If \(m\) and \(n\) are rational numbers, what type of number is \(m+n\)?
Answer and explanation
Correct answer: Rational number
Rational numbers are closed under addition. If \(m=\frac{a}{b}\) and \(n=\frac{c}{d}\) with integers \(a,b,c,d\) and \(b,d\neq0\), then \(m+n=\frac{ad+bc}{bd}\), which is a ratio of integers and thus rational. Option B is incorrect because the sum of two rationals is not generally irrational. Options C and D hold only in special cases, not in general. Exam tip: express numbers as fractions and add to verify rationality quickly.
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What is the correct answer to this question?
Rational number
Why is this the correct answer?
Rational numbers are closed under addition. If \(m=\frac{a}{b}\) and \(n=\frac{c}{d}\) with integers \(a,b,c,d\) and \(b,d\neq0\), then \(m+n=\frac{ad+bc}{bd}\), which is a ratio of integers and thus rational. Option B is incorrect because the sum of two rationals is not generally irrational. Options C and D hold only in special cases, not in general. Exam tip: express numbers as fractions and add to verify rationality quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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