Solve 3(19/15)+2(-2/9)-(8/45)=1

$$3 ( \frac { 19 } { 15 } ) + 2 ( - \frac { 2 } { 9 } ) - ( \frac { 8 } { 45 } ) = 1$$

Verify

Solution Steps

Express 3\times \frac{19}{15} as a single fraction.

$$\frac{3\times 19}{15}+2\left(-\frac{2}{9}\right)-\frac{8}{45}=1$$

Multiply 3 and 19 to get 57.

$$\frac{57}{15}+2\left(-\frac{2}{9}\right)-\frac{8}{45}=1$$

Reduce the fraction \frac{57}{15} to lowest terms by extracting and canceling out 3.

$$\frac{19}{5}+2\left(-\frac{2}{9}\right)-\frac{8}{45}=1$$

Express 2\left(-\frac{2}{9}\right) as a single fraction.

$$\frac{19}{5}+\frac{2\left(-2\right)}{9}-\frac{8}{45}=1$$

Multiply 2 and -2 to get -4.

$$\frac{19}{5}+\frac{-4}{9}-\frac{8}{45}=1$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$\frac{19}{5}-\frac{4}{9}-\frac{8}{45}=1$$

Least common multiple of 5 and 9 is 45. Convert \frac{19}{5} and \frac{4}{9} to fractions with denominator 45.

$$\frac{171}{45}-\frac{20}{45}-\frac{8}{45}=1$$

Since \frac{171}{45} and \frac{20}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{171-20}{45}-\frac{8}{45}=1$$

Subtract 20 from 171 to get 151.

$$\frac{151}{45}-\frac{8}{45}=1$$

Since \frac{151}{45} and \frac{8}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{151-8}{45}=1$$

Subtract 8 from 151 to get 143.

$$\frac{143}{45}=1$$

Convert 1 to fraction \frac{45}{45}.

$$\frac{143}{45}=\frac{45}{45}$$

Compare \frac{143}{45} and \frac{45}{45}.

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