Video Transcript
Find one-quarter times four-fifths
divided by two-fifths plus 0.25.
In this question, we are asked to
evaluate an expression involving multiple operations on various rational
numbers. To answer this question, we can
first note that it is usually easiest to perform operations on rational numbers in
the same form. In general, multiplication and
division are easiest for fractions. So we will write all of the
rational numbers as fractions. We have one-quarter times
four-fifths divided by two-fifths plus one-quarter.
To evaluate this expression, we now
need to recall the order of operations. We can do this by using the acronym
PEMDAS. We can recall that this stands for
parentheses, exponents, multiplication, division, addition, and subtraction. This tells us the order in which we
should evaluate the operations in an expression. Though it is worth noting that we
can apply multiplication and division in either order and addition and subtraction
in either order.
If we look at the given expression,
we can see that there is a product inside parentheses. We need to start by evaluating the
expression inside the parentheses. To evaluate this product, we recall
that we multiply fractions by multiplying their numerators and denominators
separately. We have one times four over four
times five. We can then cancel the shared
factor of four in the numerator and denominator to obtain one-fifth. Therefore, we have rewritten our
expression as one-fifth divided by two-fifths plus one-quarter.
We can now note that there are no
parentheses or exponents left in the expression. So we move on to multiplication and
division. To evaluate the division of two
fractions, we can recall that dividing by a fraction is the same as multiplying by
its reciprocal. So 𝑎 over 𝑏 divided by 𝑐 over 𝑑
is equal to 𝑎 over 𝑏 times 𝑑 over 𝑐, provided that we are not dividing by
zero. Therefore, instead of dividing by
two-fifths, we can multiply by five-halves to get one-fifth times five-halves plus
one-quarter.
We can now evaluate the product to
obtain one times five over five times two plus one-quarter. We can then cancel the shared
factor of five in the numerator and denominator to get one-half plus
one-quarter. There is one final operation left,
which is addition. To add two fractions together, we
want them to have the same denominator. So we rewrite one-half as
two-quarters. Finally, we add these fractions
together to get three-quarters.
