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# Multi-digit multiplication and division: FAQ

## Why do we need to learn multi-digit multiplication and division?

There are many situations in the real world where we need to multiply or divide numbers that are larger than just one digit. For example, if we want to calculate the cost of 17 items that each cost 12, we'll need to multiply 17, times, 12.

## How can we estimate multi-digit multiplication and division problems?

One way to estimate is to round each number to the nearest ten, hundred, or thousand (depending on the size of the numbers) and then multiply the rounded numbers together. For example, to estimate 238, times, 24, we could round each number to the nearest ten: 240, times, 20, equals, 4, comma, 800.
For division, we can estimate the dividend and divisor to the nearest ten, hundred, or thousand (depending on the size of the numbers) and then divide the rounded numbers. For example, to estimate 314, divided by, 27, we could round each number to the nearest ten: 310, divided by, 30, equals, 10.
Try it yourself with these exercises:

## Why do we need to learn how to factor out multiples of ten when multiplying and dividing?

Working with multiples of ten is often easier because of the way our base-ten number system is structured. So, by factoring out tens, we may be able to break down a difficult multiplication or division problem into a simpler one.
Try it yourself with these exercises:

## What is the standard algorithm for multiplication and how do we use it?

The standard algorithm for multiplication involves breaking one of the numbers down into its place values, multiplying each place value by the other number, and then adding the results together.
For example, we can use the standard algorithm to multiply 83, times, 9.
First, we multiply start color #9e034e, 9, end color #9e034e, times, start color #0c7f99, 3, end color #0c7f99.
\begin{aligned} \overset{\purpleE2}8\overset{\phantom2}{\blueE{3}}&\\ \underline{{} \times \maroonE{9}}&\\ \purpleE{7}&\quad \maroonE{9} \times \blueE{3} = \purpleE{27} \end{aligned}
Next, we multiply left parenthesis, start color #9e034e, 9, end color #9e034e, times, start color #0c7f99, 80, end color #0c7f99, right parenthesis, plus, start color #543b78, 20, end color #543b78.
\begin{aligned} \overset{\purpleE2}{\blueE8}\overset{\phantom2}{3}&\\ \underline{{} \times{\maroonE9}}&\\ \goldE{74}\purpleE{7}&\quad (\maroonE{9} \times \blueE{80}) + \purpleE{20} = \goldE{740} \end{aligned}
Try it yourself with these exercises:

## What are remainders and how do they relate to division?

The remainder is the amount left over when you divide one number by another and the division doesn't come out evenly. For example, if we divide 10 by 2, we get a whole number result of 5, with no "leftovers." But if we divide 10 by 3, you get a result of 3 with a remainder of 1.
Try it yourself with these exercises: