HELP ASAP :
1 answer:
You might be interested in
Answer: 8/25
Step-by-step explanation: Using the place value chart, we can see that the decimal 0.32 is thirty-two hundredths so we can write 0.32 as 32/100.
Since 32/100 is not in lowest terms, we divide both the numerator and the denominator by 4 and we get the equivalent fraction 8/25.
This means that 0.32 can be written as the fraction 8/25 which is in lowest terms.
Sum/difference:
Let
This means that
Now, assume that is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that
was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.