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Given a rational number, express it in the form of a ratio. You can then calculate equivalent rational fractions if you multiply both, its numerator and denominator, by any non-zero integer.

Q: How do you find equivalent rational number s?

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The product of two rational numbers is always a rational number.

no # all numbers are real #'s

because the # line shows the rational #'s in order from least to greatest

-4/12 equals -1/3, which has the pattern of 3's after the decimal point repeat infinitely. That is how -4/12 is a rational number.

No: Let r be some irrational number; as such it cannot be represented as s/t where s and t are both non-zero integers. Assume the square root of this irrational number r was rational. Then it can be represented in the form of p/q where p and q are both non-zero integers, ie √r = p/q As p is an integer, p² = p×p is also an integer, let y = p² And as q is an integer, q² = q×q is also an integer, let x = q² The number is the square of its square root, thus: (√r)² = (p/q)² = p²/q² = y/x but (√r)² = r, thus r = y/x and is a rational number. But r was chosen to be an irrational number, which is a contradiction (r cannot be both rational and irrational at the same time, so it cannot exist). Thus the square root of an irrational number cannot be rational. However, the square root of a rational number can be irrational, eg for the rational number ½ its square root (√½) is not rational.

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Let R + S = T, and suppose that T is a rational number.The set of rational number is a group.This implies that since R is rational, -R is rational [invertibility].Then, since T and -R are rational, T - R must be rational [closure].But T - R = S which implies that S is rational.That contradicts the fact that y is an irrational number. The contradiction implies that the assumption [that T is rational] is incorrect.Thus, the sum of a rational number R and an irrational number S cannot be rational.

The product of two rational numbers is always a rational number.

Yes

A rational number is one that can be written as a ratio of two integers. In this case the number 3.3333 can be written as the ratio: 33333/10000 If the intent was to write 3.3333... with the 3's repeating infinitely, it would be equivalent to 3 1/3 or 10/3.

Whether that's all there is to it, or the '135's keep going on forever, either way, it's a rational number.

Whether that's all there is to it, or the '135's keep going on forever, either way, it's a rational number.

If the 6's continue, it is -5/3, and therefore it is rational. If they do not continue, it is -166/100, and still rational.

no # all numbers are real #'s

Rational. It can be expressed a s fraction having integers for the denominator and numerator. ie 93,808,315/100,000,000

because the # line shows the rational #'s in order from least to greatest

A rational number is a number which can be expressed in the form p/q where p and q are integers and p>0.If p/q and r/s are two rational numbers then(p/q)*(r/s) = (p*r)/(q*s).You may need to check that this fraction is in its lowest (simplest) form.

A rational number is a number of the form p/q where p and q are integers and q > 0.If p/q and r/s are two rational numbers thenp/q + r/s = (p*s + q*r) / (q*r)andp/q - r/s = (p*s - q*r) / (q*r)The answers may need simplification.