Solve 3/7+7/9+1/7div1/4

$$\frac { 3 } { 7 } + \frac { 7 } { 9 } + \frac { 1 } { 7 } \div \frac { 1 } { 4 }$$

Evaluate

$$\frac{16}{9}\approx 1.777777778$$

Solution Steps

Least common multiple of 7 and 9 is 63. Convert \frac{3}{7} and \frac{7}{9} to fractions with denominator 63.

$$\frac{27}{63}+\frac{49}{63}+\frac{\frac{1}{7}}{\frac{1}{4}}$$

Since \frac{27}{63} and \frac{49}{63} have the same denominator, add them by adding their numerators.

$$\frac{27+49}{63}+\frac{\frac{1}{7}}{\frac{1}{4}}$$

Add 27 and 49 to get 76.

$$\frac{76}{63}+\frac{\frac{1}{7}}{\frac{1}{4}}$$

Divide \frac{1}{7} by \frac{1}{4} by multiplying \frac{1}{7} by the reciprocal of \frac{1}{4}.

$$\frac{76}{63}+\frac{1}{7}\times 4$$

Multiply \frac{1}{7} and 4 to get \frac{4}{7}.

$$\frac{76}{63}+\frac{4}{7}$$

Least common multiple of 63 and 7 is 63. Convert \frac{76}{63} and \frac{4}{7} to fractions with denominator 63.

$$\frac{76}{63}+\frac{36}{63}$$

Since \frac{76}{63} and \frac{36}{63} have the same denominator, add them by adding their numerators.

$$\frac{76+36}{63}$$

Add 76 and 36 to get 112.

$$\frac{112}{63}$$

Reduce the fraction \frac{112}{63} to lowest terms by extracting and canceling out 7.

$$\frac{16}{9}$$

Factor

$$\frac{2 ^ {4}}{3 ^ {2}} = 1\frac{7}{9} = 1.7777777777777777$$