Evaluate seven 𝑞 over 𝑞 plus two
times 𝑝 plus five for 𝑝 is equal to three and 𝑞 is equal to 12.
In this question, we are asked to
evaluate a given expression in terms of 𝑝 and 𝑞 using the given values of 𝑝 and
𝑞. To answer this question, the first
thing we need to do is substitute 𝑝 equals three and 𝑞 equals 12 into the given
expression. We obtain seven times 12 over 12
plus two times three plus five.
We now need to evaluate this
expression. And to do this, we will recall two
things. First, we recall that the acronym
PEMDAS can help us recall the order of operations. We start by evaluating expressions
inside parentheses; then, we move on to evaluating the exponents. Next, we evaluate multiplication,
then division. After this, we evaluate any
additions. And finally, we evaluate the
It is worth noting that the stages
of multiplication and division can be done in any order. Similarly, the stages of addition
and subtraction can be done in either order. These pairs of operations are often
considered in the same step.
There is one extra thing that we
should note before we begin evaluating. That is that the fraction notation
means that we evaluate the numerator and denominator separately and leave the
division until last. We can think of this as adding
parentheses over the numerator and denominator. However, we usually leave these out
since it is implied by the fraction notation.
We are now ready to start
evaluating the expression. We need to start with the
expressions inside the parentheses. We see that only three plus five is
in the parentheses, so we evaluate this to obtain eight. This gives us seven times 12 over
12 plus two times eight. We can now move on to evaluating
any exponents. In this expression, we see that
there are no exponents to evaluate.
So we will move onto the
multiplication and division stage. Remember, we do not evaluate the
division of the numerator and denominator until the end, since we are using fraction
notation. We can evaluate the products in the
numerator and denominator separately. We have that seven times 12 is
equal to 84 and two times eight is equal to 16. This gives us 84 over 12 plus
We can now move on to the final
stage in the order of operations, addition and subtraction. We see that there is only one such
operation, which is in the denominator of the fraction. We can calculate that 12 plus 16 is
equal to 28. Therefore, we have 84 over 28.
Now that we have evaluated the
expressions in the numerator and denominator, we can evaluate the division. One way of doing this is to note
that 84 is equal to 28 times three. This means that 28 goes into 84
three times with no remainder. So 84 over 28 is equal to