Solve 4/9-6/7:24/7=1/9

$$\frac { 4 } { 9 } - \frac { 6 } { 7 } : 2 \frac { 4 } { 7 } = \frac { 1 } { 9 }$$

Verify

Solution Steps

Divide \frac{6}{7} by \frac{2\times 7+4}{7} by multiplying \frac{6}{7} by the reciprocal of \frac{2\times 7+4}{7}.

$$\frac{4}{9}-\frac{6\times 7}{7\left(2\times 7+4\right)}=\frac{1}{9}$$

Cancel out 7 in both numerator and denominator.

$$\frac{4}{9}-\frac{6}{4+2\times 7}=\frac{1}{9}$$

Multiply 2 and 7 to get 14.

$$\frac{4}{9}-\frac{6}{4+14}=\frac{1}{9}$$

Add 4 and 14 to get 18.

$$\frac{4}{9}-\frac{6}{18}=\frac{1}{9}$$

Reduce the fraction \frac{6}{18} to lowest terms by extracting and canceling out 6.

$$\frac{4}{9}-\frac{1}{3}=\frac{1}{9}$$

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{4}{9}-\frac{3}{9}=\frac{1}{9}$$

Since \frac{4}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{9}=\frac{1}{9}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{9}=\frac{1}{9}$$

Compare \frac{1}{9} and \frac{1}{9}.

$$\text{true}$$