Solve 21/3+15/4text{(b)}65/6-42/3text{(c)}1frac{7}{15}*2frac{2}{3}

$$2 \frac { 1 } { 3 } + 1 \frac { 5 } { 4 } \text { (b) } 6 \frac { 5 } { 6 } - 4 \frac { 2 } { 3 } \text { (c) } 1 \frac { 7 } { 15 } \times 2 \frac { 2 } { 3 }$$

Evaluate

$$\frac{123b}{8}-\frac{2464c}{135}+\frac{7}{3}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+1}{3}+\frac{1\times 4+5}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 6 and 1 to get 7.

$$\frac{7}{3}+\frac{1\times 4+5}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 1 and 4 to get 4.

$$\frac{7}{3}+\frac{4+5}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 4 and 5 to get 9.

$$\frac{7}{3}+\frac{9}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 6 and 6 to get 36.

$$\frac{7}{3}+\frac{9}{4}b\times \frac{36+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 36 and 5 to get 41.

$$\frac{7}{3}+\frac{9}{4}b\times \frac{41}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply \frac{9}{4} times \frac{41}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}+\frac{9\times 41}{4\times 6}b-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Do the multiplications in the fraction \frac{9\times 41}{4\times 6}.

$$\frac{7}{3}+\frac{369}{24}b-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Reduce the fraction \frac{369}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{3}+\frac{123}{8}b-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{7}{3}+\frac{123}{8}b-\frac{12+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 12 and 2 to get 14.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 1 and 15 to get 15.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14}{3}c\times \frac{15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 15 and 7 to get 22.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14}{3}c\times \frac{22}{15}\times \frac{2\times 3+2}{3}$$

Multiply \frac{14}{3} times \frac{22}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14\times 22}{3\times 15}c\times \frac{2\times 3+2}{3}$$

Do the multiplications in the fraction \frac{14\times 22}{3\times 15}.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308}{45}c\times \frac{2\times 3+2}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308}{45}c\times \frac{6+2}{3}$$

Add 6 and 2 to get 8.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308}{45}c\times \frac{8}{3}$$

Multiply \frac{308}{45} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308\times 8}{45\times 3}c$$

Do the multiplications in the fraction \frac{308\times 8}{45\times 3}.

$$\frac{7}{3}+\frac{123}{8}b-\frac{2464}{135}c$$

Expand

$$\frac{123b}{8}-\frac{2464c}{135}+\frac{7}{3}$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{6+1}{3}+\frac{1\times 4+5}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 6 and 1 to get 7.

$$\frac{7}{3}+\frac{1\times 4+5}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 1 and 4 to get 4.

$$\frac{7}{3}+\frac{4+5}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 4 and 5 to get 9.

$$\frac{7}{3}+\frac{9}{4}b\times \frac{6\times 6+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 6 and 6 to get 36.

$$\frac{7}{3}+\frac{9}{4}b\times \frac{36+5}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 36 and 5 to get 41.

$$\frac{7}{3}+\frac{9}{4}b\times \frac{41}{6}-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply \frac{9}{4} times \frac{41}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}+\frac{9\times 41}{4\times 6}b-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Do the multiplications in the fraction \frac{9\times 41}{4\times 6}.

$$\frac{7}{3}+\frac{369}{24}b-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Reduce the fraction \frac{369}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{3}+\frac{123}{8}b-\frac{4\times 3+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{7}{3}+\frac{123}{8}b-\frac{12+2}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 12 and 2 to get 14.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14}{3}c\times \frac{1\times 15+7}{15}\times \frac{2\times 3+2}{3}$$

Multiply 1 and 15 to get 15.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14}{3}c\times \frac{15+7}{15}\times \frac{2\times 3+2}{3}$$

Add 15 and 7 to get 22.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14}{3}c\times \frac{22}{15}\times \frac{2\times 3+2}{3}$$

Multiply \frac{14}{3} times \frac{22}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}+\frac{123}{8}b-\frac{14\times 22}{3\times 15}c\times \frac{2\times 3+2}{3}$$

Do the multiplications in the fraction \frac{14\times 22}{3\times 15}.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308}{45}c\times \frac{2\times 3+2}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308}{45}c\times \frac{6+2}{3}$$

Add 6 and 2 to get 8.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308}{45}c\times \frac{8}{3}$$

Multiply \frac{308}{45} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{3}+\frac{123}{8}b-\frac{308\times 8}{45\times 3}c$$

Do the multiplications in the fraction \frac{308\times 8}{45\times 3}.

$$\frac{7}{3}+\frac{123}{8}b-\frac{2464}{135}c$$