Multiplying fractions is easier than adding them

Why can you multiply two fractions together just by multiplying the tops together and by multiplying the bottoms together; but you cannot add fractions by adding the tops together and the bottoms together? The answer goes back to the meaning of multiply and divide. Whereas you cannot add different things together, you can multiply different things. You cannot add one ten and two units together, when you try you end up with 12 – that is one ten (a 1 in the tens column) and two units (a 2 in the units column) – that’s right a ten and a two… right back where you started. But you can multiply a ten by a two. Two times ten is two lots of ten, which we write as a 2 in the tens column. Similarly, when we divide, we can divide one ten by two units. So if we are multiplying a third by a half, we can either understand it as a half split into 3 (which is a sixth) or we can understand it as a third split in half, (which is a sixth). Either way the resulting quantity can be found by multiplying the denominators of the fraction together. This leads to the paradox that multiplying fractions is easier than adding fractions… when most children think that multiplication is hard and adding is easier. But it’s all easy when you learn with Puppet Maths, because Puppet Maths makes arithmetic accessible to children. Puppet Maths explains all the basic ideas which allows children to understand exactly what they’re doing rather than become lost trying to solve problems in a language (the language of maths) they don’t understand.