2.2 Add and Subtract Fractions

Izabela Mazur

CHAPTER 2 Operations with Rational Numbers and Introduction to Real Numbers

2.2 Add and Subtract Fractions

Learning Objectives

By the end of this section, you will be able to:

Add or subtract fractions with a common denominator
Add or subtract fractions with different denominators
Use the order of operations to simplify complex fractions
Evaluate variable expressions with fractions

As we have seen, to add or subtract fractions, their denominators must be the same. The least common denominator (LCD) of two fractions is the smallest number that can be used as a common denominator of the fractions. The LCD of the two fractions is the least common multiple (LCM) of their denominators.

Least Common Denominator

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.

After we find the least common denominator of two fractions, we convert the fractions to equivalent fractions with the LCD. Putting these steps together allows us to add and subtract fractions because their denominators will be the same!

EXAMPLE 5

Add: $\frac{7}{12}+\frac{5}{18}$ .

Solution

$In this figure, we have a table with directions on the left, hints or explanations in the middle, and mathematical statements on the right. On the first line, we have “Step 1. Do they have a common denominator? No – rewrite each fraction with the LCD (least common denominator).” To the right of this, we have the statement “No. Find the LCD 12, 18.” To the right of this, we have 12 equals 2 times 2 times 3 and 18 equals 2 times 3 times 3. The LCD is hence 2 times 2 times 3 times 3, which equals 36. As another hint, we have “Change into equivalent fractions with the LCD,. Do not simplify the equivalent fractions! If you do, you’ll get back to the original fractions and lose the common denominator!” To the right of this, we have 7/12 plus 5/18, which becomes the quantity (7 times 3) over the quantity (12 times 3) plus the quantity (5 times 2) over the quantity (18 times 2), which becomes 21/36 plus 10/36.$ $The next step reads “Step 2. Add or subtract the fractions.” The hint reads “Add.” And we have 31/36.$ The final step reads “Step 3. Simplify, if possible.” The explanation reads “Because 31 is a prime number, it has no factors in common with 36. The answer is simplified.”

TRY IT 5.1

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

Show answer

$\frac{79}{60}$

TRY IT 5.2

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

Show answer

$\frac{103}{60}$

HOW TO: Add or Subtract Fractions

Do they have a common denominator?
- Yes—go to step 2.
- No—rewrite each fraction with the LCD (least common denominator). Find the LCD. Change each fraction into an equivalent fraction with the LCD as its denominator.
Add or subtract the fractions.
Simplify, if possible.

When finding the equivalent fractions needed to create the common denominators, there is a quick way to find the number we need to multiply both the numerator and denominator. This method works if we found the LCD by factoring into primes.

Look at the factors of the LCD and then at each column above those factors. The “missing” factors of each denominator are the numbers we need.

In (Example 5), the LCD, 36, has two factors of 2 and two factors of $3$ .

The numerator 12 has two factors of 2 but only one of 3—so it is “missing” one 3—we multiply the numerator and denominator by 3

The numerator 18 is missing one factor of 2—so we multiply the numerator and denominator by 2

We will apply this method as we subtract the fractions in (Example 6).

EXAMPLE 6

Subtract: $\frac{7}{15}-\phantom{\rule{0.2em}{0ex}}\frac{19}{24}$ .

Solution

Do the fractions have a common denominator? No, so we need to find the LCD.

Find the LCD. $\phantom{\rule{5em}{0ex}}$
Notice, 15 is “missing” three factors of 2 and 24 is “missing” the 5 from the factors of the LCD. So we multiply 8 in the first fraction and 5 in the second fraction to get the LCD.
Rewrite as equivalent fractions with the LCD.
Simplify.
Subtract.	$\phantom{\rule{2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{39}{120}$
Check to see if the answer can be simplified.	$\phantom{\rule{2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{13\cdot 3}{40\cdot 3}$
Both 39 and 120 have a factor of 3.
Simplify.	$\phantom{\rule{2em}{0ex}}-\phantom{\rule{0.2em}{0ex}}\frac{13}{40}$

Do not simplify the equivalent fractions! If you do, you’ll get back to the original fractions and lose the common denominator!

