# Need help w/: If A/B = 2/3, B/C = 4/7, find the value of A/C.

#### gabriellahe

##### New member
If A is divided by B the result is 2/3.

If B is divided by C the result is 4/7.What is the result if A is divided by C?

Last edited:

#### Subhotosh Khan

##### Super Moderator
Staff member
If A is divided by B the result is 2/3.

If B is divided by C the result is 4/7.What is the result if A is divided by C?

Is a one whole, and b is 6?

I'm not sure where to start, could someone give me a help to start off please.
From A/B = 2/3, write A as a function of B → A = 2/3 * B ..........................(1)

From B/C = 4/7, write C as a function of B → ?? ..........................(2)

Now what??

#### gabriellahe

##### New member

Thank you for your help. Can you please give a similar example worked out so I can follow formula. I am still not understanding what to do. I am age 11 . I tried but can't understand it yet.

Thank you.

Gabriella

Got it now.

A/B x b/c = A/C

#### mmm4444bot

##### Super Moderator
Staff member
A/B x b/c = A/C
That's correct! Symbols cancel in the same ways that numbers do. (I got 8/21.)

Here are two notes about notation.

Do not use the letter x as a multiplication symbol, anymore. Instead, use an asterisk (when typing, or a centered dot, when writing) or grouping symbols:

A/B * B/C = A/C

(A/B)(B/C) = A/C

Symbols b and c are not the same as B and C, so do not use them interchangably in the same exercise. :cool:

#### JeffM

##### Elite Member
If A is divided by B the result is 2/3.

If B is divided by C the result is 4/7.What is the result if A is divided by C?
This is a subtle problem for a beginner. Two common techniques are to multiply by some expression that equals 1 (and so changes nothing) or to add some expression that equals 0 (and so changes nothing). In this case, you know what A/B is so you may think of multiplying A/C by 1/B. But such a multiplication does involve a change. But ((1/B)/(1/B)) = 1 because anything other than zero divided by itself = 1. So let's try multiplying by that double-barreled fraction.

$$\displaystyle \dfrac{A}{C} = \dfrac{A}{C} * 1 = \dfrac{A}{C} * \dfrac{\dfrac{1}{B}}{\dfrac{1}{B}} =$$

$$\displaystyle \dfrac{\dfrac{A}{B}}{\dfrac{C}{B}} = \dfrac{A}{B} * \dfrac{B}{C} = \dfrac{2}{3} * \dfrac{4}{7} = \dfrac{8}{21}.$$