Question

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

Answer 1

Convert the mixed numbers to the improper fractions:

$2\dfrac{3}{4}=\dfrac{2\cdot4+3}{4}=\dfrac{11}{4}\\\\19\dfrac{1}{4}=\dfrac{19\cdot4+1}{4}=\dfrac{77}{4}$

$2\dfrac{3}{4}a=19\dfrac{1}{4}\\\\\dfrac{11}{4}a=\dfrac{77}{4}\qquad\text{multiply both sides by 4}\\\\\not4^1\cdot\dfrac{11}{\not4_1}a=\not4^1\cdot\dfrac{77}{\not4_1}\\\\11a=77\qquad\text{divide both sides by 11}\\\\\boxed{a=7}$