Question

Are the equations a/b=c/d and ad=bc equivalent? Explain.

Answer 1

Step-by-step explanation:

The relation given is a/b = c/d, if we cross multiply we will get ad = bc which we got from the first relation only. Let's take an example and assign a,b,c,d some numbers.

We know, 1/2 = 3/6 (equivalent fractions). Then a = 1, b = 2, c = 3, d = 6. Now put these values into the 2nd relation,

• ad = 1 * 6 = 6
• bc = 2 * 3 = 6

ad = bc relation is satisfied. Hence the equations a/b = c/d and ad = bc equivalent
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Answer 2

The equations a/b = c/d and ad = bc are equivalent; this is demonstrated through the process of cross-multiplication of proportions and holds true as long as none of the included variables are zero.

Step-by-step explanation:

The equations a/b = c/d and ad = bc are indeed equivalent; this relationship is known as the cross-multiplication of proportions. To show the equivalence, one can cross-multiply the elements of the first equation. Multiplying each side of the equation a/b = c/d by b and d gives us ad = bc, which is the original second equation. This demonstrates that if two fractions are equal, the product of the numerator of one fraction and the denominator of the other is equal to the product of the other two terms.

For example, consider the proportions 2/3 = 4/6. Cross-multiplying gives us 2*6 = 3*4, which simplifies to 12 = 12, showing the proportions are equivalent.

Remember that this equivalence holds true provided that none of the terms (a, b, c, or d) are zero, since division by zero is undefined.