Video Transcript
Calculate five multiplied by two
divided by two plus three over four plus five multiplied by two squared.
In order to answer this question,
we begin by recalling the order of operations. One way of doing this is using the
acronym PEMDAS. The letters stand for parentheses,
exponents, multiplication, division, addition, and subtraction. It is worth noting that this is
often written as four stages by grouping multiplication and division as well as
addition and subtraction. In this question, we will use
PEMDAS to simplify the expressions on the numerator and denominator separately.
On the numerator, we have five
multiplied by two divided by two plus three. We have both a multiplication and
division sign. Convention dictates that we perform
these from left to right. However, they can be done in either
order. Five multiplied by two is equal to
10, and dividing this by two gives us five. Our expression simplifies to five
plus three, which is equal to eight. So five multiplied by two divided
by two plus three equals eight.
Now let’s consider the denominator,
four plus five multiplied by two squared. The third term contains an
exponent, so we begin here. Two squared is equal to four. So our expression simplifies to
four plus five multiplied by four. Next, we calculate the
multiplication. Five multiplied by four equals 20,
leaving us with four plus 20, which is equal to 24. Four plus five multiplied by two
squared equals 24.
The original expression is
therefore equal to eight over 24. Dividing the numerator and
denominator by eight, this can be simplified to one-third. We can therefore conclude that five
multiplied by two divided by two plus three over four plus five multiplied by two
squared is equal to one-third.
