If \(m\) and \(n\) are rational numbers, what type of number is \(m\times n\)?
Answer and explanation
Correct answer: Rational number
Write rationals as fractions: let \(m=\frac{a}{b}\) and \(n=\frac{c}{d}\) with integers \(a,b,c,d\) and \(b,d\neq0\). Then \(m\times n=\frac{ac}{bd}\), a ratio of integers, so it is rational. Option C is wrong because the product need not be an integer (e.g. \(1/2\times1/3=1/6\)); option D is wrong because the product need not be negative. Exam tip: test closure by expressing numbers as fractions and multiplying numerator with numerator, denominator with denominator.
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What is the correct answer to this question?
Rational number
Why is this the correct answer?
Write rationals as fractions: let \(m=\frac{a}{b}\) and \(n=\frac{c}{d}\) with integers \(a,b,c,d\) and \(b,d\neq0\). Then \(m\times n=\frac{ac}{bd}\), a ratio of integers, so it is rational. Option C is wrong because the product need not be an integer (e.g. \(1/2\times1/3=1/6\)); option D is wrong because the product need not be negative. Exam tip: test closure by expressing numbers as fractions and multiplying numerator with numerator, denominator with denominator.
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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