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Lesson 4: Multiplying by tens

# More with multiplication and division: FAQ

## What do the letters in multiplication and division equations stand for?

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

## What is the associative property of multiplication?

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, left parenthesis, 2, times, 3, right parenthesis, times, 4 is the same as 2, times, left parenthesis, 3, times, 4, right parenthesis.

## What is special about multiplying by tens?

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.

## How can I use the associative property to multiply $2$2-digit 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.
start color #9e034e, 28, end color #9e034e is the same as start color #9e034e, 7, end color #9e034e groups of start color #9e034e, 4, end color #9e034e.
\begin{aligned} \maroonE{28} \times \blueE{2} &= \maroonE{7}\times \maroonE{4} \times \blueE{2}\\\\ &= 7 \times (4 \times 2)\\\\ &= 7 \times 8 \\\\ &= 56 \end{aligned}