prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. stepsreasons 1. a over b plus c over dgiven 2.multiply to get a common denominator 3. ad plus cb all over bdsimplify fill in the missing step in the proof. (1 point)

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08-09-2022
Mathematics

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prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. stepsreasons 1. a over b plus c over dgiven 2.multiply to get a common denominator 3. ad plus cb all over bdsimplify fill in the missing step in the proof. (1 point)

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AFOKE88 AFOKE88 · Answer 1 · 2022-09-12T21:25:45-04:00

The missing step in the rational number proof is; Reason 2; Multiply to get a common denominator

How to prove Rational Numbers?

Let a/b and c/d be two rational numbers, where b and d are not zero and a, b, c and d are integers.

Step 1; a/b + c/d

Reason 1; Given

Step 2; a/b + c/d = ad/bd + cb/bd

Reason 2; Multiply to get a common denominator

Step 3; a/b + c/d = ad/bd + cb/bd = (ad + cb)/bd

Reason 3; Simplify

Since b and d cannot be zero, then bd cannot be zero. Also, since a, b, c, and d are integers, then bd, ad, bc and ad + bc are integers too. Thus, the fraction(ad + cb)/bd is a rational number.

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