More with multiplication and division: FAQ

The letters are variables - they can stand for any number.

The associative property of multiplication means that when we multiply three or more numbers together, we can group them in any way we want and still get the same answer. For example, $(2\times 3)\times 4$‍ is the same as $2\times (3\times 4)$‍.

When you multiply a number by ten, you are essentially just adding a zero to the end of the number. This is because of how place value works.

For example, consider the number $34$‍. The "$3$‍" is in the tens place, and the "$4$‍" is in the ones place. When you multiply $34$‍ by $10$‍, you end up with $340$‍. The "$3$‍" has shifted over to the hundreds place, the "$4$‍" has shifted to the tens place, and the new zero is now in the ones place. This pattern holds true for any whole number: when you multiply by ten, you just add a zero to the end. This makes multiplying by ten relatively easy compared to multiplying by other numbers.

The associative property of multiplication tells us that we can group factors in different ways and still get the same product. So when multiplying a $2$‍-digit number by a $1$‍-digit number, we can use the associative property to break down the $2$‍-digit number into two separate $1$‍-digit multiplications, and then combine the two products to get the final answer.

$28$‍ is the same as $7$‍ groups of $4$‍.