Consider that 𝑥 is equal to
three-quarters and 𝑦 is equal to 30 percent. By converting both 𝑥 and 𝑦 into
decimal form, find the value of 𝑥 minus 𝑦 in decimal form.
In this question, we are asked to
find the difference between two rational numbers, one given as a fraction and the
other given as a percentage. It is always a good idea to write
both numbers in the same form to make the subtraction easier. Usually, we would rewrite the
numbers to be in a fractional form. However, we can also do this by
rewriting both numbers into a decimal form.
Let’s start by converting
three-quarters into a decimal. There are many ways that we can do
this. For instance, we may just recall
that three-quarters is 0.75. However, if we cannot remember this
conversion, we can always rewrite three-quarters as an equivalent fraction with a
denominator of 100 by multiplying the numerator and denominator by 25. We see that three-quarters is equal
to 75 over 100. We can easily convert this fraction
into a decimal by moving its decimal point two spaces to the left. We see that three-quarters is equal
We can follow a similar process for
30 percent. We recall that percentages are
measured out of 100. So 30 percent is the same as 30
over 100, which we can convert into the decimal 0.30, which is just 0.3. We can now substitute our decimal
conversions of 𝑥 and 𝑦 into the expression to see that 𝑥 minus 𝑦 is equal to
0.75 minus 0.3. Finally, we can calculate that 0.75
minus 0.3 is 0.45.
It is worth noting that we can see
this from our fractional conversions as well. We have 75 over 100 minus 30 over
100 is equal to 45 over 100, which is equal to 0.45.