TRY IT 6.1

Subtract: $\frac{13}{24}-\phantom{\rule{0.2em}{0ex}}\frac{17}{32}$ .

Show answer

$\frac{1}{96}$

TRY IT 6.2

Subtract: $\frac{21}{32}-\phantom{\rule{0.2em}{0ex}}\frac{9}{28}$ .

Show answer

$\frac{75}{224}$

In the next example, one of the fractions has a variable in its numerator. Notice that we do the same steps as when both numerators are numbers.

EXAMPLE 7

Add: $\frac{3}{5}+\frac{x}{8}$ .

Solution

The fractions have different denominators.

		$\phantom{\rule{2em}{0ex}}$
Find the LCD. $\phantom{\rule{4em}{0ex}}$
Rewrite as equivalent fractions with the LCD.		$\phantom{\rule{2em}{0ex}}$
Simplify.		$\phantom{\rule{2em}{0ex}}$
Add.		$\phantom{\rule{2em}{0ex}}$

TRY IT 7.1

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

Show answer

$\frac{9y+42}{54}$

TRY IT 7.2

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

Show answer

$\frac{15x+42}{135}$

We now have all four operations for fractions. The table below summarizes fraction operations.

Summary of Fraction Operations
Fraction Operation	Sample Equation	What to Do
Fraction multiplication	$\frac{a}{b} \cdot \frac{c}{d}=\frac{ac}{bd}$	Multiply the numerators and multiply the denominators
Fraction division	$\frac{a}{b} \div \frac{c}{d}=\frac{a}{b}\cdot \frac{d}{c}$	Multiply the first fraction by the reciprocal of the second.
Fraction addition	$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$	Add the numerators and place the sum over the common denominator.
Fraction subtraction	$\frac{a}{c}-\phantom{\rule{0.2em}{0ex}}\frac{b}{c}=\frac{a-b}{c}$	Subtract the numerators and place the difference over the common denominator.

To multiply or divide fractions, an LCD is NOT needed. To add or subtract fractions, an LCD is needed.

EXAMPLE 8

Simplify: a) $\frac{5x}{6}-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}$ b) $\frac{5x}{6}\cdot\frac{3}{10}$ .

Solution

First ask, “What is the operation?” Once we identify the operation that will determine whether we need a common denominator. Remember, we need a common denominator to add or subtract, but not to multiply or divide.

a) What is the operation? The operation is subtraction.
Do the fractions have a common denominator? No.	$\frac{5x}{6}-\frac{3}{10}$
Rewrite each fraction as an equivalent fraction with the LCD.	$\frac{5x\cdot5}{6\cdot5}-\frac{3\cdot3}{10\cdot3}$ $\frac{25x}{30}-\frac{9}{30}$
Subtract the numerators and place the difference over the common denominators.	$\frac{25x-9}{30}$
Simplify, if possible.	There are no common factors. The fraction is simplified.

b) What is the operation? Multiplication.	$\frac{5x}{6}\cdot\frac{3}{10}$
To multiply fractions, multiply the numerators and multiply the denominators.	$\frac{5x\cdot3}{6\cdot10}$
Rewrite, showing common factors. Remove common factors.	$\frac{\overline{)5}x \cdot \overline{)3}}{2\cdot\overline{)3}\cdot2\cdot\overline{)5}}$
Simplify.	$\frac{x}{4}$

Notice we needed an LCD to add $\frac{5x}{6}-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}$ , but not to multiply $\frac{5x}{6}\cdot\frac{3}{10}$ .

TRY IT 8.1

Simplify. a) $\frac{27a-32}{36}$ b) $\frac{2a}{3}$

Show answer

a) $\frac{27a-32}{36}$ b) $\frac{2a}{3}$

TRY IT 8.2

Simplify: a) $\frac{4k}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$ b) $\frac{4k}{5}\cdot \frac{1}{6}$ .

