Fractions That Finally Make Sense
For grades 4–8, or anyone who never really got fractions. Every chapter follows the same path: a real mistake → why it happens → a picture that fixes it → practice that changes the situation → a re-check.
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What's inside (draft outline)
Start here
15-question diagnostic with an answer map
Part 1 · What a fraction really is
"Equal parts" and why the whole matters · Bigger denominator, bigger fraction? · Equivalent fractions
Part 2 · Operations without memorized rules
Why 1/2 + 1/3 isn't 2/5 · Mixed numbers · Does multiplying always make bigger? · Why "flip and multiply" works
Part 3 · Fractions in word problems
"A fraction of what?" — finding the whole with bar models · "1/3 of the rest": multi-step problems
Part 4 · Bridge to ratios, percents and equations
Fractions ↔ decimals ↔ percents · Part-to-part vs part-to-whole · Percent of what? · From a bar model to x
Final re-check
Matches the diagnostic question by question, so you can see what changed