Solve =2/9*1/8+3/9*2/8+frac{4}{9}*frac{3}{8}=frac{2+6+12}{72}=frac{5}{18}

$$= \frac { 2 } { 9 } \times \frac { 1 } { 8 } + \frac { 3 } { 9 } \times \frac { 2 } { 8 } + \frac { 4 } { 9 } \times \frac { 3 } { 8 } = \frac { 2 + 6 + 12 } { 72 } = \frac { 5 } { 18 }$$

Verify

Solution Steps

Multiply \frac{2}{9} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{9\times 8}+\frac{3}{9}\times \frac{2}{8}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Do the multiplications in the fraction \frac{2\times 1}{9\times 8}.

$$\frac{2}{72}+\frac{3}{9}\times \frac{2}{8}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Reduce the fraction \frac{2}{72} to lowest terms by extracting and canceling out 2.

$$\frac{1}{36}+\frac{3}{9}\times \frac{2}{8}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1}{36}+\frac{1}{3}\times \frac{2}{8}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{36}+\frac{1}{3}\times \frac{1}{4}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Multiply \frac{1}{3} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{36}+\frac{1\times 1}{3\times 4}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Do the multiplications in the fraction \frac{1\times 1}{3\times 4}.

$$\frac{1}{36}+\frac{1}{12}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Least common multiple of 36 and 12 is 36. Convert \frac{1}{36} and \frac{1}{12} to fractions with denominator 36.

$$\frac{1}{36}+\frac{3}{36}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Since \frac{1}{36} and \frac{3}{36} have the same denominator, add them by adding their numerators.

$$\frac{1+3}{36}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Add 1 and 3 to get 4.

$$\frac{4}{36}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Reduce the fraction \frac{4}{36} to lowest terms by extracting and canceling out 4.

$$\frac{1}{9}+\frac{4}{9}\times \frac{3}{8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Multiply \frac{4}{9} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{9}+\frac{4\times 3}{9\times 8}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Do the multiplications in the fraction \frac{4\times 3}{9\times 8}.

$$\frac{1}{9}+\frac{12}{72}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Reduce the fraction \frac{12}{72} to lowest terms by extracting and canceling out 12.

$$\frac{1}{9}+\frac{1}{6}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Least common multiple of 9 and 6 is 18. Convert \frac{1}{9} and \frac{1}{6} to fractions with denominator 18.

$$\frac{2}{18}+\frac{3}{18}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Since \frac{2}{18} and \frac{3}{18} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{18}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Add 2 and 3 to get 5.

$$\frac{5}{18}=\frac{2+6+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Add 2 and 6 to get 8.

$$\frac{5}{18}=\frac{8+12}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Add 8 and 12 to get 20.

$$\frac{5}{18}=\frac{20}{72}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Reduce the fraction \frac{20}{72} to lowest terms by extracting and canceling out 4.

$$\frac{5}{18}=\frac{5}{18}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Compare \frac{5}{18} and \frac{5}{18}.

$$\text{true}\text{ and }\frac{2+6+12}{72}=\frac{5}{18}$$

Add 2 and 6 to get 8.

$$\text{true}\text{ and }\frac{8+12}{72}=\frac{5}{18}$$

Add 8 and 12 to get 20.

$$\text{true}\text{ and }\frac{20}{72}=\frac{5}{18}$$

Reduce the fraction \frac{20}{72} to lowest terms by extracting and canceling out 4.

$$\text{true}\text{ and }\frac{5}{18}=\frac{5}{18}$$

Compare \frac{5}{18} and \frac{5}{18}.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$