### Video Transcript

Calculate seven and one-fourth
minus four and five-eighths. Give your answer as a mixed
number.

When we look at the expression
seven and one-fourth minus four and five-eighths, they’re both mixed numbers. However, the fraction portion of
the mixed numbers do not have a common denominator. And we know in order to work with
these values, we need them to be in the same format. Since we’re dealing with
denominators four and eight and we know that four is a factor of eight, four times
two equals eight, which means we could rewrite one-fourth as two-eighths. Once we do that, we have seven and
two-eighths minus four and five-eighths.

However, we’re still not quite
ready to subtract because we’re trying to take five-eighths from two-eighths. And that means that for our first
mixed number seven and two-eighths, we need to borrow from the whole number
portion. If we take one whole away from
seven, we leave six. And that whole value that we took
away is equal to the fraction eight-eighths. If we add two-eighths plus
eight-eighths, we get ten-eighths. The mixed number six and
ten-eighths is the same value as seven and one-fourth written in a different
format.

Now, we’re ready to subtract, six
and ten-eighths minus four and five-eighths. To subtract the fraction portion,
since we have common denominators, we’ll say 10 minus five. That is, we’re subtracting the
values of the numerator. And the denominator isn’t
changing. Ten-eighths minus five-eighths
equals five-eighths. And then, we subtract the whole
number portions. Six minus four equals two, giving
us the result of two and five-eighths. Five-eighths can’t be simplified
any further. Two and five-eighths is a mixed
number and is our final answer.

So far, we’ve only been calculating
values that are already given in the same format. In our next example, we’ll have to
find the difference between a decimal and a fraction.

Find the difference between
negative 0.85 and two-fifths giving your answer as a fraction in its simplest
form.

The difference between negative
0.85 and two-fifths can be written as negative 0.85 minus two-fifths. But once we get to this point, we
have a problem. And that is that our two values are
given in different formats, which means we have a choice to make. We can convert two-fifths to a
decimal so that we’re subtracting a decimal from a decimal. Or we can convert negative 0.85
into a fraction so that we’re subtracting a fraction from a fraction. Both methods will work, but we’ve
been told to give the answer as a fraction in its simplest form. And that means it’s probably worth
it to subtract a fraction from a fraction.

And that means we need to think
about how we would write negative 0.85 as a fraction. Since the five in negative 0.85 is
in the hundredths place, we say that this is negative eighty-five hundredths. And as a fraction that is negative
85 over 100. But before we move on, we might
want to see if we can simplify eighty-five hundredths. Both 85 and 100 are divisible by
five. Negative 85 divided by five equals
negative 17, and 100 divided by five equals 20, which means we’re trying to say
negative 17 over 20 minus two-fifths.

However, we now see that we don’t
have common denominators in our two fractions. But we know that five times four
equals 20. And that means we can multiply
two-fifths by four over four. Two times four is eight, and five
times four is 20. We now have negative seventeen
twentieths minus eight twentieths. Since we have common denominators,
we can do subtraction by subtracting the numerators, which will be negative 17 minus
eight. The denominator doesn’t change. That remains 20. Negative 17 minus eight will be
equal to the negative value of 17 plus eight. That’s negative 25.

So, we have negative 25 over
20. Both of these values are divisible
by five. Negative 25 divided by five equals
negative five. 20 divided by five equals four. And this means negative 0.85 minus
two-fifths is equal to negative five-fourths.