how to do this?

Question

how do you simplify these problems im really confused

12/21

54/9

a/3ac

plz tell me how to? and plz if you could include the answer as well

Answer 1

for the first sum 12/21 its simple 3x4/ 3x7= 12/21 both 3s are cancelled and the answers that remains is 4/7
for second sum 54/9, 9x6 = 54 therefore answer is 6
for the third sum, it is a/3ac then both As are cancelled & answer remains 1/3c

Answer 2

For the 12/21 one. You have to find the largest common factor of both numbers. (The biggest number that both can be divided by is 3) So you divide the top by 3 and the bottom by 3 and you get 4/7. When the numbers can't be divided by a same number anymore, then it's simplified.

54/9 simply means 54 divided by 9. Which is 6.
Cause 9 times 6 is 54.

a/3ac The a's cross each other out. a/a just equals 1. But you have to still keep a 1 on the top because there is an invisible 1 on the bottom also. so the answer is 1/3c.

Good luck!

Answer 3

These are pretty easy, don't worry. All you have to do is find the same number that will divide into the top number and the bottom number, evenly.

Like 4/2 - you can divide both the top and the bottom by 2. So, you get 4 divided by 2 = 2, and 2 divided by 2 = 1.

The "simplified" answer is 2/1, and if something is over a 1, you can get rid of the 1 and just write it out evenly. 2/1 = 2.
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So, 12/21 - you just try out numbers until you see that 3 divides into both the top (the "numerator") and the bottom (the "denominator"), evenly. 12 divided by 3 = 4, and 21 divided by 4 = 7. That's as far as you can go. The "simplified answer is 4/7. That's it. 4/7.

54/9 - you try 3. That works. 54 divided by 3 = 18, and 9 divided by 3 = 3. The simplified answer is 18/3. But wait! You can go further. Both 18 and 3 are evenly divisible by 3. 18 divided by 3 = 6, and 3 divided by 3 = 1. You get 6/1. And, like always, when something is on top of 1, you can just get rid of the 1 and write the top number only - 6. So, 54/9 = 6. (Did you see that you could have done it in one step? Both 54 and 9 are evenly divisible by 9. You get 6/1 again, and that equals 6.)

a/3ac is weirder. All you can divide both the top and bottom by is the letter "a". But you can do that. So, a divided by a = 1, and 3ac divided by a = 3c (that's the most difficult one, and it isn't that difficult. Anything divided by the same thing just cancels it out. Like, 6x/x = 6/1 = 6).

Anyway, a/3ac divides down to 1/3c, and that's as far as you can go.
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12/21 (divide the top and bottom by 3) = 4/7.

54/9 (divide the top and bottom by 9) = 9/1 = 9

a/3ac (divide the top and bottom by a) = 1/3c

That's it.

Hope I helped.

Answer 4

12/21, At first glance we can see that both terms are divisible by 3, remember, what we do to the 'bottom' we do to the 'top'- hence they are often called denominators and numerators. So, 12/3=4 and 21/3=7 Answer= 4/7 we cannot simplify this anymore so this is called SIMPLEST FORM.

54/9- We do exactly the same method, at first glance we see that both the terms are divisible by 9. 54 divided by 9 = 6 & 9 divided by 9 is obviously 1. Answer= 6/1 which is the same as 6. (6 divided by 1 = 6)

a/3ac- Algebraic simplifications are much simpler there are 1 a on both sides so they cancel out leaving us with 3c. (Hence there are no others that can be simplified nothing divisible by 3 or a c term.) so this is in its simplest form.

~Ramadulla

Answer 5

The the way to simplify these are to cancel. for ex: 12/21 = (3*4)/(3*7). as they both have a 3 in common, it can be cancelled and the left over numbers is the simplified answer. 12/21 = 4/7.
54/9 = (6*9)/9 = 6/1 = 6
If this is followed, a/3ac is the easiest to answer.

Answer 6

to reduce a fraction, you find something called the Greatest Common Denominator. This is the largest number that both numbers are evenly divisible by. if there is no common denominator then the fraction is already simplified.

So for 12/21, we know that 3 goes into 12 and 3 goes into 21 so 3 is your GCD. so you divide 12 by 3 to get 4 and divide 21 by 3 to get 7, so your reduced fraction is 4/7.

With top-heavy fractions (as we used to call them, dolly parton fractions, retarded I know) you say how many times does the bottom one go into the top one? So how many times does 9 go into 54? Well it just so happens that 9 goes into 54 exactly 6 times, so the answer is 6. If there was a remainder then the fraction would be 6 and whatever-the-remainder-was over 9.

With the last one, you have an "a" in both the top and bottom parts, so you can cross both of them out, giving you 1/3c.

Answer 7

12 / 21 = 4 / 7

54 / 9 = 6

a / (3ac) = 1 / 3c

Answer 8

Figure out what is the same (base) in both of them. 12 and 21 both have 3 in them. (12=3X4 and 21=3x7) So, just take the biggest number in common (3 in this example) and what's left is simplified. If the top or first number is bigger than the other, it is not simplified. If you had 5/2 for example, you would divide the top number by the bottom number and put it in front of your answer (5 divided by 2 = 2 with 1 left over or 2 1/2).

Answer 9

12/21 = (4*3)/(7*3) = 3/3 * 4/7 = 4/7

54/9 = (9*6)/9 = 9/9 * 6 = 6

a/3ac = a/a * 1/3c = 1/3c

Answer 10

12/21= 4/7
54/9=6
a/3ac= 1/3c