Asha counts the cubes as $2\times (3\times 5)$: two trays of 15. Vivek counts them as $(2\times 3)\times 5$: six rows of 5. How many cubes do they each get, and which property does this show?

Adding two whole numbers always gives a whole number — addition is **closed** on whole numbers. Multiplying two whole numbers always gives a whole number — multiplication is **closed** too. But subtraction is **not** closed: 5 − 7 = −2, which is not a whole number. Division is also not closed: 7 ÷ 2 = 3.5, not a whole number. Closure is the property that lets us trust an operation never to take us 'outside' the world of whole numbers.