why 6/5x5/9 is 2/3

Question

why if I multiplied 6/5 x 5/9 the result is 2/3

Answer 1

If you multiply or divide the top (numerator) and bottom (denominator) by the same value (number) the fraction stays the same.
~~~~~~~~
   6      5  
  --- • --- =
   5      9  

  6 (÷3)       5 (÷5) 
 ---------- • --------- =
  5 (÷5)       9 (÷3)

  2       1   
---- • ---- =
  1       3 

 2 • 1      2 
------- = ---
 1 • 3      3 

Answer 2

 

HI,

 

If your math problem is stated in fractions then there is another method below, but if your problem is for you to figure out the precedence of operations, then see the above reply.

 

If you are doing the problem from a multiplication standpoint:

 

6/5 * 5/9

 

First you multiple the numerators: 6*5=30, then you multiply the denominators: 5X9 = 45

 

Now you have 30/45, reduce this fraction by dividing by 5 = 6/9 and reduce again = 2/3

 

Hope that helps,

CIndy

Answer 3

Hi Ruben,

In order to do fractions, you first need to understand that order of algebraic operation. 

When both writing down and reading the algebraic expressions, the binary operation (including addition+, subtraction-, multiply*, divide/, exponential^) follow a conventional order:

0) Parenthesis, including {}, [], ()
1) Exponent, multiply and divide
2) Addition and subtraction

The ordering is 0)>1)>2). Then there is no ordering within each group, eg multiply and divide are at the same level of priority except that 0) comes in such as a parenthesis.

 

In this case 6/5*5/9, the ordering of multiplication and dividing can be changed with no problem.  Thus

 

6/5*5/9=5/5*6/9=1*6/9

 

Then we can simplify 6/9 by noticing that there is a common factor 3 for both nominator and denominator. Divide 3 on both sides, 

6/9=(6/3) / (9/3)=2/3.

 

I add parenthesis in order to let you know that you should divide 3 on both nominator and denominator first and then 3 will be factored out.

 

Hope it helps!

 

Yingda Z.