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Ava and Emily both love reading books. 2/7 of Ava's books is equal to 1/9 of Emily's books. What is the ratio of Ava's to Emily's books? (Express your answer in the simplest form)

Jun 23, 2017

#1
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Ava and Emily both love reading books. 2/7 of Ava's books is equal to 1/9 of Emily's books. What is the ratio of Ava's to Emily's books? (Express your answer in the simplest form)

2:7 = 1:9    Find the LCM of 7 and 9 which is 63. Equalize the denominators, so that we have:

18:63 = 7:63 Since the denominators are the same, we conclude that ratio is:

18 : 7, which is the ratio of Emily's books to Eva's.

Jun 23, 2017
edited by Guest  Jun 23, 2017
#2
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Let A = number of Ava's books and E = number of Emily's books:

(2/7)*A = (1/9)*E

A = (7/2)*(1/9)*E

A/E = (7/2)*(1/9)

A/E = 7/18  or A:E = 7:18

(Note that Emily must have more books than Ava).

Jun 23, 2017
#3
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(2/7) Ava's  books   = (1/9) Emily's books

Multiply both sides by (7/2)

Ava's books  =  (7/2)(1/9) Emily's books

Ava's  books = (7/18) Emily's books   ...so....

Ava's books / Emily's books   =  7 /18

To see this let us suppose that Ava has 63 books.....then  2/7 of her books = 18

But this is  1/9 of Emily's books  = 162

And 63 / 162  =   7/18

Jun 23, 2017