How to Solve Equations with Brackets on Both Sides
The safest order is expand first, tidy both sides, move variable terms together, then solve.
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Maths notebook
Short explanations for the bits that usually cause mistakes
These posts focus on one question at a time: why a method works, where people commonly go wrong, and how to check the result.
Converting Area Units Without Forgetting to Square the Scale Factor
Area conversions use the square of the length conversion, which is why they change much faster than ordinary units.
Read the explanation →A Fast Way to Turn Common Fractions into Percentages
Some fractions are worth memorising because they appear everywhere in percentage work and mental maths.
Read the explanation →Why Does a Term Change Sign When You Move It Across an Equation?
Terms do not magically change sign. What really happens is that you add or subtract the same amount on both sides of the equation.
Read the explanation →Best Buy Questions: Use a Unit Rate, Not a Guess
Turn each option into a price per one item, per 100 g, or per litre so the comparison is fair.
Read the explanation →The 20-Second Check That Catches Algebra Mistakes
Substitution is one of the quickest ways to catch a sign error or arithmetic slip after solving an equation.
Read the explanation →Area of a Compound Shape by Splitting into Rectangles
Many compound-area questions become simple once you redraw the shape as two or three ordinary rectangles.
Read the explanation →How to Share an Amount in a Given Ratio
Add the ratio parts, find the value of one part, then build each share from there.
Read the explanation →Can You Use Percentage Change Across Zero?
When a value crosses zero, the usual percentage-change formula still computes something, but the result often needs careful interpretation.
Read the explanation →How to Find the Original Price Before VAT Was Added
If a bill already includes VAT, divide by the VAT multiplier to recover the original amount before tax.
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