Show answer

a) $\frac{24k-5}{30}$ b) $\frac{2k}{15}$

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	$-\phantom{\rule{0.2em}{0ex}}\frac{23}{24}-\phantom{\rule{0.2em}{0ex}}\frac{13}{24}$
Subtract the numerators and place the difference over the common denominator.	$\frac{-23-13}{24}$
Simplify.	$\frac{-36}{24}$
Simplify. Remember, $-\phantom{\rule{0.2em}{0ex}}\frac{a}{b}=\frac{-a}{b}$ .	$-\phantom{\rule{0.2em}{0ex}}\frac{3}{2}$

	$-\phantom{\rule{0.2em}{0ex}}\frac{10}{x}-\phantom{\rule{0.2em}{0ex}}\frac{4}{x}$
Subtract the numerators and place the difference over the common denominator.	$\frac{-14}{x}$
Rewrite with the sign in front of the fraction.	$-\phantom{\rule{0.2em}{0ex}}\frac{14}{x}$

Add and subtract fractions—do they have a common denominator? Yes.	$\frac{3}{8}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}\right)-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}$
Add and subtract the numerators and place the difference over the common denominator.	$\frac{3+\left(-5\right)-1}{8}$
Simplify left to right.	$\frac{-2-1}{8}$
Simplify.	$-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}$

	$\frac{\left(\frac{1}{2}+\frac{2}{3}\right)}{\left(\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}\right)}$
Simplify the numerator (LCD = 6) and simplify the denominator (LCD = 12).	$\frac{\left(\frac{3}{6}+\frac{4}{6}\right)}{\left(\frac{9}{12}-\phantom{\rule{0.2em}{0ex}}\frac{2}{12}\right)}$
Simplify.	$\frac{\left(\frac{7}{6}\right)}{\left(\frac{7}{12}\right)}$
Divide the numerator by the denominator.	$\frac{7}{6}\div \frac{7}{12}$
Simplify.	$\frac{7}{6}\cdot\frac{12}{7}$
Divide out common factors.	$\frac{7\cdot6\cdot2}{6\cdot7}$
Simplify.	$2$

	$2{x}^{2}y$

Simplify exponents first.	$2\left(\frac{1}{16}\right)\left(-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}\right)$
Multiply. Divide out the common factors. Notice we write 16 as $2\cdot 2\cdot 4$ to make it easy to remove common factors.	$-\phantom{\rule{0.2em}{0ex}}\frac{\overline{)2}\cdot 1\cdot \overline{)2}}{\overline{)2}\cdot \overline{)2}\cdot 4\cdot 3}$
Simplify.	$-\phantom{\rule{0.2em}{0ex}}\frac{1}{12}$

2.2 Add and Subtract Fractions

Add and Subtract Fractions with a Common Denominator

Mixed Practice

Add or Subtract Fractions with Different Denominators

Mixed Practice

Use the Order of Operations to Simplify Complex Fractions

Evaluate Variable Expressions with Fractions

Everyday Math

Writing Exercises

License

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

	$\frac{p+q}{r}$

Add in the numerator first.	$\frac{-6}{8}$
Simplify.	$-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$

1. $\frac{6}{13}+\frac{5}{13}$	2. $\frac{4}{15}+\frac{7}{15}$
3. $\frac{x}{4}+\frac{3}{4}$	4. $\frac{8}{q}+\frac{6}{q}$
5. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{16}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{7}{16}\right)$	6. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{16}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{9}{16}\right)$
7. $-\phantom{\rule{0.2em}{0ex}}\frac{8}{17}+\frac{15}{17}$	8. $-\phantom{\rule{0.2em}{0ex}}\frac{9}{19}+\frac{17}{19}$
9. $\frac{6}{13}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{10}{13}\right)+\left(-\phantom{\rule{0.2em}{0ex}}\frac{12}{13}\right)$	10. $\frac{5}{12}+\left(-\phantom{\rule{0.2em}{0ex}}\frac{7}{12}\right)+\left(-\phantom{\rule{0.2em}{0ex}}\frac{11}{12}\right)$

