4.5 Add and Subtract Fractions with Different Denominators

Before you get started, take this readiness quiz.

Find two fractions equivalent to $\frac{5}{6} .$
If you missed this problem, review the reference.

Simplify: $\frac{1 + 5 \cdot 3}{2^{2} + 4} .$
If you missed this problem, review the reference.

Find the least common denominator for the fractions: $\frac{7}{12}$ and $\frac{11}{15} .$

Find the least common denominator for the fractions: $\frac{13}{15}$ and $\frac{17}{5} .$

Find the least common denominator for the fractions: $\frac{13}{24}$ and $\frac{17}{32} .$

Find the least common denominator for the fractions: $\frac{9}{28}$ and $\frac{21}{32} .$

Change to equivalent fractions with the LCD:

$\frac{3}{4}$ and $\frac{5}{6} ,$ LCD $= 12$

Change to equivalent fractions with the LCD:

$- \frac{7}{12}$ and $\frac{11}{15} ,$ LCD $= 60$

Change to equivalent fractions with the LCD:

$\frac{13}{24}$ and $\frac{17}{32} ,$ LCD $96$

Change to equivalent fractions with the LCD:

$\frac{9}{28}$ and $\frac{27}{32} ,$ LCD $224$

Add: $\frac{1}{4} + \frac{1}{3} .$

Add: $\frac{1}{2} + \frac{1}{5} .$

Simplify: $\frac{1}{2} - \left(- \frac{1}{8}\right) .$

Simplify: $\frac{1}{3} - \left(- \frac{1}{6}\right) .$

Add: $\frac{7}{12} + \frac{11}{15} .$

Add: $\frac{13}{15} + \frac{17}{20} .$

Subtract: $\frac{13}{24} - \frac{17}{32} .$

Subtract: $\frac{21}{32} - \frac{9}{28} .$

Add: $- \frac{13}{42} + \frac{17}{35} .$

Add: $- \frac{19}{24} + \frac{17}{32} .$

Add: $\frac{y}{6} + \frac{7}{9} .$

Add: $\frac{x}{6} + \frac{7}{15} .$

Simplify each expression:

1. ⓐ $- \frac{3}{4} - \frac{1}{6}$
2. ⓑ $- \frac{3}{4} \cdot \frac{1}{6}$

Simplify each expression:

1. ⓐ $\frac{5}{6} \div \left(- \frac{1}{4}\right)$
2. ⓑ $\frac{5}{6} - \left(- \frac{1}{4}\right)$

Simplify:

1. ⓐ $\frac{5 x}{6} - \frac{3}{10}$
2. ⓑ $\frac{5 x}{6} \cdot \frac{3}{10}$

Simplify:

1. ⓐ $\frac{\left(27 a - 32\right)}{36}$
2. ⓑ $\frac{2 a}{3}$

Simplify:

1. ⓐ $\frac{\left(24 k + 25\right)}{30}$
2. ⓑ $\frac{24 k}{5}$

Simplify: $\frac{\left(\frac{1}{2}\right)^{2}}{4 + 3^{2}} .$

Simplify: $\frac{\left(\frac{1}{3}\right)^{2}}{2^{3} + 2}$.

Simplify: $\frac{1 + 4^{2}}{\left(\frac{1}{4}\right)^{2}}$.

Simplify: $\frac{\frac{1}{2} + \frac{2}{3}}{\frac{3}{4} - \frac{1}{6}} .$

Simplify: $\frac{\frac{1}{3} + \frac{1}{2}}{\frac{3}{4} - \frac{1}{3}}$.

Simplify: $\frac{\frac{2}{3} - \frac{1}{2}}{\frac{1}{4} + \frac{1}{3}}$.

