(Y-1/4)-(y-4/5)=(y+4/10)-1

Mathematics

2 answers:

erica [24]3 years ago

7 0

Answer:

$y=\frac{23}{60}$

Step-by-step explanation:

$(y-\frac{1}{4})-(y-\frac{4}{5})=(y+\frac{4}{10} )-1$

First, let's deal with everything in our parentheses. This includes simplification of fractions and distributing signs.
Remember than when distributing, everything in the parentheses is affected by whatever is being distributed.

$(y-\frac{1}{4})-(y-\frac{4}{5})=(y+\frac{4}{10} )-1\\(y-\frac{1}{4})-(y-\frac{4}{5})=(y+\frac{2}{5})-1$

A quick note that we can get rid of the parentheses once there is only addition and subtraction left next to the parentheses.

$(y-\frac{1}{4})-(y-\frac{4}{5})=(y+\frac{2}{5})-1\\y-\frac{1}{4}-y+\frac{4}{5}=y+\frac{2}{5}-1$

Now that the parentheses are gone, we can add and subtract in any order as long as we don't break the rules of addition and subtraction.

$y-\frac{1}{4}-y+\frac{4}{5}=y+\frac{2}{5}-1\\y-y-\frac{1}{4}+\frac{4}{5}=y+\frac{2}{5}-1\\-2y-\frac{1}{4}+\frac{4}{5}=y+\frac{2}{5}-1$

Let's move all our fractions to one side, and all our unknowns to the other.

$-2y-\frac{1}{4}+\frac{4}{5}=y+\frac{2}{5}-1\\-3y=\frac{1}{4}-\frac{4}{5}+\frac{2}{5}-1$

We need a common denominator for our fractions. The quickest way to do this only two different denominators is to multiply the two denominators together. $4*5=20$ , so we will multiply both the numerator and the denominator by whatever we need to to get $20$ .

$-3y=\frac{1}{4}-\frac{4}{5}+\frac{2}{5}-1\\-3y=\frac{1}{4}(\frac{5}{5})-\frac{4}{5}(\frac{4}{4})+\frac{2}{5}(\frac{4}{4})-1\\-3y=\frac{5}{20}-\frac{16}{20}+\frac{8}{20}-1$

add the denominators together. $-1=-\frac{20}{20}$

$-3y=\frac{5}{20}-\frac{16}{20}+\frac{8}{20}-1\\-3y=\frac{5}{20}-\frac{16}{20}+\frac{8}{20}-\frac{20}{20}\\-3y=\frac{13}{20}-\frac{36}{20}\\-3y=\frac{-23}{20}\\-\frac{1}{3}(-3y)=-\frac{1}{3}(-\frac{23}{20})\\y=\frac{23}{60}$