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Add and Subtract Fractions with Common Denominators

Answers

EXAMPLE 4.53

Solution

  \frac{3}{5}+\frac{1}{5}
Add the numerators and place the sum over the common denominator. \frac{3+1}{5}
Simplify. \frac{4}{5}


EXAMPLE 4.54

Solution

  \frac{x}{3}+\frac{2}{3}
Add the numerators and place the sum over the common denominator. \frac{x+2}{3}


Note that we cannot simplify this fraction any more. Since x and 2 are not like terms, we cannot combine them.

 

EXAMPLE 4.55 

Solution

We will begin by rewriting the first fraction with the negative sign in the numerator.

-\frac{a}{b}=\frac{-a}{b}

  -\frac{9}{d}+\frac{3}{d}
Rewrite the first fraction with the negative in the numerator. \frac{-9}{d}+\frac{3}{d}
Add the numerators and place the sum over the common denominator. \frac{-9+3}{d}
Simplify the numerator. \frac{-6}{d}
Rewrite with negative sign in front of the fraction. -\frac{6}{d}

 

EXAMPLE 4.56

Solution

  \frac{2 n}{11}+\frac{5 n}{11}
Add the numerators and place the sum over the common denominator. \frac{2 n+5 n}{11}
Combine like terms. \frac{7 n}{11}

 

EXAMPLE 4.57

Solution

  -\frac{3}{12}+\left(-\frac{5}{12}\right)
Add the numerators and place the sum over the common denominator. \frac{-3+(-5)}{12}
Add. \frac{-8}{12}
Simplify the fraction. -\frac{2}{3}

 

EXAMPLE 4.59

Solution

  \frac{23}{24}-\frac{14}{24}
Subtract the numerators and place the difference over the common denominator. \frac{23-14}{24}
Simplify the numerator. \frac{9}{24}
Simplify the fraction by removing common factors. \frac{3}{8}

 

Example 4.60
Solution

  \frac{y}{6}-\frac{1}{6}
Subtract the numerators and place the difference over the common denominator. \frac{y-1}{6}


The fraction is simplified because we cannot combine the terms in the numerator.

 

Example 4.61

Solution

Remember, the fraction -\frac{10}{x} can be written as \frac{-10}{x}.

  -\frac{10}{x}-\frac{4}{x}
Subtract the numerators. \frac{-10-4}{x}
Simplify. \frac{-14}{x}
Rewrite with the negative sign in front of the fraction. -\frac{14}{x}

 

Example 4.62

Solution

  \frac{3}{8}+\left(-\frac{5}{8}\right)-\frac{1}{8}
Combine the numerators over the common denominator. \frac{3+(-5)-1}{8}
Simplify the numerator, working left to right. \frac{-2-1}{8}
Subtract the terms in the numerator. \frac{-3}{8}
Rewrite with the negative sign in front of the fraction. -\frac{3}{8}