Problem 447 Subtract. $$ -\frac{7}{9}-\l... [FREE SOLUTION]

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Chapter 1: Problem 447

Subtract. $$ -\frac{7}{9}-\left(-\frac{5}{9}\right) $$

Short Answer

Expert verified

-\frac{2}{9}

Step by step solution

Identify the Expression

The given expression is \[-\frac{7}{9} - \left(-\frac{5}{9}\right)\].

Simplify the Double Negative

Notice that the expression includes a double negative. Simplify it: \[-\frac{7}{9} + \frac{5}{9}\].

Subtract the Fractions

Since the denominators are the same, subtract the numerators directly: \[-\frac{7}{9} + \frac{5}{9} = \frac{-7 + 5}{9} = \frac{-2}{9}\].

Simplify the Result

The result \[-\frac{2}{9}\] is already in its simplest form.

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Key Concepts

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

Double Negative

A double negative occurs when two negative signs are used together in an expression. In mathematics, two negatives make a positive.
This is based on the rule that multiplying or adding two negative figures flips the sign.

For example:
-(-2) becomes +2.
In the given exercise, we have \[- - \left( \frac{5}{9} \right)\].
This simplifies to \[+ \frac{5}{9}\].
Simply replace the double negative with a positive to move forward with your calculation.

Common Denominators

When subtracting fractions, ensure the fractions have a common denominator.
The denominator is the bottom part of a fraction that shows the total number of equal parts.
Fractions with the same denominator can be subtracted by simply subtracting the numerators.

For example:
\[-\frac{7}{9} + \frac{5}{9}\]
Here, both fractions have a denominator of 9.
This allows us to subtract the numerators directly: \[-7 + 5\].
The result is \[-2\], so the fraction becomes \[-\frac{2}{9}\].

Simplifying Fractions

After performing arithmetic operations on fractions, it's essential to simplify them if possible.
A fraction is simplified when the numerator and denominator have no common factors other than 1.

Steps to simplify a fraction:

Identify the greatest common divisor (GCD) of the numerator and denominator.
Divide both numerator and denominator by this GCD.

In this exercise, \[-\frac{2}{9}\] is already in its simplest form because 2 and 9 share no common factors.
Thus, the fraction remains \[-\frac{2}{9}\].
Remember, simplifying fractions makes them easier to understand and work with.

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91影视

Subtract. $$ -\frac{7}{9}-\left(-\frac{5}{9}\right) $$

Short Answer

Step by step solution

Identify the Expression

Simplify the Double Negative

Subtract the Fractions

Simplify the Result

Key Concepts

Double Negative

Common Denominators

Simplifying Fractions

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