Questions: Add the rational numbers. Express the sum as a rational number in lowest terms. -3/8 + 1/14 -3/8 + 1/14 = (Type an integer or a simplified fraction.)

$Add the rational numbers. Express the sum as a rational number in lowest terms. -3/8 + 1/14 -3/8 + 1/14 = (Type an integer or a simplified fraction.)$

Transcript text: Add the rational numbers. Express the sum as a rational number in lowest terms. \[ -\frac{3}{8}+\frac{1}{14} \] $-\frac{3}{8}+\frac{1}{14}=$ $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

Step 1: Find the Least Common Denominator (LCD)

The denominators are $8$ and $14$. The least common denominator (LCD) of $8$ and $14$ is $56$.

Step 2: Rewrite Each Fraction with the LCD

Rewrite $-\frac{3}{8}$ and $\frac{1}{14}$ with the denominator $56$: \[ -\frac{3}{8} = -\frac{3 \times 7}{8 \times 7} = -\frac{21}{56} \] \[ \frac{1}{14} = \frac{1 \times 4}{14 \times 4} = \frac{4}{56} \]

Step 3: Add the Fractions

Add the rewritten fractions: \[ -\frac{21}{56} + \frac{4}{56} = \frac{-21 + 4}{56} = \frac{-17}{56} \]

Step 4: Simplify the Fraction

The fraction $\frac{-17}{56}$ is already in its lowest terms since $17$ and $56$ have no common factors other than $1$.