Which statement is true about the product of a non-zero rational number and an irrational number? A) The product of a non-zero r
ational number and an irrational number is always a rational number. B) The product of a non-zero rational number and an irrational number is never an irrational number. C) The product of a non-zero rational number and an irrational number is sometimes a rational number. Eliminate D) The product of a non-zero rational number and an irrational number is always an irrational number.
The answer is D. A non-zero rational number multiplied by an irrational number is always an irrational number. This link might help: http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/70477
The fractions are: and . Let's take a look at the denominators: 5 and 3. The LCD of 5 and 3 is 15. 5x3=15, 3x5=15. So now we would multiply the denominators to make them the same number like this: and . Remember that if you multiply the denominator by a certain number, you must multiply the numerator by the same number as well. For example, in , we multiply 3 by 5 and 2 by 5. Same number. Now with that out of the way, let's work on the equation: + . We know it is the same as and . So now all we do is add the numerators together: 5+10=15 or . Now we have to reduce the fraction. can be reduced to 3 by dividing 15 by 5=3. The final fraction is or can be simply put as 3 since 3/3 is a whole number. That's it - you're done!