Question

Simplify the expression. $$-7 \cdot\left(-\frac{2 w}{-7}\right)$$

   Simplify the expression.
$$-7 \cdot\left(-\frac{2 w}{-7}\right)$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 2, Problem 47

Instant Answer

Solved by Expert Amy Jiang

08/30/2020

Step 1

The negative signs in the numerator and denominator of the fraction will cancel each other out, leaving us with $\frac{2w}{7}$. So, the expression becomes: $$-7 \cdot \frac{2w}{7}$$ Show more…

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Simplify the expression. $$-7 \cdot\left(-\frac{2 w}{-7}\right)$$

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Key Concepts

Operations with Negative Numbers

Working with negative numbers requires careful attention to the rules of multiplication and division. Specifically, the product or quotient of two negative numbers is positive, while the product or quotient of a negative number and a positive number is negative. Mastery of these rules is essential for correctly simplifying expressions that involve multiple negative signs.

Cancellation in Fractions

Cancellation in fractions involves simplifying expressions by reducing common factors in the numerator and denominator. This property allows one to simplify complex expressions by eliminating factors, provided that the cancelled term is not zero. Recognizing opportunities for cancellation helps simplify and evaluate expressions more efficiently.

Order of Operations

Understanding the correct sequence in which arithmetic operations should be performed is crucial. This involves recognizing that operations inside parentheses are addressed first, followed by multiplication and division from left to right, and finally addition and subtraction. This ensures that expressions are simplified accurately.

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