28 Part 1: The World of Numbers
Division
Division is the inverse, or opposite, of multiplication. If multiplication answers questions like “If I
have 3 boxes of cookies and each box has 12 cookies, how many cookies do I have?” then division
is for questions like “If I have 36 cookies and I’m going to put them in 3 boxes, how many cookies
go in each box?” The division problem “36 z 3 = what number?” is equivalent to “3 v what
number = 36?”DEFINITION
The result of a division is called a quotient. The number you divide by is the divisor,
and the number you’re dividing is called the dividend. Dividend z divisor = quotient.
In the equation 12 z 3 = 4, 12 is the dividend, 3 is the divisor, and 4 is the quotient.Just as knowing your addition facts helps with subtraction, knowing your multiplication facts,
or times tables, will help with division. And just as you used the place value system to deal with
larger numbers in other operations, a process called long division will use a similar strategy.MATH TRAP
Division by zero is impossible. If you divide 12 by 4, you’re asking 4 v what number =- If you try to divide 12 by 0, you’re asking 0 v what number = 12, and the answer is
there isn’t one. Zero times anything is 0.
When you need to divide a number like 45 by 9, you can rely on basic facts (9 v 5 = 45), but if
you need to divide 738 by 9, that’s not in the basic facts you’ve memorized.
The strategy you want to use instead has a logic, a way of thinking about what’s going on, and an
algorithm, a step-by-step process for actually doing it. Algorithms can feel like magic, especially if
you don’t understand the logic behind them, so let’s look at the logic first.DEFINITION
An algorithm is a list of steps necessary to perform a process.The number 738 is made up of 7 hundreds, 3 tens, and 8 ones. Think of them like paper money.
You want to divide by 9. Look first at the hundreds. Can you deal out 7 hundred dollar bills into
9 piles? Not without leaving some piles empty, because there are 9 piles but only 7 hundreds.
So exchange all the hundred dollar bills for ten dollar bills. 7 hundreds give you 70 tens, and the
3 tens you already had make 73 tens.
Can you deal the 73 tens out into 9 piles? You could deal 8 tens into each pile and have 1 ten left
over. Okay, each pile has 8 tens. Take the extra 1 ten, trade it for 10 ones, and add on the 8 ones