### Brain Teasers

# A Compounding Question.

Simplify the following expression:

(a/b) / (c/d) - (d/c) / (b/a)

(a/b) / (c/d) - (d/c) / (b/a)

### Answer

Zero.Hide Answer Show Answer

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## Comments

I don't get it

The typographical presentation is a bit confusing.

--- It is the difference between two fractions.

--- The first fraction is (a/b) / (c/d). It is equal to (a/b) x (d/c) = ad/bc

--- The second fraction is (d/c) / (b/a). It is equal to (d/c) x (a/b) = da/cb

--- It is the difference between two fractions.

--- The first fraction is (a/b) / (c/d). It is equal to (a/b) x (d/c) = ad/bc

--- The second fraction is (d/c) / (b/a). It is equal to (d/c) x (a/b) = da/cb

my head hurts lol

To solve it:

(a/b)/(c/d) - (d/c)/(b/a)

This represents the difference of two fractions with different denominators. In order to subtract the two fractions, you need to come up with a common denominator. The easiest way is to multiply and divide the first fraction by the denominator of the second, and vice-versa.

Like this: 3/4 - 2/5

(5/5)*(3/4) - (4/4)*(2/5)

(15/20) - (8/20) = 7/20

It's perfectly fine to multiply a fraction by a number over itself, as this is the same thing as multiplying by 1 (i.e. 5/5 = 1, so (5/5)*(3/4) = 1*(3/4) = 3/4.)

So, to solve this problem:

(a/b)/(c/d) - (d/c)/(b/a)

or

(a/b) (d/c)

------ - -----

(c/d) (b/a)

(b/a)*(a/b) (c/d)*(d/c)

------------- - -------------

(b/a)*(c/d) (c/d)*(b/a)

The numerators here both multiply to one, since multiplying reciprocal fractions always equals 1:

(b/a)*(a/b) = 1 and

(c/d)*(d/c) = 1, so the above equation now is:

1 1

---------- - -----------

(b/a)*(c/d) (c/d)*(b/a)

Since the order in which you multiply two numbers is interchangable, this is also:

1 1

---------- - -----------

(b/a)*(c/d) (b/a)*(c/d)

since you are subtracting the same fraction from itself, the answer must be zero.

Clear as mud, right?!?

(a/b)/(c/d) - (d/c)/(b/a)

This represents the difference of two fractions with different denominators. In order to subtract the two fractions, you need to come up with a common denominator. The easiest way is to multiply and divide the first fraction by the denominator of the second, and vice-versa.

Like this: 3/4 - 2/5

(5/5)*(3/4) - (4/4)*(2/5)

(15/20) - (8/20) = 7/20

It's perfectly fine to multiply a fraction by a number over itself, as this is the same thing as multiplying by 1 (i.e. 5/5 = 1, so (5/5)*(3/4) = 1*(3/4) = 3/4.)

So, to solve this problem:

(a/b)/(c/d) - (d/c)/(b/a)

or

(a/b) (d/c)

------ - -----

(c/d) (b/a)

(b/a)*(a/b) (c/d)*(d/c)

------------- - -------------

(b/a)*(c/d) (c/d)*(b/a)

The numerators here both multiply to one, since multiplying reciprocal fractions always equals 1:

(b/a)*(a/b) = 1 and

(c/d)*(d/c) = 1, so the above equation now is:

1 1

---------- - -----------

(b/a)*(c/d) (c/d)*(b/a)

Since the order in which you multiply two numbers is interchangable, this is also:

1 1

---------- - -----------

(b/a)*(c/d) (b/a)*(c/d)

since you are subtracting the same fraction from itself, the answer must be zero.

Clear as mud, right?!?

Argh, the spacing of the 1's was put too close together... Oh well, I tried!

why is there an open calculator you can get the answer just by looking at it

I think the "Open Calculator" button appears for any problem labeled "Math". Also, this problem says "Solve the equation", but there is no equation. It should read, "Simplify the expression."

well...ummm...i knew the answer was 0 but i dont know how

How about common fraction? With everything expressed as divided by abcd (the product a*b*c*d), the numerator is (aacd/abcc)-(abdd/bbcd). With its common divisor as abbccd, the its numerator becomes aabcdd-aabcdd, which equals zero. tah-dah

this was extremely easy for me. First for everything! thank you for making me feel smart.

Simple. Just follow the order of operations!

I did it the same as Canu.

I think Musicmaker made the problem about as difficult as possible.

I think Musicmaker made the problem about as difficult as possible.

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