Solve Exercice 2 -Calculer : 13 + (- 45); - 4 + (- 6) −19, - 74 - (- 6) * 4 - (- 4) ; -9.5- | 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

$$\left. \begin{array} { l } { 13 + ( - 45 ) : - 4 + ( - 6 ) : - 19 } \\ { - 74 - ( - 6 ) : 4 - ( - 4 ) : - 9 , 5 } \end{array} \right.$$

Sort

$-\frac{1313}{18},5,\frac{1867}{76}$

Solution Steps

Fraction $\frac{-45}{-4}$ can be simplified to $\frac{45}{4}$ by removing the negative sign from both the numerator and the denominator.

$$sort(13+\frac{45}{4}+\frac{-6}{-19},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Convert $13$ to fraction $\frac{52}{4}$.

$$sort(\frac{52}{4}+\frac{45}{4}+\frac{-6}{-19},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Since $\frac{52}{4}$ and $\frac{45}{4}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{52+45}{4}+\frac{-6}{-19},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Add $52$ and $45$ to get $97$.

$$sort(\frac{97}{4}+\frac{-6}{-19},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Fraction $\frac{-6}{-19}$ can be simplified to $\frac{6}{19}$ by removing the negative sign from both the numerator and the denominator.

$$sort(\frac{97}{4}+\frac{6}{19},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Least common multiple of $4$ and $19$ is $76$. Convert $\frac{97}{4}$ and $\frac{6}{19}$ to fractions with denominator $76$.

$$sort(\frac{1843}{76}+\frac{24}{76},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Since $\frac{1843}{76}$ and $\frac{24}{76}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{1843+24}{76},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Add $1843$ and $24$ to get $1867$.

$$sort(\frac{1867}{76},-74-\frac{-6}{4}-\frac{-4}{-9},5)$$

Reduce the fraction $\frac{-6}{4}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{1867}{76},-74-\left(-\frac{3}{2}\right)-\frac{-4}{-9},5)$$

The opposite of $-\frac{3}{2}$ is $\frac{3}{2}$.

$$sort(\frac{1867}{76},-74+\frac{3}{2}-\frac{-4}{-9},5)$$

Convert $-74$ to fraction $-\frac{148}{2}$.

$$sort(\frac{1867}{76},-\frac{148}{2}+\frac{3}{2}-\frac{-4}{-9},5)$$

Since $-\frac{148}{2}$ and $\frac{3}{2}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{1867}{76},\frac{-148+3}{2}-\frac{-4}{-9},5)$$

Add $-148$ and $3$ to get $-145$.

$$sort(\frac{1867}{76},-\frac{145}{2}-\frac{-4}{-9},5)$$

Fraction $\frac{-4}{-9}$ can be simplified to $\frac{4}{9}$ by removing the negative sign from both the numerator and the denominator.

$$sort(\frac{1867}{76},-\frac{145}{2}-\frac{4}{9},5)$$

Least common multiple of $2$ and $9$ is $18$. Convert $-\frac{145}{2}$ and $\frac{4}{9}$ to fractions with denominator $18$.

$$sort(\frac{1867}{76},-\frac{1305}{18}-\frac{8}{18},5)$$

Since $-\frac{1305}{18}$ and $\frac{8}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{1867}{76},\frac{-1305-8}{18},5)$$

Subtract $8$ from $-1305$ to get $-1313$.

$$sort(\frac{1867}{76},-\frac{1313}{18},5)$$

Convert decimal numbers in the list $\frac{1867}{76},-\frac{1313}{18},5$ to fractions.

$$\frac{1867}{76},-\frac{1313}{18},5$$

Least common denominator of the numbers in the list $\frac{1867}{76},-\frac{1313}{18},5$ is $684$. Convert numbers in the list to fractions with denominator $684$.

$$\frac{16803}{684},-\frac{49894}{684},\frac{3420}{684}$$

To sort the list, start from a single element $\frac{16803}{684}$.

$$\frac{16803}{684}$$

Insert $-\frac{49894}{684}$ to the appropriate location in the new list.

$$-\frac{49894}{684},\frac{16803}{684}$$

Insert $\frac{3420}{684}$ to the appropriate location in the new list.

$$-\frac{49894}{684},\frac{3420}{684},\frac{16803}{684}$$

Replace the obtained fractions with the initial values.

$$-\frac{1313}{18},5,\frac{1867}{76}$$

Evaluate

$\frac{1867}{76},\ -\frac{1313}{18},\ 5$