Solve ((1,2:36)+ 6 5 *0,25); (128/45 - 1/15) / (125/9) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$((1,2:36)+\frac{6}{5}\cdot0,25); (\frac{128}{45}-\frac{1}{15}):\frac{125}{9}$$

Sort

$0,2;\frac{1}{3}$

Solution Steps

Expand $\frac{1,2}{36}$ by multiplying both numerator and the denominator by $10$.

$$sort(\frac{12}{360}+\frac{6}{5}\times 0,25;\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Reduce the fraction $\frac{12}{360}$ to lowest terms by extracting and canceling out $12$.

$$sort(\frac{1}{30}+\frac{6}{5}\times 0,25;\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Convert decimal number $0,25$ to fraction $\frac{25}{100}$. Reduce the fraction $\frac{25}{100}$ to lowest terms by extracting and canceling out $25$.

$$sort(\frac{1}{30}+\frac{6}{5}\times \frac{1}{4};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Multiply $\frac{6}{5}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1}{30}+\frac{6\times 1}{5\times 4};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Do the multiplications in the fraction $\frac{6\times 1}{5\times 4}$.

$$sort(\frac{1}{30}+\frac{6}{20};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Reduce the fraction $\frac{6}{20}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{1}{30}+\frac{3}{10};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Least common multiple of $30$ and $10$ is $30$. Convert $\frac{1}{30}$ and $\frac{3}{10}$ to fractions with denominator $30$.

$$sort(\frac{1}{30}+\frac{9}{30};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Since $\frac{1}{30}$ and $\frac{9}{30}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{1+9}{30};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Add $1$ and $9$ to get $10$.

$$sort(\frac{10}{30};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Reduce the fraction $\frac{10}{30}$ to lowest terms by extracting and canceling out $10$.

$$sort(\frac{1}{3};\frac{\frac{128}{45}-\frac{1}{15}}{\frac{125}{9}})$$

Least common multiple of $45$ and $15$ is $45$. Convert $\frac{128}{45}$ and $\frac{1}{15}$ to fractions with denominator $45$.

$$sort(\frac{1}{3};\frac{\frac{128}{45}-\frac{3}{45}}{\frac{125}{9}})$$

Since $\frac{128}{45}$ and $\frac{3}{45}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{1}{3};\frac{\frac{128-3}{45}}{\frac{125}{9}})$$

Subtract $3$ from $128$ to get $125$.

$$sort(\frac{1}{3};\frac{\frac{125}{45}}{\frac{125}{9}})$$

Reduce the fraction $\frac{125}{45}$ to lowest terms by extracting and canceling out $5$.

$$sort(\frac{1}{3};\frac{\frac{25}{9}}{\frac{125}{9}})$$

Divide $\frac{25}{9}$ by $\frac{125}{9}$ by multiplying $\frac{25}{9}$ by the reciprocal of $\frac{125}{9}$.

$$sort(\frac{1}{3};\frac{25}{9}\times \frac{9}{125})$$

Multiply $\frac{25}{9}$ times $\frac{9}{125}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1}{3};\frac{25\times 9}{9\times 125})$$

Cancel out $9$ in both numerator and denominator.

$$sort(\frac{1}{3};\frac{25}{125})$$

Reduce the fraction $\frac{25}{125}$ to lowest terms by extracting and canceling out $25$.

$$sort(\frac{1}{3};\frac{1}{5})$$

Least common denominator of the numbers in the list $\frac{1}{3};\frac{1}{5}$ is $15$. Convert numbers in the list to fractions with denominator $15$.

$$\frac{5}{15};\frac{3}{15}$$

To sort the list, start from a single element $\frac{5}{15}$.

$$\frac{5}{15}$$

Insert $\frac{3}{15}$ to the appropriate location in the new list.

$$\frac{3}{15};\frac{5}{15}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{5};\frac{1}{3}$$

Evaluate

$\frac{1}{3};0,2$