Rational and Irrational Numbers Question
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Grade 11 Rational and Irrational Numbers CCSS: HSN-RN.B.3
Chose the correct missing reason in step 6 of the following proof.
Prove that for rational numbers a,b≠0, their product is also a rational number.
Prove that for rational numbers a,b≠0, their product is also a rational number.
| Statement | Reason |
| 1.a,b∈ℚ | 1.Given |
| 2.a=pq,b=mn, where p,q,m,n∈ℤ | 2.Defition of rational numbers |
| 3.a⋅b=(pq)⋅(mn) | 3.Multiplication Property of Equality |
| 4.a⋅b=p⋅mq⋅n | 4.Associative Property of Multiplication |
| 5.p⋅m, q⋅n∈ℤ | 5.Product of two integers is always an integer |
| 6.a⋅b=p⋅mq⋅n∈ℚ | 6. |
- Substitution Property of Equality
- An integer divided by an integer is still an integer
- Division Property of Equality
- Definition of rational numbers