Evaluate: $x + \frac{3}{4}$ when

1. ⓐ $x = - \frac{7}{4}$
2. ⓑ $x = - \frac{5}{4}$

Evaluate: $y + \frac{1}{2}$ when

1. ⓐ $y = \frac{2}{3}$
2. ⓑ $y = - \frac{3}{4}$

Evaluate: $y - \frac{1}{2}$ when $y = - \frac{1}{4} .$

Evaluate: $x - \frac{3}{8}$ when $x = - \frac{5}{2} .$

Evaluate. $3 a b^{2}$ when $a = - \frac{2}{3}$ and $b = - \frac{1}{2} .$

Evaluate. $4 c^{3} d$ when $c = - \frac{1}{2}$ and $d = - \frac{4}{3} .$

Evaluate: $\frac{a + b}{c}$ when $a = −8 , b = −7 ,$ and $c = 6 .$

Evaluate: $\frac{x + y}{z}$ when $x = 9 , y = −18 ,$ and $z = −6 .$

Find the least common denominator (LCD) for each set of fractions.

$\frac{3}{4}$ and $\frac{2}{5}$

Find the least common denominator (LCD) for each set of fractions.

$\frac{9}{16}$ and $\frac{7}{12}$

Find the least common denominator (LCD) for each set of fractions.

$\frac{23}{30}$ and $\frac{5}{48}$

Find the least common denominator (LCD) for each set of fractions.

$\frac{18}{35}$ and $\frac{33}{49}$

Find the least common denominator (LCD) for each set of fractions.

$\frac{2}{3} , \frac{1}{4} ,$ and $\frac{3}{5}$

Convert to equivalent fractions using the LCD.

$\frac{1}{4}$ and $\frac{1}{5} ,$ LCD $= 20$

Convert to equivalent fractions using the LCD.

$\frac{7}{12}$ and $\frac{5}{8} ,$ LCD $= 24$

Convert to equivalent fractions using the LCD.

$\frac{11}{16}$ and $- \frac{5}{12} ,$ LCD $= 48$

Convert to equivalent fractions using the LCD.

$\frac{1}{3} , \frac{3}{4} ,$ and $\frac{3}{5} ,$ LCD $= 60$

Add or subtract. Write the result in simplified form.

$\frac{1}{4} + \frac{1}{5}$

Add or subtract. Write the result in simplified form.

$\frac{1}{3} + \frac{1}{8}$

Add or subtract. Write the result in simplified form.

$\frac{1}{4} - \left(- \frac{1}{8}\right)$

Add or subtract. Write the result in simplified form.

$\frac{1}{2} - \left(- \frac{1}{6}\right)$

Add or subtract. Write the result in simplified form.

$\frac{3}{4} + \frac{2}{5}$

Add or subtract. Write the result in simplified form.

$\frac{5}{12} + \frac{3}{8}$

Add or subtract. Write the result in simplified form.

$\frac{7}{16} - \frac{5}{12}$

Add or subtract. Write the result in simplified form.

$\frac{5}{8} - \frac{7}{12}$

Add or subtract. Write the result in simplified form.

$\frac{5}{6} - \frac{3}{4}$

Add or subtract. Write the result in simplified form.

$- \frac{9}{20} + \frac{17}{30}$

Add or subtract. Write the result in simplified form.

$- \frac{23}{30} + \frac{5}{48}$

Add or subtract. Write the result in simplified form.

$- \frac{33}{49} - \frac{18}{35}$

Add or subtract. Write the result in simplified form.

$- \frac{3}{4} - \left(- \frac{4}{5}\right)$

Add or subtract. Write the result in simplified form.

$- \frac{7}{20} - \left(- \frac{5}{8}\right)$

Add or subtract. Write the result in simplified form.

$1 + \frac{5}{6}$

Add or subtract. Write the result in simplified form.

$1 - \frac{3}{10}$

Add or subtract. Write the result in simplified form.

$\frac{y}{2} + \frac{2}{3}$

Add or subtract. Write the result in simplified form.

$\frac{x}{5} - \frac{1}{4}$

Perform the indicated operations. Write your answers in simplified form.

1. ⓐ $\frac{2}{3} + \frac{1}{6}$
2. ⓑ $\frac{2}{3} \div \frac{1}{6}$

Perform the indicated operations. Write your answers in simplified form.

