Number · Fractions & decimals
Chapter 1 · 4
The idea
The four operations with fractions
Why adding fractions needs a common denominator but multiplying doesn't, why dividing flips the second fraction, and why mixed numbers must become improper before multiplying or dividing.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Number · Fractions & decimals
The four operations with fractions
Why adding fractions needs a common denominator but multiplying doesn't, why dividing flips the second fraction, and why mixed numbers must become improper before multiplying or dividing.
Why it works
A count of same-sized pieces
A fraction is a count of pieces of a particular size: is three quarter-sized pieces. Every rule on this page follows from that one reading — adding needs matching sizes, multiplying re-cuts the pieces, and dividing asks how many fit.Adding needs same-sized pieces
You can't add 1 third and 1 quarter as a count — the pieces are different sizes ( is the classic wrong answer, and it's smaller than , which no sum of positives can be). Recut both into twelfths:Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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