Problem 29 Simplify. $$-\frac{1}{3} \cdot... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 4: Problem 29

Simplify. $$-\frac{1}{3} \cdot\left|-\frac{21}{4} \cdot \frac{8}{7}\right|$$

Short Answer

Expert verified

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Step by step solution

Simplify the Expression Inside the Absolute Value

First simplify $-\frac{21}{4} \cdot \frac{8}{7}$. Multiply the numerators together and the denominators together: $ -\frac{21 \cdot 8}{4 \cdot 7} = -\frac{168}{28} $. Now simplify $ -\frac{168}{28} = -6 $.

Apply the Absolute Value

Next, apply the absolute value to $-6$: \left| -6 \right| = 6 \.

Multiply by -1/3

Finally, multiply the result by $-\frac{1}{3}$: -\frac{1}{3} \cdot 6 = -2 \.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

absolute value

The concept of absolute value is crucial in mathematics, especially when dealing with negative numbers. The absolute value of a number is its distance from zero on the number line, regardless of direction. In other words, it is always a non-negative number. For example, $|-6|$ is equal to 6 because the distance from -6 to 0 is 6 units. Here, in our exercise, we have $|-6|$, which simplifies to 6.

multiplication of fractions

Understanding how to multiply fractions is essential in pre-algebra. When multiplying fractions, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together. Consider the fractions $-\frac{21}{4}$ and $\frac{8}{7}$. Multiply the numerators: $-21 \times 8 = -168$, and then the denominators: $4 \times 7 = 28$, resulting in $-\frac{168}{28}$. Simplify this to $-6$.

simplifying expressions

Simplifying expressions involves reducing them to their most basic form. Start by performing any operations inside grouping symbols, such as parentheses. In our example, $-\frac{21}{4} \cdot \frac{8}{7}$ simplifies within the absolute value brackets first. After simplifying the fraction $-\frac{168}{28} = -6$, you apply the absolute value to get 6. Then multiply by $-\frac{1}{3}$ to get the final answer: -2.

prealgebra

Prealgebra lays the groundwork for understanding algebra. It involves basic arithmetic, working with fractions, and understanding properties of numbers like absolute value. Our exercise requires these basic skills: multiplying fractions, simplifying expressions inside absolute value signs, and applying the order of operations. These concepts ensure a solid foundation for more advanced algebra topics.

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91影视

Simplify. $$-\frac{1}{3} \cdot\left|-\frac{21}{4} \cdot \frac{8}{7}\right|$$

Short Answer

Step by step solution

Simplify the Expression Inside the Absolute Value

Apply the Absolute Value

Multiply by -1/3

Key Concepts

absolute value

multiplication of fractions

simplifying expressions

prealgebra

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