When students work on linear equations with a lot of fractions in Year 10, they often make a few common mistakes. Here are some things to watch out for:

1. Ignoring the Denominator:
   Students sometimes forget to get rid of fractions by multiplying by the least common denominator (LCD).
   For example, in the equation
   $\frac{x}{3} + \frac{2}{5} = 1$,
   they might try to solve it directly without multiplying by 15 (the LCD).
   This can lead to confusion.

2. Miscalculating when Multiplying Fractions:
   Sometimes, students have trouble when they multiply fractions.
   For example, in an equation like
   $\frac{2x}{5} = \frac{3}{4}$,
   they might multiply incorrectly and forget to simplify it properly.

3. Forgetting to Distribute:
   When equations have parentheses with fractions,
   students may forget to distribute correctly.
   For example, in
   $\frac{1}{2}(x + 4) = 6$,
   some forget to apply the fraction to both parts inside the parentheses.

By being careful about these mistakes, students can feel more confident when solving equations with fractions!