Answer:
[tex]\dfrac{8}{12}[/tex]
Step-by-step explanation:
Let the unknown fraction be:
If the sum of the numerator and denominator is 20 then:
[tex]\implies a+b=20[/tex]
Rewrite the equation to isolate b:
[tex]\implies b=20-a[/tex]
If the fraction is equal to 2/3 then:
[tex]\implies \dfrac{a}{b}=\dfrac{2}{3}[/tex]
Cross multiply:
[tex]\implies 3a=2b[/tex]
Substitute the expression for b into the cross-multiplied equation and solve for a:
[tex]\implies 3a=2(20-a)[/tex]
[tex]\implies 3a=40-2a[/tex]
[tex]\implies 5a=40[/tex]
[tex]\implies a=8[/tex]
Substitute the found value of a into the equation for b and solve for b:
[tex]\implies b=20-8[/tex]
[tex]\implies b=12[/tex]
Therefore, the fraction for which the sum of the numerator and denominator is 20, and the value of the fraction is equal to 2/3 is:
