Question

Find the values of A and B from the following expressions:

$5\frac{1}{2}-2\frac{1}{3}=A$

$A-2\frac{1}{12}=B$

• A. $A=3\frac{1}{6};B=1\frac{2}{3}$
• B. $A=3\frac{1}{12};B=1\frac{1}{6}$
• C. $A=3\frac{1}{6};B=1\frac{1}{12}$
• D. $A=3\frac{1}{12};B=1\frac{1}{3}$

Answer 1

The correct option is C $A=3\frac{1}{6};B=1\frac{1}{12}$

$\text{Calculating for A, we get:}$

$5\frac{1}{2}-2\frac{1}{3}=A$

$⟹A=(5-2)+(\frac{1}{2}-\frac{1}{3})$

$=3+(\frac{1\times 3}{2\times 3}-\frac{1\times 2}{3\times 2})$

$=3+(\frac{3}{6}-\frac{2}{6})$

$=3+\frac{1}{6}$

$⟹A=3\frac{1}{6}$

$\text{Now, calculating for B, we find:}$

$A-2\frac{1}{12}=B$

$⟹B=3\frac{1}{6}-2\frac{1}{12}$

$=(3-2)+(\frac{1}{6}-\frac{1}{12})$

$=1+(\frac{1\times 2}{6\times 2}-\frac{1}{12})$

$=1+(\frac{2}{12}-\frac{1}{12})$

$=1+\frac{1}{12}$

$⟹B=1\frac{1}{12}$

$\therefore A=3\frac{1}{6};B=1\frac{1}{12}$