Question

12. Consider the general rational equation a/b=c/d

Answer 1

Part (a)

Answer:  ad = bc

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Explanation:

In the equation a/b = c/d, we have b and d in the denominator.

If we multiply both sides by bd, then the denominators will cancel. The expression bd is the same as bd/1.

As a similar example, consider the equation

a/b = 12

if we multiply both sides by b, then we clear out the denominator to end up with a = 12b

As another example, let's consider

a/b = c

Multiplying both sides by b leads to

a = bc

The same idea applies with the denominator d as well.

When going from a/b = c/d to ad = bc, your textbook may refer to this process as "cross multiplication".

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Part (b)

Answer:  bd is the product of the denominators

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Explanation:

Often in math, writing two variables next to each other represents multiplication.

bd is the same as b*d which means "b times d". The term "product" is the result of multiplying two or more values.

b and d are both in the denominator of each fraction, so bd represents the product of the denominators.