Let u, v, and w be rational numbers. Prove the following statements. - v is a ra
ID: 3119550 • Letter: L
Question
Let u, v, and w be rational numbers. Prove the following statements. - v is a rational number. u - v is a rational number. (You can prove this by going back to the definition of a rational number. Alternatively, you can prove it by observing that u - v = u + (-v) and combining the results of part (a) and Example 4.21. The second way is shorter but the first is self-contained It to know both ways). uv is a rational number If w notequalto 0, then 1/w is a rational number. If w notequalto 0 then u/w is a rational number (You can prove this by going back to the definition of a rational number. Alternatively, you can prove it by combining the results of parts (c) and (d). The second way is shorter but the first way is self-contained. It is good to know both ways.)Explanation / Answer
We know the definition of rational no. is : a number that can be expressed in the form p/q, where p and q are integers and q is not equal to zero..
If u v w are rational number then .. then -v is also a rational number as it is multiplied by a constant -1.
the rational numbers can be a natural no. , whole no. , integers , decimals that stop and that repeat..
hence -v is also a rational no.
ADDITION OR SUBSTRACTION OF TWO RATIONAL NO.S IS ALWAYS A RATIONAL NUMBER . hence if u is a rational no. then u +(-v) is also a rational number .
Similar rule is in product hence uv is also a rational number .
The most imporatant rule is that demnominator of rational number should be a non zero value . hence w cant be equal to zero in u/w .
if both u and w are rational then u/w is also a rational number
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