Video Transcript
Find the value of 𝑥 over 𝑦 minus
𝑧 over 𝑦 given 𝑥 is equal to one-half, 𝑦 is equal to negative three-halves, and
𝑧 is equal to negative one.
In this question, we are asked to
evaluate a given algebraic expression using the values of three variables. To evaluate this expression at the
given values, we need to start by substituting the values of the variables into the
expression. Substituting 𝑥 equals one-half, 𝑦
equals negative three-halves, and 𝑧 equals negative one into the expression gives
us one-half over negative three-halves minus negative one over negative
three-halves. We add parentheses in the numerator
and denominator of each of the terms to help us keep track of the order of
operations. Remember, we want to divide 𝑥 by
𝑦 and 𝑧 by 𝑦.
To help us evaluate this
expression, we can start by recalling that dividing by a fraction is the same as
multiplying by its reciprocal. Therefore, instead of dividing by
negative three-halves, we can instead multiply it by the reciprocal of negative
three-halves, which is negative two-thirds. This gives us one-half times
negative two-thirds minus negative one times negative two-thirds.
We now need to evaluate the
multiplications. In the first product, we can cancel
the shared factor of two in the numerator and denominator to get negative
one-third. In the second product, we have
negative one times negative one, which is equal to one. So, we are left with negative
two-thirds. This gives us negative one-third
minus two-thirds.
We now have the difference between
two fractions. We note that the fractions have the
same denominator. So we subtract their numerators to
get negative one minus two all over three, which we can calculate is equal to
negative one.
