Divide 4 1/5 by 3 1/7. Write in the simplest form.?

Question

I know you start out with 21/5 divided by 22/7. I get lost after there. If someone could show me where to go from there, I would really appreciate it.

ok, I know you are supposed to invert the second number which would be
21/5 dividided by 7/22. I got that far, and I know I need to find the common denominator somewhere. This is where I get totally lost.

Answer 1

You need a common denominator when adding or subtracting.
When you are multiplying or dividing you do NOT need a common denominator.
(21/5)(7/22)
Multiply the numbers on the top together (that will be the numerator), and multiply the numbers on the bottom together (that will be the denominator)
= (21*7)/(5*22)
= 147/110 = 1 & 37/110

Answer 2

First, change the mixed numner to improper fraction. Let me know if its not clear what I did:

4 1/5 = 21/5
3 1/7 = 22/7

The original question then asks:
(21/5) / (22/7)

To divide fractions, you do not need a common denominator (only in adding and subtracting them). But, what you do is "flip" the second fraction and change the "divide" to "multiply":

(21/5) * (7/22)

= (21*7 / 5*22) = (147/110)

Change back to a mixed number by doing long division:

1 37/110

Answer 3

When you divide by a fraction, you can invert the fraction and then multiply, so that the problem becomes 21/5 times 7/22. This is the same as (21*7)/(5*22). Likewise, if you were to divide 21/5 by 5 (same as 5/1), you could invert 5/1 to 1/5 and multiply. It becomes very easy this way.

Answer 4

No common denominator needed here - only when adding and subtracting.

You converted the mixed numbers to improper fractions correctly.

So we have a big numerator N divided by a big denominator D, where

N = 21/5
D = 22/7

What happens when I multiply the denominator D by its inverse?

D(7/22) = (22/7)(7/22) = (22*7)/7*22) = 1

I can change the denominator to 1 by multiplying it by its inverse.

Whatever you do to the denominator must also be done to the numerator - this is why the rule for dividing fractions is to rewrite the numerator and multiply it by the inverse of the denominator.

(21/5)(7/22) = 147/110

Answer 5

As you say, you'll divide 21/5 by 22/7, but the reason to "flip" the 2nd fraction (use its reciprocal) is to change the dividing to multiplying.

21/5 ÷ 22/7 = 21/5 × 7/22

Since there are no common factors, you can just multiply the numerators (21×7) and denominators (5×22) to get your final answer.

Good news: you don't need to worry about least common denominators unless you're *adding or subtracting* fractions.

Hope that helps!

Answer 6

5/a million divided through 2/3 is 5/a million x 3/2 = 15/2 or 7 a million/2. 4/5 divided through 5/a million is 4/5 x a million/5 = 4/25 7/a million divided through 3/8 is 7/a million x 8/3 = fifty six/3 or 18 2/3. 2/3 divided through 4/5 is two/3 x 5/4 = 5/6. 7/8 divided through 3/8 is 7/8 x 8/3 = 7/3 or 2 a million/3. 7/8 divided through 2/a million is 7/8 x a million/2 = 7/16. 2/3 divided through 4/5 is two/3 x 5/4 = 5/6. 7/8 divided through 2/3 is 7/8 x 3/2 = 21/16 or a million 5/16. 4/7 divided through 3/8 is 4/7 x 8/3 = 32/21 or a million 11/21 5/12 divided through 3/4 is 5/12 x 4/3 = 5/9. 3 a million/8 divided through 2 a million/2 is 25/8 x 2/5 = 5/4 or a million a million/4. 4 2/3 divided through 3 a million/2 is 14/3 x 2/7 = 4/3 or a million a million/3. a million a million/2 divided through 3 a million/8 is 3/2 x 8/25 = 12/25. this isn't "one" question.

Answer 7

21/5 x 7/22 = 147/110 = 1.3363636363 >continues indefinitely

Answer 8

(21 / 5) / (22 / 7) = 21*7 / 22*5 = 147 / 110

Answer 9

Invert the second fraction (making it 7/22) and multiply.

Answer 10

21/5 divided by 22/7 = ----both x35 (= 5x7)
147 / 110 = 1 37/110
Good luck with it.