Is it true that if a/b = c/d, then (a + 2b)/b = (c + 2d)/d?

a/b = c/d

a/b + 2 = c/d +2 [ add 2 on both sides ]

or ( a + 2b)/b = ( c+2d)/d

so true

Is it true that if a/b = c/d, then (a + 2b)/b = (c + 2d)/d?

Let a = 1, b = 2, c = 3 and d = 6.

a/b = c/d =>1/2 = 3/6

(a + 2b)/b = (c + 2d)/d =>5/2 = 15/6

True

I can genuinely say I've never seen that equation before in my life but it surely must be true. If the a+2b is divided by b, then I'll go down to just one b, you have to think of your rules of indices. Like a^4 x a^2=a^6 and a^4/a^2=a=a^2. I hope that helps!

Yes. (a+2b)/b = a/b +2. (c+2d)/d = c/d +2. Subtract 2 from each.

Yes

a/b = c/d

Add 2 to both sides:

a/b + 2 = c/d + 2

Factor out a 1/b from the left and a 1/d from the right:

(a + 2b)/b = (c + 2d)/d

Yes, if a=c and b=d, and if the operations you set them to are identical, they'll always be equal.