5/6-9/13

Let's evaluate: $\frac{5}{6}-\frac{9}{13}$

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose $78$, the least common multiple of $6$ and $13$. Multiplying the numerator and the denominator by the same number does not change the fraction: $\frac{5}{6}-\frac{9}{13}$ = $\frac{5\times 13}{6\times 13}-\frac{9\times 6}{13\times 6}$ = $\frac{5\times 13-9\times 6}{6\times 13}$

$\frac{5\times 13-9\times 6}{6\times 13}$

ⓘ Multiplications are done before additions and subtractions: $5\times 13$ = $5\times (10+3)$ = $5\times 10+5\times 3$ = $50+15$ = $65$, $9\times 6$ = $54$

ⅰ $6\times 13$ = $6\times (10+3)$ = $6\times 10+6\times 3$ = $60+18$ = $78$

$\frac{65-54}{78}$

ⓘ The numerator and the denominator are computed before the division: $65-54$ = $11$

▶Result:   $\frac{11}{78}$

The numeric value of: $\frac{11}{78}$ equals:

▷ $\approx 0.1410$