Solve (4)/(9)\div(4)/(5)\times(4)/(25)-(7)/(10)+(1)/(2)

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac{ 4 }{ 9 } \div \frac{ 4 }{ 5 } \times \frac{ 4 }{ 25 } - \frac{ 7 }{ 10 } + \frac{ 1 }{ 2 }$$

Evaluate

$-\frac{1}{9}\approx -0.111111111$

Solution Steps

Divide $\frac{4}{9}$ by $\frac{4}{5}$ by multiplying $\frac{4}{9}$ by the reciprocal of $\frac{4}{5}$.

$$\frac{4}{9}\times \frac{5}{4}\times \frac{4}{25}-\frac{7}{10}+\frac{1}{2}$$

Multiply $\frac{4}{9}$ times $\frac{5}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 5}{9\times 4}\times \frac{4}{25}-\frac{7}{10}+\frac{1}{2}$$

Cancel out $4$ in both numerator and denominator.

$$\frac{5}{9}\times \frac{4}{25}-\frac{7}{10}+\frac{1}{2}$$

Multiply $\frac{5}{9}$ times $\frac{4}{25}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{9\times 25}-\frac{7}{10}+\frac{1}{2}$$

Do the multiplications in the fraction $\frac{5\times 4}{9\times 25}$.

$$\frac{20}{225}-\frac{7}{10}+\frac{1}{2}$$

Reduce the fraction $\frac{20}{225}$ to lowest terms by extracting and canceling out $5$.

$$\frac{4}{45}-\frac{7}{10}+\frac{1}{2}$$

Least common multiple of $45$ and $10$ is $90$. Convert $\frac{4}{45}$ and $\frac{7}{10}$ to fractions with denominator $90$.

$$\frac{8}{90}-\frac{63}{90}+\frac{1}{2}$$

Since $\frac{8}{90}$ and $\frac{63}{90}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-63}{90}+\frac{1}{2}$$

Subtract $63$ from $8$ to get $-55$.

$$\frac{-55}{90}+\frac{1}{2}$$

Reduce the fraction $\frac{-55}{90}$ to lowest terms by extracting and canceling out $5$.

$$-\frac{11}{18}+\frac{1}{2}$$

Least common multiple of $18$ and $2$ is $18$. Convert $-\frac{11}{18}$ and $\frac{1}{2}$ to fractions with denominator $18$.

$$-\frac{11}{18}+\frac{9}{18}$$

Since $-\frac{11}{18}$ and $\frac{9}{18}$ have the same denominator, add them by adding their numerators.

$$\frac{-11+9}{18}$$

Add $-11$ and $9$ to get $-2$.

$$\frac{-2}{18}$$

Reduce the fraction $\frac{-2}{18}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{1}{9}$$

Show Solution

Factor

$-\frac{1}{9} = -0.1111111111111111$