Prove: a/c & c/d implies ac/bd

Thread starter aorick21
Start date Sep 10, 2007
Tags

Proof

In summary, "Prove: a/c & c/d implies ac/bd" is a mathematical statement that states if the ratio of a to c is equal to the ratio of c to d, then the ratio of a to b is equal to the ratio of c to d. This can be proven using properties of proportions and cross-multiplication. Real-life applications of this statement include engineering, physics, and finance. However, there are exceptions to this statement, such as when any of the variables are equal to zero or when dealing with imaginary or complex numbers.

Sep 10, 2007

aorick21

suppose a, b, c, and d are integers. prove that if a/c and c/d, then (ac/bd)

Physics news on Phys.org

Sep 10, 2007

bomba923

Counterexample: a=c=d=2, b=1

Sep 10, 2007

CompuChip

Science Advisor

Homework Helper

At least, assuming that by a/c you mean that a divides c.

FAQ: Prove: a/c & c/d implies ac/bd

What is the meaning of "Prove: a/c & c/d implies ac/bd"?

"Prove: a/c & c/d implies ac/bd" is a mathematical statement, also known as a conditional statement or implication. It means that if the ratio of a to c is equal to the ratio of c to d, then the ratio of a to b is equal to the ratio of c to d.

How do you prove the statement "a/c & c/d implies ac/bd"?

To prove this statement, we can use the properties of proportions and cross-multiplication. We start by assuming that a/c and c/d are equal, and then we multiply both sides of the equation by d. This gives us ad = bc. Then, we can divide both sides by b, giving us a/b = c/d. Therefore, we have shown that a/c & c/d implies ac/bd.

Can you give an example to illustrate "a/c & c/d implies ac/bd"?

Yes, for example, if we have two fractions, 2/4 and 6/12, we can see that the ratio of the numerators (2) to the denominators (4) is equal to the ratio of the numerators (6) to the denominators (12). This means that 2/4 & 6/12 implies (2*12)/(4*12) = (6*4)/(12*4), or 24/48 = 24/48.

What are some real-life applications of the statement "a/c & c/d implies ac/bd"?

This statement has many practical applications in fields such as engineering, physics, and finance. For example, in engineering, it can be used to calculate the dimensions of scaled models or to determine the equivalent resistance in a parallel circuit. In physics, it can be used to solve problems involving similar triangles or to calculate the velocity of an object. In finance, it can be used to calculate exchange rates or to determine the value of a portfolio.

Are there any exceptions to the statement "a/c & c/d implies ac/bd"?

In general, this statement holds true for all numbers except for zero. If any of the variables a, b, c, or d are equal to zero, then the statement becomes undefined. Additionally, the statement may not hold true for imaginary or complex numbers, as they do not follow the same rules of proportionality as real numbers.