why does dividing the numerator by the denominator result in an equivalen decimal?

Answer 1

Decimals and fractions are ways to express non-whole numbers. Basically they tell the value of one amount versus the value of another amount:

3/5 of the apples are green. The 3/5 means that 3 apples are green and the rest, 2/5, are not green.

3/20 of the children are tall. The 3/20 means that 2 children are tall, and the rest, 17/20, are not tall.

The decimal system is used to make everything based out of 100. However, not all amounts of things are compared to values of 100. The examples above show a certain value of apples out of 5 total apples, and also a certain number of children out of 20 total children. However, a fraction can be converted into a decimal by multiplying both the numerator and denominator by a certain value that turns the denominator into 100, and therefore the numerator would be the decimal:

2/5 can be converted into (numerator)/100 by multiplying the fraction by 20/20. When multiplying across, you get 40/100. Now that the denominator is 100, the numerator is a certain value out of 100. In this case, it is 40.00. Move the decimal over to the right twice, and you get the decimal 0.40. That is the equivalent decimal.

With the other example, you can do the same thing:
3/20, when multiplied by 5/5, brings you to 15/100. Take 15, move its decimal over two over to the right, and the answer is 0.15.

The above process is actually what is done when you divide the numerator by the denominator.

Some all fractions can be made into equivalent decimals, but some fractions such as 2/3 have a decimal that repeats forever.

Answer 2

It doesn't always result in an equivalent decimal. For example, if someone gave you the fraction 6/12, you could just write 1/2 which is an equivalent fraction (you reduced it). But if they asked you to write it as a decimal, you would divide the denominator into the numerator in order to produce an equivalent decimal. Usually, the denominator is a larger number than the numerator and you can't divide a larger number into a smaller without resorting to using decimals.
For example: 1/2. In order to produce a decimal representation of the number, you would have to divide 2 into 1. By using a decimal point when doing the long division, you get 0.5. Since .5 is 5/10, you have said 1/2 (which is what 5/10 is when reduced). They are both equal proportions: 1/2 = 5/10. If you cross multiply, 1 times 10 gives you the same result as 2 times 5.
Proportions show relationships of parts and wholes. In both cases of decimal and its equivalent fraction, the relationship is the same.

Answer 3

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why does dividing the numerator by the denominator result in an equivalen decimal?

Answer 4

If I am right, Divide the denominator by the numerator. Ex: 6/10 is another way to write 6 divided by 10, so you should get .60 which is 60%. 4/5 divide 4 by 5 and you would get .8 or .80 which is 80%.

Answer 5

It's called the 'equivalent decimal', but what it really *is* is the decimal representation of the fraction.

Hope that helps.


Doug

Answer 6

did you not answer the question yourself??

because u are DIVIDING :P

the fraction bar always carries the meaning of division. So A/B is also saying A divided by B

Answer 7

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Yup! :) Just plug it into your calculator :P Good luck!