Question

What is the answer to 2 3/4a =
19 1/4

Answer 1

Convert the mixed numbers to the improper fractions:

`2(3)/(4)=(2\cdot4+3)/(4)=(11)/(4)\\\\19(1)/(4)=(19\cdot4+1)/(4)=(77)/(4)`

`2(3)/(4)a=19(1)/(4)\\\\(11)/(4)a=(77)/(4)\qquad\text{multiply both sides by 4}\\\\\\ot4^1\cdot(11)/(\\ot4_1)a=\\ot4^1\cdot(77)/(\\ot4_1)\\\\11a=77\qquad\text{divide both sides by 11}\\\\\boxed{a=7}`