Problem 37 - Algebra 1

Question

Find the opposite of the number. $$-\frac{5}{6}$$

Step-by-Step Solution

Answer

The opposite of \(-\frac{5}{6}\) is \(\frac{5}{6}\).

Step 1: Understanding the Concept of Opposites

The opposite of a number is the same number but with the reverse sign. If given a positive number, its opposite would be negative, and vice versa.

Step 2: Locate the Given Number

Here, the given number is \(-\frac{5}{6}\). It is a negative number.

Step 3: Find the Opposite

Therefore, the opposite of \(-\frac{5}{6}\) would be the same fraction but with a positive sign, that is, \(\frac{5}{6}\).

Key Concepts

Understanding Opposite Numbers

Opposite numbers are numbers that are the same distance from zero on the number line, but on opposite sides. They are also known as additive inverses. This means if you add a number to its opposite, the result is zero. For example:

• The opposite of 2 is -2 because 2 + (-2) = 0.
• The opposite of -6 is 6 because -6 + 6 = 0.

When given a fractional number like \(-\frac{5}{6}\), finding the opposite simply involves changing the sign from negative to positive, resulting in \(\frac{5}{6}\). Understanding this concept helps in simplifying expressions and solving equations involving opposites. It's essential in balancing equations and maintaining equality.

Exploring Rational Numbers

Rational numbers are numbers that can be expressed as a fraction, where the numerator and the denominator are both integers and the denominator is not zero. In mathematical terms, it can be represented as \(\frac{a}{b}\), with \(a\) and \(b\) being integers, and \(b eq 0\). Examples include:

• \(\frac{1}{2}\)
• \(-\frac{5}{6}\)
• 0 (as it can be written as \(\frac{0}{1}\))

A rational number can also be a whole number since whole numbers can be expressed with a denominator of 1. Rational numbers are fundamental in various math applications, enabling clear representation of values and simplifying arithmetic operations.

Understanding Negative Numbers

Negative numbers are values that are less than zero. They are often used to express loss, deficiency, or decrease in mathematics and everyday situations such as temperatures below freezing or bank account withdrawals. Important points to remember:

• Negative numbers are typically represented with a minus sign (e.g., -3, -\(\frac{5}{6}\)).
• On a number line, they are located to the left of zero.
• Adding a negative number is the same as subtracting a positive number.

In math operations, handling negative numbers requires understanding rules like when two negative numbers are multiplied or divided, the result is positive. But when a negative and a positive number are multiplied or divided, the result is negative. Mastery of these rules is crucial for success in solving algebraic expressions and equations.