{84}{35} have the same denominator, add them by adding their numerators.

$$\frac{128+84}{35}+\frac{1}{35}\times 8$$

Add 128 and 84 to get 212.

$$\frac{212}{35}+\frac{1}{35}\times 8$$

Multiply \frac{1}{35} and 8 to get \frac{8}{35}.

$$\frac{212}{35}+\frac{8}{35}$$

Since \frac{212}{35} and \frac{8}{35} have the same denominator, add them by adding their numerators.

$$\frac{212+8}{35}$$

Add 212 and 8 to get 220.

$$\frac{220}{35}$$

Reduce the fraction \frac{220}{35} to lowest terms by extracting and canceling out 5.

$$\frac{44}{7}$$

Factor

$$\frac{2 ^ {2} \cdot 11}{7} = 6\frac{2}{7} = 6.285714285714286$$