Coaching Centre
Equations with fractions
Solving linear equations that contain fractions by multiplying both sides by the denominator.
Clear the fraction
Solve $\dfrac{x}{4} + 3 = 8$.
$\dfrac{x}{4} = 5$
Subtract 3.
$x = 20$
Multiply by 4.
Solve $\dfrac{2a + 1}{3} = 5$.
$2a + 1 = 15$
Multiply by 3 (the whole top is divided by 3).
$2a = 14$, so $a = 7$.
Solve $\dfrac{3m}{5} = 6$.
$3m = 30$
$m = 10$
Undo $div 5$
Multiply both sides by 5.
Solve $dfrac{x}{2} = 9$
$x = 18$
Solve $dfrac{x + 1}{2} = 4$
$x = 7$
Solve $\dfrac{x}{4} + 3 = 8$.
$\tfrac{x}{4} = 5$.
Solve $\dfrac{2a + 1}{3} = 5$.
$2a + 1 = 15$.
Solve $\dfrac{3m}{5} = 6$.
$3m = 30$.
Solve $\dfrac{x}{2} = 9$.
$x = 9 \times 2$.
Solve $\dfrac{x + 1}{2} = 4$.
$x + 1 = 8$.
Solve $\dfrac{y}{3} = -4$.
$y = -12$.
Solve $\dfrac{k}{7} - 1 = 1$.
$\tfrac{k}{7} = 2$.
Solve $\dfrac{n - 5}{2} = 3$.
$n - 5 = 6$.
New numbers every time. Keep going until you get five in a row.