Question

The sum of 2 fractions is 5/6. Their difference is 1/2. Their least common denominator is 6. The denominator of one is twice the size of the other. The sum of their numerators is 3. Find both fractions.

Answer 1

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose the first fraction is : $\frac{a}{b}$

Suppose the second fraction is : $\frac{c}{d}$

The sum of both fraction is given as : $\frac{5}{6}$

$\frac{a}{b}+\frac{c}{d}=\frac{5}{6}$    .......................equation (1)

The difference of both fraction is given as : $\frac{1}{2}$

$\frac{a}{b}-\frac{c}{d}=\frac{1}{2}$   .........................equation (2)

Adding equation (1) and equation (2)

$\frac{c}{d} \ will \ be \ cancelled$

$\frac{2a}{b}=\frac{5}{6}+\frac{1}{2}$

making common denominator

$\frac{2a}{b}=\frac{5}{6}+ \frac{3}{6}$

$\frac{2a}{b}=\frac{8}{6}$

Hence,

$\frac{a}{b}=\frac{2}{3}$

Plugging the value of $\frac{a}{b}$ in equation (1)

$\frac{2}{3}+\frac{c}{d}=\frac{5}{6}$

Subtracting $\frac{2}{3}$ in both sides

$\frac{c}{d}=\frac{5}{6}-\frac{2}{3}$

$\frac{c}{d}=\frac{1}{6}$

Hence both fractions are $\frac{2}{3} \ and \ \frac{1}{6}$     ...................Answer

Hope it will help :)