Evaluate one twelfth minus negative
one-third minus 0.75, giving the answer as a fraction in its simplest form.
In this question, we are asked to
evaluate an expression involving the difference of rational numbers. We want to give our answer as a
fraction in its simplest form.
To answer this question, we can
start by recalling that in order to add and subtract fractions, we want their
denominators to be equal. In general, we have 𝑎 over 𝑐 plus
𝑏 over 𝑐 is equal to 𝑎 plus 𝑏 over 𝑐. And 𝑎 over 𝑐 minus 𝑏 over 𝑐 is
equal to 𝑎 minus 𝑏 over 𝑐. In other words, we can add or
subtract fractions with the same denominator by adding or subtracting their
numerators. We can use this to evaluate the
expression by rewriting each rational number as a fraction with the same
Let’s start by rewriting 0.75 as a
fraction. We can recall that 0.25 is
one-quarter. So we can multiply this by three to
see that three-quarters is 0.75. Next, we can simplify the
expression we want to evaluate by recalling that subtracting a negative number is
the same as adding the positive value. So we obtain one twelfth plus
one-third minus three-quarters.
We now want to rewrite all of the
fractions so that they have the same denominator. To do this, we need to find the
lowest common multiple of the denominators. We can start by noting that the
lowest common multiple of 12 and three is 12, since 12 is a multiple of three. Similarly, we can note that 12 is a
multiple of four. So the lowest common multiple of
the denominators is 12.
Therefore, we want to rewrite each
fraction to have a denominator of 12. We note that the first fraction
already has this denominator. We can multiply the numerator and
denominator of the second fraction by four and the numerator and denominator of the
third fraction by three so that they are equivalent fractions with denominators
equal to 12.
We can now evaluate each of the
products. Remember, we want the denominators
to be equal to 12. We get one twelfth plus four
twelfths minus nine twelfths.
Now that the denominators are
equal, we can add and subtract all of the fractions by adding and subtracting their
numerators. We obtain one plus four minus nine
all over 12. We can then calculate that one plus
four minus nine is negative four. So we get negative four over
12. Remember, we need to give our
answer as simplified as possible. We can cancel the shared factor of
four in the numerator and denominator to get negative one-third. We cannot simplify this fraction
any further. Hence, one twelfth minus negative
one-third minus 0.75 is equal to negative one-third.