Six in eleven dogs at the shelter are female.if there are 154 dogs at the shelter,how many are female?

Whenever dealing with proportions, the fractional amount in one population is the same as the fractional amount in the other.

You'll notice that I used the phrase "is the same as". In math, that translates to "=". In other words, you do such problems by saying that the fraction of one population = the fraction of the other.

In this case, one "population" is group of eleven dogs whose sex was determined. You were told outright that 6 out of 11 (translated into math, that means "6/11") of them were female. The other population is the group of all 154 dogs at the shelter. You don't know how many are female (that's what you're supposed to determine). So the fraction there is x out of 154 (written with math as "x/154"), where x is the number you're trying to find.

So now you have everything you need. The two fractions are equal to each other. So you end up with this equation:

\frac{6}{11}=\frac{x}{154}

Can you solve for x?