Math Problem Statement

Evaluate the following if a = -8, b = -3 and c = 2: \[\frac{abc}{c} + 2(ab) - c\]

Solution

To evaluate the expression

abcc+2(ab)c\frac{abc}{c} + 2(ab) - c

given a=8a = -8, b=3b = -3, and c=2c = 2, let's proceed step-by-step.

Step 1: Substitute Values

  1. Calculate abab: ab=(8)×(3)=24ab = (-8) \times (-3) = 24

  2. Calculate abcabc: abc=(8)×(3)×2=48abc = (-8) \times (-3) \times 2 = 48

Step 2: Simplify Each Part of the Expression

  1. abcc\frac{abc}{c}: abcc=482=24\frac{abc}{c} = \frac{48}{2} = 24

  2. 2(ab)2(ab): 2(ab)=2×24=482(ab) = 2 \times 24 = 48

  3. Subtract cc: c=2-c = -2

Step 3: Put It All Together

Now, substitute each part into the original expression: abcc+2(ab)c=24+482=70\frac{abc}{c} + 2(ab) - c = 24 + 48 - 2 = 70

Final Answer:

70\boxed{70}

Would you like further details on any step?


Here are 5 related questions:

  1. How would the answer change if aa, bb, or cc were different values?
  2. Can this expression be simplified before substituting values?
  3. What happens if c=0c = 0? How does that affect the expression?
  4. How do you solve if there are multiple variables with negative values in a similar expression?
  5. Can this method be used for expressions with different powers of variables?

Tip: Always check for possible simplifications in expressions before substituting values.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution

Formulas

Multiplication of constants with variables: ab, abc
Division of expressions: \( \frac{abc}{c} \)
Distributive property: 2(ab)

Theorems

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Suitable Grade Level

Grades 8-10