Mental Math

What is $3\cdot 14$? Split 14 into 10 and 4. Three groups of 14 are three groups of 10 and three groups of 4, so $3\left(10+4\right)$ is $3\cdot 10+3\cdot 4$, which is $30+12$, or 42. Multiplying a sum is the same as multiplying each part and adding the results.

This is the distributive property: $a\left(c+d\right) = ac+ad$. The number outside the parentheses is shared out, or distributed, to every part inside. It works with a difference too, as $a\left(c-d\right) = ac-ad$.

It turns hard products into easy ones. $6\cdot 99$: 99 is 100 - 1, so the product is $6\cdot 100-6\cdot 1$, which is $600-6$, or 594. Rounding to a friendly number and then correcting is how quick mental arithmetic works.