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Chapter 0: Problem 117

Use the order of operations to simplify each expression. $$\frac{2(-2)-4(-3)}{5-8}$$

Short Answer

Expert verified
The simplified expression is \( -\frac{8}{3} \)

Step by step solution

01

Apply BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction)

The first operations in the numerator are multiplication and the operation in the denominator is subtraction. In the numerator we have two multiplications to perform: \( 2(-2) \) and \( -4(-3) \). In the denominator, perform the subtraction operation \( 5-8 \).
02

Simplify the calculations

Performing the multiplication in the numerator gives us \( -4 \) and \( 12 \) correspondingly. Subtracting \( 8 \) from \( 5 \) in the denominator gives us \( -3 \). Our expression is now \( \frac{-4+12}{-3} \)
03

Continue to simplify the numerator

By adding \( -4 \) and \( 12 \) we get \( 8 \). Substitute this back into the expression to get \( \frac{8}{-3} \)
04

Perform the division operation

Finally, divide \( 8 \) by \( -3 \). The result is \( -\frac{8}{3} \), which is the simplified version of the original expression.

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