# How do you solve -\frac { 5} { 4} a + \frac { 1} { 5} a = - \frac { 21} { 50}?

May 3, 2018

$a = 0.4$

#### Explanation:

Get both terms on the left side to have the same denominator, in this case $20$ is convenient because it it is the LCM
$\left(\frac{- 5 \cdot 5}{4 \cdot 5}\right) a + \left(\frac{1 \cdot 4}{5 \cdot 4}\right) a = \left(\frac{- 21}{50}\right)$
$\left(\frac{- 25}{20}\right) a + \left(\frac{4}{20}\right) a = \left(\frac{- 21}{50}\right)$
$\left(\frac{- 21}{20}\right) a = \left(\frac{- 21}{50}\right)$ we can remove $-$ signs
when dividing one fraction by another, we can flip the numerator and denominator of the fraction to be divided.
$a = \left(\frac{21}{50}\right) \cdot \left(\frac{20}{21}\right)$
$a = \left(\frac{20}{50}\right) = 0.4$
Check the solution By substituting in $a = 0.4$. It should result in $- 0.42$

May 3, 2018

Arrange the equation and get $a = \frac{2}{5}$

#### Explanation:

$- 1.25 a + 0.2 a = - \frac{21}{50}$

due to the fact that $- \frac{5}{4} = - 1.25$ and $\frac{1}{5} = 0.2$

$- 1.05 a = - \frac{21}{50}$

$a = \frac{21}{50 \times 1.05}$

$a = 0.4 = \frac{2}{5}$

May 3, 2018

$a = \frac{2}{5}$

#### Explanation:

$\text{one way is to multiply all terms by the }$
$\textcolor{b l u e}{\text{lowest common multiple of 4, 5 and 50}}$

$\text{the lowest common multiple is 100}$

${\cancel{100}}^{25} \times - \frac{5}{\cancel{4}} ^ 1 a + {\cancel{100}}^{20} / {\cancel{5}}^{1} a = {\cancel{100}}^{2} \times - \frac{21}{\cancel{50}} ^ 1$

$\Rightarrow - 125 a + 20 a = - 42 \leftarrow \textcolor{b l u e}{\text{no fractions}}$

$\Rightarrow - 105 a = - 42$

$\text{divide both sides by } - 105$

$\frac{\cancel{- 105} a}{\cancel{- 105}} = \frac{- 42}{- 105}$

$\Rightarrow a = \frac{42}{105} = \frac{2}{5}$