Question

Which two of the given fractions add up to give the highest value?

$A:\frac{5}{6}$

$B:\frac{2}{3}$

$C:\frac{7}{9}$

• A. B and C
• B. A and C
• C. A and B
• D. Cannot be determined

Answer 1

The correct option is B A and C

Given:

$A:\frac{5}{6}$

$B:\frac{2}{3}$

$C:\frac{7}{9}$

Now, $A=\frac{5}{6}$ can be reprresented as:


Similarly, $B=\frac{2}{3}$ can be represented as:


Finally, rewriting $C=\frac{7}{9}$, we get:


So,

$A=\frac{5}{6}=\frac{15}{18}$

$B=\frac{2}{3}=\frac{12}{18}$

$C=\frac{7}{9}=\frac{14}{18}$

Now, we calculate each of the three sums:

Calculating A + B, we get:


Calculating B + C, we get:


Calculating A + C, we get:


Now,
$29>27>26$

$⟹\frac{29}{18}>\frac{27}{18}>\frac{26}{18}$

$⟹(A+C)>(A+B)>(B+C)$

$\therefore$ The fractions that add up to give the highest value are A and C