Question
Dear Mitch,
I am having trouble with my homework for the summer. I hope you can help.
The directions are: "Without finding or changing each quotient, change each problem so that the divisor is a whole number."
What do they mean?
Sincerely,
Manuela D.
Answer
Dear Manuela,
It's usually best to include one of the examples from your homework or a similar one, because math can be much trickier when a question is just words without the numbers to show where they're going and what they're trying to do! Here, though, I think we're lucky because the instruction you were given is a fairly common one. It deals with decimals in a division problem.
So, the first thing you want to do is make sure you know exactly what each word means, so you don't get mixed up before you even get to the interesting part. So, for this type of problem, the three important words are dividend, divisor, and quotient.
And with those three words, division problems look like this:
DIVIDEND (divided by) DIVISOR = QUOTIENT.
_ quotient
Or, another way you could see it is like this: divisor) dividend
Now we go back to a simplified version of the question they asked you:
Without doing anything to the quotient, change each problem so that the divisor is a whole number.
Since numbers which have some (or all) of their digits on the right-hand side of a decimal point are not considered "whole numbers" (remember that all decimals are fractions -- like tenths, hundredths, thousandths...), they want you to make the decimal point in the divisor disappear. Sounds weird, but it is actually easy to do once you understand how.
You can multiply a divisor by any number you wish AND IT DOES NOT CHANGE THE ANSWER YOU WILL GET, SO YOUR ANSWER WILL STILL BE CORRECT. BUT, this ONLY works if you multiply the dividend by the same number that you used on the divisor.
What?????? Why?????? How?????????????
Well, let's look at one more way of showing a division problem, because this third way makes the whole idea VERY clear (in my opinion, anyway).
A fraction, a regular fraction, with a numerator on the top and a denominator on the bottom, is a kind of division problem, and the line between the numerator and the denominator can be read like this: "divided by".
SO, for example,
"10 divided by 5"
can be written like this:
10
5
and it is dividend
divisor
(You might remember hearing that you can always mult8ply anything you like by the number one, because one is the "identity element" of multiplication (it doesn't change anything). You probably also remember that any number 'over itself', (or) "divided by itself" equals one.
Like this: 5
5
or this: 12
12 ...
And so, to do what the question is asking you to do, you need to "multiply away" the decimal. How? You need to use a "power of ten", like 10 or 100 or 1000, because our system is set up so that each decimal place movement is one "power" of ten.
GOOD NEWS: It just so happens that the number of places you need to move the decimal to the right gives you the number of zeros in the whole number you use to multiply the decimal away.
Example:
For .576, you would need to multiply it by 1,000 (that's 3 zeros, for 3 "powers" of 10) to get the decimal all the way over to the right of the number.
REMEMBER: All whole numbers have invisible decimals at their very end (on their right-hand side).
Example: a book at a garage sale might say $1, and the same book in a store would say $1.00, because it includes the decimal followed by a couple of zeros to show no extra cents.
_____
So, from all that you realize that you can make this: .30) 50.
_____.__
into this: 30)5000.
And all you had to do was multiply the divisor and the dividend by the same number (here it was 100, to get two place-value jumps to the right. Then you bring the decimal straight up so that your quotient will have it in the right spot, and you are done!!
That, I believe, is what the question is asking you to do.
Good luck.
I hope this helped.
Sincerely,
Mitch