Evaluate the following expression involving fractions: -\frac{2}{3} + \frac{1}{4} What is … — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the following expression involving fractions:

-\frac{2}{3} + \frac{1}{4}

What is the value of the expression in simplest form?

The correct value is

-\frac{5}{12}

The correct answer is found by first determining the least common denominator, which is 12. The expression is rewritten as

-\frac{8}{12} + \frac{3}{12}

. By combining the numerators (

-8 + 3

), we get

-5

, resulting in a final simplified fraction of

-\frac{5}{12}

Find the least common denominator (LCD) for the fractions.

The LCD for 3 and 4 is 12.

Fractions must have the same denominator before they can be added or subtracted.

Rewrite both fractions as equivalent fractions with a denominator of 12.

-\frac{2}{3} = -\frac{8}{12}

and

\frac{1}{4} = \frac{3}{12}

Multiply the numerator and denominator of the first fraction by 4, and the second fraction by 3.

Add the numerators while keeping the denominator the same, applying integer sign rules.

\frac{-8 + 3}{12} = -\frac{5}{12}

Adding a positive 3 to a negative 8 results in a negative 5.

Adding fractions with unlike denominators and applying integer sign rules.

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