Basic Arithmetic and Inverse Operations

The product of two numbers means the result of multiplying them.

Counting in 3s five times gives 3, 6, 9, 12, 15.

So $3\times 5=15$.

Losing points means subtracting, so work out 150 − 45.

A quick mental method: $150-40=110$, then $110-5=105$.

The new score is 105.

5 + 5 + 5 + 5 is four lots of 5, and multiplication is the short way of recording repeated addition: $4\times 5=20$.

Addition is the long form we started with, so naming it does not shorten anything. Subtraction is the inverse of addition and division is the inverse of multiplication: each undoes a total rather than building one from equal groups.

Multiplication and division are inverse operations, so the fact $84÷7=12$ can be rearranged as $12\times 7=84$.

There is nothing new to work out: 12 sevens are exactly the 84 we started with before dividing. You can check the same fact family the other way round, $84÷12=7$.

Sharing equally means dividing: £125 ÷ 5.

$5\times 20=100$, leaving 25, and $25÷5=5$, so each person gets $20+5=$ £25. Check with the inverse operation: $25\times 5=125$.

Subtraction is the inverse of addition, so adding 123456 and then subtracting it again leaves the starting number unchanged.

$123456-123456=0$, so the expression is $5+0=5$. You never have to work out 5 + 123456 at all: spotting the inverse pair does the whole job.