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How do you multiply and divide rational expressions?
When multiplying two rational expressions, simply multiply their numerators together, and their denominators together: (a / b) * (c / d) = (a * c) / (b * d) Dividing one fraction by another is the same as multiplying the first fraction by the reciprocal of the second one: (a / b) / (c / d) = (a / b) * (d / c) = (a * d) / (b * c) This is often referred to as cross multiplication.
Can you add two irrational numbers to get an rational number?
NoA rational number is a one that can be written as a fraction i.e a/b. where a and be are integers (whole numbers)Considera/b and c/d. Where a b c and d are integers and as such rational numbersa/b + c/d = (ad + bd)/cdad, bd and cd will all be integers and as such a/b + c/d will always be rational
Why the sum difference and product of 2 rational numbers rational?
A rational number is one that can be expressed as a/b The sum of two rational numbers is: a/b + c/d =ad/bd + bc/bd =(ad+bc)/bd =e/f which is rational The difference of two rational numbers is: a/b - c/d =ab/bd - bc/bd =(ab-bc)/bd =e/f which is rational The product of two rational numbers is: (a/b)(c/d) =ac/bd =e/f which is rational
Which of the following expressions will produce an answer with 3 significant figures?
A, B and C.
What does radical conjugates mean?
if you have the expression a + b*sqrt(c), the radical conjugate is a - b*sqrt(c). this is important because multiplying those two expressions together gives you an integer if a, b, and c are integers.
How do you multiply and divide rational expressions?
When multiplying two rational expressions, simply multiply their numerators together, and their denominators together: (a / b) * (c / d) = (a * c) / (b * d) Dividing one fraction by another is the same as multiplying the first fraction by the reciprocal of the second one: (a / b) / (c / d) = (a / b) * (d / c) = (a * d) / (b * c) This is often referred to as cross multiplication.
Can you add an irrational number and a rational number?
Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational. 1.a +b =c Where a and c are rational and b is irrational. 2.b=c-a Subtracting the same number a from each side. 3.b is irrational c-a is a rational number we arrived at a contradiction. So the sum is an irrational number.
Why does a rational number plus an irrational number equal an irrational number?
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.
Can you add two irrational numbers to get an rational number?
NoA rational number is a one that can be written as a fraction i.e a/b. where a and be are integers (whole numbers)Considera/b and c/d. Where a b c and d are integers and as such rational numbersa/b + c/d = (ad + bd)/cdad, bd and cd will all be integers and as such a/b + c/d will always be rational
Describe similarities between dividing two fractions and dividing two rational expressions?
They are the same. A fraction is one integer divided by another integer. A rational number can be expressed as the quotient of two integers. If you're wondering about the easier method for dividing two fractions, say ( a / b ) / ( c / d ) it would be ( a / b ) * ( d / c ).
Why does the sum of rational number and irrational numbers are always irrational?
Let your sum be a + b = c, where "a" is irrational, "b" is rational, and "c" may be either (that's what we want to find out). In this case, c - b = a. If we assume that c is rational, you would have: a rational number minus a rational number is an irrational number, which can't be true (both addition and subtraction are closed in the set of rational numbers). Therefore, we have a contradiction with the assumption that "c" (the sum in the original equation) is rational.
Adding rational number and an irrational number to get a rational number?
The sum of a rational and an irrational number is always irrational. Here is a brief proof:Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that bis rational as well. But we already said that b is an irrational number. This is a contradiction, and hence the original assumption was false. Namely, the sum c must be an irrational number.
Can you add two irrational numbers that are not conjugates of one another ie a plus b and a minus b to get a rational number?
You can also have any numbers like (a + c) and (b - c), where "c" is the irrational part, and "a" and "b" are rational.
Why is the sum of an rational number and irrational number an irrational number?
The rational numbers form a field. In particular, the sum or difference of two rational numbers is rational. (This is easy to check directly). Suppose now that a + b = c, with a rational and c rational. Since b = c - a, it would have to be rational too. Thus you can't ever have a rational plus an irrational equalling a rational.
Why the sum difference and product of 2 rational numbers rational?
A rational number is one that can be expressed as a/b The sum of two rational numbers is: a/b + c/d =ad/bd + bc/bd =(ad+bc)/bd =e/f which is rational The difference of two rational numbers is: a/b - c/d =ab/bd - bc/bd =(ab-bc)/bd =e/f which is rational The product of two rational numbers is: (a/b)(c/d) =ac/bd =e/f which is rational
Why rational number plus an irrational number is equal to an irrational number?
You can easily prove (doing some basic manipulations with fractions) that the addition of two rational numbers gives you a rational number. As a corollary, a subtraction of two rational numbers also results in a rational number.Now, assume an addition: a + b = c Also, assume that "a" and "c" are rational. Solving for "b": b = c - a Since "c" and "a" are rational, so is "c - a" - this is a contradiction to the assumption.
Which of the following expressions will produce an answer with 3 significant figures?
A, B and C.
