Video Transcript
Evaluate and simplify negative
three-quarters minus 30 percent.
In this question, we are asked to
evaluate and simplify the difference between two given rational numbers. To do this, it is a good idea to
write the numbers in the same form. Usually, it is easiest to rewrite
the rational numbers as fractions. So, we will rewrite 30 percent as a
fraction. We can do this by recalling that
fractions are measured out of 100. So, 30 percent is equal to 30 over
100. We can simplify this by canceling
the shared factor of 10 in the numerator and denominator. We get negative three-quarters
minus three-tenths.
We can then recall that we can find
the difference of two fractions with the same denominators by finding the difference
in their numerators. We have that 𝑎 over 𝑐 minus 𝑏
over 𝑐 is equal to 𝑎 minus 𝑏 all over 𝑐. To apply this result, we need both
fractions to have the same denominator. We can find that the lowest common
multiple of the denominators is 20. So, we want to rewrite both of the
fractions to have a denominator of 20. We do this by multiplying the first
fraction by five over five and multiplying the second fraction by two over two. Evaluating these products gives us
negative 15 over 20 minus six over 20.
Now that the denominators are the
same, we can find the difference in the fractions by finding the difference of the
numerators. We obtain negative 15 minus six all
over 20, which is equal to negative 21 over 20. We can then convert this value into
any form we want. For instance, we could write our
answer as the mixed number negative one and one-twentieth.
