Solve 6 - \{1 1/2 - 3/5 * (1 7/9 - 1/2)\}

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Question

$$6-\{1\frac{1}{2}-\frac{3}{5}\times(1\frac{7}{9}-\frac{1}{2})\}$$

Evaluate

$\frac{79}{15}\approx 5.266666667$

Solution Steps

Multiply $1$ and $2$ to get $2$.

$$6-\left(\frac{2+1}{2}-\frac{3}{5}\left(\frac{1\times 9+7}{9}-\frac{1}{2}\right)\right)$$

Add $2$ and $1$ to get $3$.

$$6-\left(\frac{3}{2}-\frac{3}{5}\left(\frac{1\times 9+7}{9}-\frac{1}{2}\right)\right)$$

Multiply $1$ and $9$ to get $9$.

$$6-\left(\frac{3}{2}-\frac{3}{5}\left(\frac{9+7}{9}-\frac{1}{2}\right)\right)$$

Add $9$ and $7$ to get $16$.

$$6-\left(\frac{3}{2}-\frac{3}{5}\left(\frac{16}{9}-\frac{1}{2}\right)\right)$$

Least common multiple of $9$ and $2$ is $18$. Convert $\frac{16}{9}$ and $\frac{1}{2}$ to fractions with denominator $18$.

$$6-\left(\frac{3}{2}-\frac{3}{5}\left(\frac{32}{18}-\frac{9}{18}\right)\right)$$

Since $\frac{32}{18}$ and $\frac{9}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$6-\left(\frac{3}{2}-\frac{3}{5}\times \frac{32-9}{18}\right)$$

Subtract $9$ from $32$ to get $23$.

$$6-\left(\frac{3}{2}-\frac{3}{5}\times \frac{23}{18}\right)$$

Multiply $\frac{3}{5}$ times $\frac{23}{18}$ by multiplying numerator times numerator and denominator times denominator.

$$6-\left(\frac{3}{2}-\frac{3\times 23}{5\times 18}\right)$$

Do the multiplications in the fraction $\frac{3\times 23}{5\times 18}$.

$$6-\left(\frac{3}{2}-\frac{69}{90}\right)$$

Reduce the fraction $\frac{69}{90}$ to lowest terms by extracting and canceling out $3$.

$$6-\left(\frac{3}{2}-\frac{23}{30}\right)$$

Least common multiple of $2$ and $30$ is $30$. Convert $\frac{3}{2}$ and $\frac{23}{30}$ to fractions with denominator $30$.

$$6-\left(\frac{45}{30}-\frac{23}{30}\right)$$

Since $\frac{45}{30}$ and $\frac{23}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$6-\frac{45-23}{30}$$

Subtract $23$ from $45$ to get $22$.

$$6-\frac{22}{30}$$

Reduce the fraction $\frac{22}{30}$ to lowest terms by extracting and canceling out $2$.

$$6-\frac{11}{15}$$

Convert $6$ to fraction $\frac{90}{15}$.

$$\frac{90}{15}-\frac{11}{15}$$

Since $\frac{90}{15}$ and $\frac{11}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{90-11}{15}$$

Subtract $11$ from $90$ to get $79$.

$$\frac{79}{15}$$

Show Solution

Factor

$\frac{79}{3 \cdot 5} = 5\frac{4}{15} = 5.266666666666667$