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

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Question

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

Evaluate

$\frac{116}{45}\approx 2.577777778$

Solution Steps

Divide $\frac{4}{9}$ by $\frac{4}{25}$ by multiplying $\frac{4}{9}$ by the reciprocal of $\frac{4}{25}$.

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

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

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

Cancel out $4$ in both numerator and denominator.

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

Least common multiple of $9$ and $10$ is $90$. Convert $\frac{25}{9}$ and $\frac{7}{10}$ to fractions with denominator $90$.

$$\frac{250}{90}-\frac{63}{90}+\frac{1}{2}$$

Since $\frac{250}{90}$ and $\frac{63}{90}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{250-63}{90}+\frac{1}{2}$$

Subtract $63$ from $250$ to get $187$.

$$\frac{187}{90}+\frac{1}{2}$$

Least common multiple of $90$ and $2$ is $90$. Convert $\frac{187}{90}$ and $\frac{1}{2}$ to fractions with denominator $90$.

$$\frac{187}{90}+\frac{45}{90}$$

Since $\frac{187}{90}$ and $\frac{45}{90}$ have the same denominator, add them by adding their numerators.

$$\frac{187+45}{90}$$

Add $187$ and $45$ to get $232$.

$$\frac{232}{90}$$

Reduce the fraction $\frac{232}{90}$ to lowest terms by extracting and canceling out $2$.

$$\frac{116}{45}$$

Show Solution

Factor

$\frac{2 ^ {2} \cdot 29}{3 ^ {2} \cdot 5} = 2\frac{26}{45} = 2.577777777777778$