I don't know what to say

Question

Alyssa said the 6/8 and 9/12 are not equivalent because there is no whole number you can multiply both parts of 6/8 by to get 9/12. Is she correct? Explain. 

Answer 1

These two numbers are equivalent because you can simply/reduce both of them to 3/4. 6 is the same as (2*3) and 8 is the same as (2*4). So we have (2*3)/(2*4), the 2's will divide out leaving you with 3/4. The same thing can be done to 9/12. 9 is the same as (3*3), and 12 is the same as (3*4). so 9/12=(3*3)/(3*4). The 3's divide out, leaving you with 3/4. Hope this makes sense.

Answer 2

The ways to determine this are:

1-Cross-multiplying:

   6    9

 --- x ---

  8     12

 

6x12 = 72

9x8 = 72

They are equivalent.

 

2-You could also determine by

having like denominators, then

seeing if the numerators would

be the same. The LCD for both

would be 4, so:

 

  6        2       3
 ---  ÷  --- = ---
  8        2       4

 

  9        3       3
 ---  ÷  --- = ---
 12         3     4

 

I hope this helps.

Go Get Your "A"