## horsealot203 2 years ago 5/4(a-8) =2/3

1. T0mmy

Do you want to find 'a'?

2. horsealot203

yes

3. howdomath

Being by isolating the variable, to do this we divide both sides of the equation by 5/4. Remember that dividing a fraction by another fraction is really multiplying the first fraction by the reciprocal of the dividing fraction. $(a - 8) = \frac{ 2 }{ 3 } \times \frac{ 4 }{ 5 }$ We get$a - 8 = \frac{ 8 }{ 15 }$ Now you add 8 to both sides to get a on it's own..$a = \frac{ 8 }{ 15 } +8$ Now we need a common denominator to add these fractions, so..$a = \frac{ 8 }{ 15 } +\frac{ 120 }{ 15 }$ Now we have $a = \frac{ 128 }{ 15 }$

4. horsealot203

okkk...

5. howdomath

What doesn't make sense, I'll try to explain better.

6. horsealot203

so can you simplify the fraction?

7. whpalmer4

No, factors of 15 are 3,5, and 128 is not divisible by either one.

8. T0mmy

No but you can create a mixed fraction.

9. howdomath

Well look at the factors of 15, there's 1, 3, 5 and 15. 128 isn't divisible by any of those, so it can't be simplified. If you want it in mixed number it's:$8\frac{ 8 }{ 15 }$

10. horsealot203

The answers I can choose from are 6 14/15 7 1/15 8 8/15 8 2/3

11. whpalmer4

You could write it as a mixed fraction = $8\frac{ 8 }{ 15 }$

12. horsealot203

ok, great. Thank you so much!