Isn't dividing the process of making smaller? How is it that One divided by One Half is equal to Two?
2006-07-13 04:59:29 · 18 answers · asked by discerner711 1 in Science & Mathematics ➔ Mathematics
Think of money. How many half-dollars are in a dollar?
(This is one dollar divided by a half-dollar.)
1 ÷ ½ = 2.
How many quarters are in a dollar?
1 ÷ ¼ = 4.
How many quarters are in three dollars?
3 ÷ ¼ = 12.
If you're at the vending machine and a granola bar costs 75¢, how many granola bars can you buy with $6.00?
(This is six dollars divided by ¾ of a dollar.)
6 ÷ ¾ = 8.
Hope these examples shed light for you. :-)
2006-07-13 05:33:51 · answer #1 · answered by Anonymous · 1⤊ 1⤋
Whole Number Divided By Fraction
2016-10-04 07:40:37 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Well. firstly, it depends upon the kind of fraction that is used as the divisor. If its an improper fraction, then the answer is less than whole number dividend. But if the fraction is a proper fraction, then it is always larger than the given whole number. The reason is that, since a proper fraction is a number less than 1, dividing a whole number by a number less than will just make it larger. As the divisor decreases, the quotient increases. Thus any number divided by 0 is undefined since it must b a very, very big number.
Based on the above expalnation, dividing is not always a process of making things smaller. To prove this using calculation, lets take ur example:
1/(1/2)
= 1 x 2/1
=2 How and why?
The rule for dividing a number by fraction is that first, get the reciprocal or multiplicative inverse of the divisor or denominator. Next, change the sign of ur division operation to multiplication operation. Then, follow the rule for multiplying fractions, that is, multiply numerator by numerator and denominator by denominator.
2006-07-13 05:20:53 · answer #3 · answered by baeyongmok 2 · 0⤊ 1⤋
Mathematical reason:
The inverse of a non-zero number a is defined by 1/a=a^(-1).
Division of x by a is defined by multiplication of x by a^(-1).
Therefore x/(1/a)= x•(1/a)^(-1)= x•a
A visual reason why:
Assume you have a group of 10 kids, and you have 10 dollars. If you divide the money up evenly between the whole group (10 kids). How much money will each kid receive? One dollar.
If you divide the money up evenly between half of the group (5 kinds), how much money will each kid receive? Two dollars.
Therefore, if you divide the money up evenly between half of the kids, each kid (that receives money) will get twice as much. OR 1/(1/2)=2.
There is something that you need to be aware of:
3/4 is a fraction, and 4 is a whole number, but 4/(3/4)=4•(4/3)=16/3 is NOT a whole number.
If the numbers are 1/a and b, where a and b are whole numbers (integers), then b/(1/a)=b•a is a whole number. Be careful, not every integer (a whole number) divided by a rational number (a fraction) is an integer.
2006-07-13 05:18:18 · answer #4 · answered by Eulercrosser 4 · 0⤊ 1⤋
Good question! In fact, when I taught my lesson on fractions, my students wondered the same thing because it looks "funny."
As I explained to them, the KEY to working with fractions is to understand the steps or rules you go through to add, subtract, multiply, and divide.
When dividing anything by a fraction, the KEY is to flip-flop the fraction you're dividng by and then multiply.
So if you have 1/2 divided by 3/5, you'd flip 3/5 making it 5/3. Then you'd multiply 1/2 by 5/3 to give you your final answer of 5/6.
In the case of a whole number, say 3 divided by 1/4, you'd flip the 1/4 making it 4/1. then you'd multiply 3 x 4 giving you 12 as your final answer.
2006-07-13 06:48:59 · answer #5 · answered by msoexpert 6 · 0⤊ 1⤋
Because a fraction is smaller than 1. If a number is divided by a number smaller than 1, it would go into it more times than 1 does, right?
2006-07-13 05:05:05 · answer #6 · answered by Anonymous · 0⤊ 1⤋
Physically, you could imagine division as splitting into pieces of a given length. Divide the 12 foot string into lengths of 3/4 feet.
However, the best way to imagine division is to think of it as 'multiplication by the reciprocal'. Division is not a binary operation and the rules of algebra do not apply to it.
You don't divide by 2/3. You multiply by 3/2. Notice that you are now multiplying by a number larger than 1 so your result number will larger than the original number.
2006-07-13 05:28:04 · answer #7 · answered by tbolling2 4 · 0⤊ 1⤋
Well it's like subtracting a negative number. You will end up with a number greater than what you started with.
In this case, dividing a number that's smaller than 1 (one whole) will give you a larger number.
2006-07-13 05:04:40 · answer #8 · answered by M 4 · 0⤊ 1⤋
Hello, there.
A number divided by a fraction of numerator as A and denominator as B means multiplication of numerator B and denominator A.
*key point: y divided by A/B = y x B/A
2006-07-13 05:26:29 · answer #9 · answered by alma_selena 3 · 0⤊ 1⤋
sens, fractions are smaller than 1 so when we divide a whole with a fraction it actually appear like a multification of its reciprocal by this way the result is increase
2006-07-13 05:21:13 · answer #10 · answered by Sayom 2 · 0⤊ 1⤋