Express five percent as a fraction
in its simplest form. Using the fraction form of five
percent, find five percent minus three over 20 minus 0.35. Express your answer as a fraction
in its simplest form.
In the first part of this question,
we are asked to express five percent as a fraction in its simplest form. To do this, we can start by
recalling that percentages are measured out of 100. So, 𝑎 percent is equal to 𝑎
divided by 100. This means that five percent must
be equal to five divided by 100. We need to write this fraction in
its simplest form. We can do this by canceling the
shared factor of five in the numerator and denominator. This gives us one divided by
In the second part of this
question, we want to use our fractional form of five percent to evaluate an
expression involving rational numbers, where we give our answer as a fraction in its
simplest form. To do this, we first note that we
are subtracting three rational numbers. We can recall that when subtracting
rational numbers, we want them to be in the same form. So we will rewrite all of the
rational numbers as fractions. Since we already know that five
percent is equal to one over 20, we only need to convert 0.35 into a fraction.
There are many ways of doing
this. We will note that 0.35 is equal to
35 over 100. And then, we can cancel the shared
factor of five in the numerator and denominator to obtain seven over 20. We can then substitute these
fractional representations of the numbers into the expression to see that it is
equal to one over 20 minus three over 20 minus seven over 20.
We can then recall that we can
subtract fractions with the same denominator by subtracting their numerators. In general, we have 𝑎 over 𝑑
minus 𝑏 over 𝑑 is equal to 𝑎 minus 𝑏 all over 𝑑. This result holds true for any
number of fractions, provided that they have the same denominator. Applying this result gives us one
minus three minus seven all over 20. We can then evaluate the
subtraction in the numerator to obtain negative nine over 20. We cannot simplify this fraction
any further, so our answer is negative nine over 20.