Solve 7/4+6/7text{of}8/9+1/4=

$$\frac { 7 } { 4 } + \frac { 6 } { 7 } \text { of } \frac { 8 } { 9 } + \frac { 1 } { 4 } =$$

Evaluate

$$\frac{58}{21}\approx 2.761904762$$

Solution Steps

Multiply \frac{6}{7} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{4}+\frac{6\times 8}{7\times 9}+\frac{1}{4}$$

Do the multiplications in the fraction \frac{6\times 8}{7\times 9}.

$$\frac{7}{4}+\frac{48}{63}+\frac{1}{4}$$

Reduce the fraction \frac{48}{63} to lowest terms by extracting and canceling out 3.

$$\frac{7}{4}+\frac{16}{21}+\frac{1}{4}$$

Least common multiple of 4 and 21 is 84. Convert \frac{7}{4} and \frac{16}{21} to fractions with denominator 84.

$$\frac{147}{84}+\frac{64}{84}+\frac{1}{4}$$

Since \frac{147}{84} and \frac{64}{84} have the same denominator, add them by adding their numerators.

$$\frac{147+64}{84}+\frac{1}{4}$$

Add 147 and 64 to get 211.

$$\frac{211}{84}+\frac{1}{4}$$

Least common multiple of 84 and 4 is 84. Convert \frac{211}{84} and \frac{1}{4} to fractions with denominator 84.

$$\frac{211}{84}+\frac{21}{84}$$

Since \frac{211}{84} and \frac{21}{84} have the same denominator, add them by adding their numerators.

$$\frac{211+21}{84}$$

Add 211 and 21 to get 232.

$$\frac{232}{84}$$

Reduce the fraction \frac{232}{84} to lowest terms by extracting and canceling out 4.

$$\frac{58}{21}$$

Factor

$$\frac{2 \cdot 29}{3 \cdot 7} = 2\frac{16}{21} = 2.761904761904762$$