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QuestionEvaluate (4a+c)÷b−(bd)÷(ac)(4a+c) \div b - (bd) \div(ac) for a=−2a=-2, b=3b=3, c=−1c=-1, d=1d=1. What is the result?

Studdy Solution

STEP 1

Assumptions1. The values of the variables are as follows a=−a=-, b=3b=3, c=−1c=-1, and d=1d=1. . The operations in the expression are addition, subtraction, multiplication, and division.
3. The order of operations is parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

The given expression is (4a+c)÷b−(bd)÷(ac)(4 a+c) \div b-(b d) \div(a c). We will first substitute the values of aa, bb, cc, and dd into the expression.
=(4(−2)+(−1))÷−(×1)÷((−2)×(−1))=(4(-2)+(-1)) \div-( \times1) \div((-2) \times (-1))

STEP 3

Now, let's simplify the expression inside the parentheses and the multiplication.
=(−8−1)÷3−(3)÷2=(-8-1) \div3-(3) \div2

STEP 4

Further simplification gives us=−9÷3−3÷2=-9 \div3-3 \div2

STEP 5

Now, perform the division operations.
=−3−32=-3-\frac{3}{2}

STEP 6

To subtract the fractions, we need to have a common denominator. The common denominator of1 and2 is2. So, we convert -3 to -6/2.
=−62−32=-\frac{6}{2}-\frac{3}{2}

STEP 7

Now, subtract the fractions.
=−92=-\frac{9}{2}

STEP 8

This is an improper fraction. Convert it to a mixed number. The mixed number of -/2 is -41/2.
So, the value of the expression when a=−2;b=3;c=−1a=-2 ; b=3 ; c=-1; and d=1d=1 is −412-4 \frac{1}{2}.

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