1. ⓐ $- \frac{4}{5} - \frac{1}{8}$
2. ⓑ $- \frac{4}{5} \cdot \frac{1}{8}$

Perform the indicated operations. Write your answers in simplified form.

1. ⓐ $\frac{3 a}{8} \div \frac{7}{12}$
2. ⓑ $\frac{3 a}{8} - \frac{7}{12}$

Perform the indicated operations. Write your answers in simplified form.

1. ⓐ $\frac{4}{15} \cdot \left(- \frac{5 q}{9}\right)$
2. ⓑ $\frac{4}{15} + \left(- \frac{5 q}{9}\right)$

Perform the indicated operations. Write your answers in simplified form.

$- \frac{5}{12} \div \left(- \frac{5}{9}\right)$

Perform the indicated operations. Write your answers in simplified form.

$- \frac{1}{8} + \frac{7}{12}$

Perform the indicated operations. Write your answers in simplified form.

$\frac{5}{9} - \frac{1}{6}$

Perform the indicated operations. Write your answers in simplified form.

$\frac{7}{12} \cdot \left(- \frac{8}{35}\right)$

Perform the indicated operations. Write your answers in simplified form.

$- \frac{3}{8} - \frac{x}{11}$

Perform the indicated operations. Write your answers in simplified form.

$\frac{10 y}{13} \cdot \frac{8}{15 y}$

Simplify.

$\frac{\left(\frac{1}{3}\right)^{2}}{5 + 2^{2}}$

Simplify.

$\frac{3^{3} - 3^{2}}{\left(\frac{3}{4}\right)^{2}}$

Simplify.

$\frac{\left(\frac{3}{4}\right)^{2}}{\left(\frac{5}{8}\right)^{2}}$

Simplify.

$\frac{5}{\frac{1}{4} + \frac{1}{3}}$

Simplify.

$\frac{\frac{3}{4} + \frac{1}{2}}{\frac{5}{6} - \frac{2}{3}}$

Simplify.

$\frac{\frac{3}{4} - \frac{3}{5}}{\frac{1}{4} + \frac{2}{5}}$

Simplify.

$\frac{1}{3} + \frac{2}{5} \cdot \frac{3}{4}$

Simplify.

$1 - \frac{5}{6} \div \frac{1}{12}$

Simplify.

$\frac{2}{3} + \frac{1}{4} + \frac{3}{5}$

Simplify.

$\frac{2}{5} + \frac{5}{8} - \frac{3}{4}$

Simplify.

$8 \left(\frac{15}{16} - \frac{5}{6}\right)$

Simplify.

$\frac{\frac{1}{6} + \frac{3}{10}}{\frac{14}{30}}$

Simplify.

$\left(\frac{3}{4} + \frac{1}{6}\right) \div \left(\frac{5}{8} - \frac{1}{3}\right)$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$x + \frac{2}{3}$ when

1. ⓐ $x = - \frac{1}{6}$
2. ⓑ $x = - \frac{5}{3}$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$x + \left(- \frac{11}{12}\right)$ when

1. ⓐ $x = \frac{11}{12}$
2. ⓑ $x = \frac{3}{4}$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$x - \frac{1}{3}$ when

1. ⓐ $x = \frac{2}{3}$
2. ⓑ $x = - \frac{2}{3}$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$\frac{5}{12} - w$ when

1. ⓐ $w = \frac{1}{4}$
2. ⓑ $w = - \frac{1}{4}$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$5 m^{2} n$ when $m = - \frac{2}{5}$ and $n = \frac{1}{3}$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$8 u^{2} v^{3}$ when $u = - \frac{3}{4}$ and $v = - \frac{1}{2}$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$\frac{m + n}{p}$ when $m = −6 , n = −2 , p = 4$

Evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary.

$\frac{r - s}{r + s}$ when $r = 10 , s = −5$

Baking Vanessa is baking chocolate chip cookies and oatmeal cookies. She needs $1 \frac{1}{4}$ cups of sugar for the chocolate chip cookies, and $1 \frac{1}{8}$ cups for the oatmeal cookies How much sugar does she need altogether?

Explain how to find the LCD of two fractions.