11. $\frac{11}{15}-\phantom{\rule{0.2em}{0ex}}\frac{7}{15}$	12. $\frac{9}{13}-\phantom{\rule{0.2em}{0ex}}\frac{4}{13}$
13. $\frac{11}{12}-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$	14. $\frac{7}{12}-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$
15. $\frac{19}{21}-\phantom{\rule{0.2em}{0ex}}\frac{4}{21}$	16. $\frac{17}{21}-\phantom{\rule{0.2em}{0ex}}\frac{8}{21}$
17. $\frac{5y}{8}-\phantom{\rule{0.2em}{0ex}}\frac{7}{8}$	18. $\frac{11z}{13}-\phantom{\rule{0.2em}{0ex}}\frac{8}{13}$
19. $-\phantom{\rule{0.2em}{0ex}}\frac{23}{u}-\phantom{\rule{0.2em}{0ex}}\frac{15}{u}$	20. $-\phantom{\rule{0.2em}{0ex}}\frac{29}{v}-\phantom{\rule{0.2em}{0ex}}\frac{26}{v}$
21. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\right)$	22. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{7}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{7}\right)$
23. $-\phantom{\rule{0.2em}{0ex}}\frac{7}{9}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{9}\right)$	24. $-\phantom{\rule{0.2em}{0ex}}\frac{8}{11}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{11}\right)$

25. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{18}\cdot \frac{9}{10}$	26. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{14}\cdot \frac{7}{12}$
27. $\frac{n}{5}-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}$	28. $\frac{6}{11}-\phantom{\rule{0.2em}{0ex}}\frac{s}{11}$
29. $-\phantom{\rule{0.2em}{0ex}}\frac{7}{24}+\frac{2}{24}$	30. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{18}+\frac{1}{18}$
31. $\frac{8}{15}\div \frac{12}{5}$	32. $\frac{7}{12}\div\frac{9}{28}$

33. $\frac{1}{2}+\frac{1}{7}$	34. $\frac{1}{3}+\frac{1}{8}$
35. $\frac{1}{3}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{9}\right)$	36. $\frac{1}{4}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}\right)$
37. $\frac{7}{12}+\frac{5}{8}$	38. $\frac{5}{12}+\frac{3}{8}$
39. $\frac{7}{12}-\phantom{\rule{0.2em}{0ex}}\frac{9}{16}$	40. $\frac{7}{16}-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}$
41. $\frac{2}{3}-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}$	42. $\frac{5}{6}-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$
43. $-\phantom{\rule{0.2em}{0ex}}\frac{11}{30}+\frac{27}{40}$	44. $-\phantom{\rule{0.2em}{0ex}}\frac{9}{20}+\frac{17}{30}$
45. $-\phantom{\rule{0.2em}{0ex}}\frac{13}{30}+\frac{25}{42}$	46. $-\phantom{\rule{0.2em}{0ex}}\frac{23}{30}+\frac{5}{48}$
47. $-\phantom{\rule{0.2em}{0ex}}\frac{39}{56}-\phantom{\rule{0.2em}{0ex}}\frac{22}{35}$	48. $-\phantom{\rule{0.2em}{0ex}}\frac{33}{49}-\phantom{\rule{0.2em}{0ex}}\frac{18}{35}$
49. $-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}\right)$	50. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}-\left(-\phantom{\rule{0.2em}{0ex}}\frac{4}{5}\right)$
51. $1+\frac{7}{8}$	52. $1-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}$
53. $\frac{x}{3}+\frac{1}{4}$	54. $\frac{y}{2}+\frac{2}{3}$
55. $\frac{y}{4}-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}$	56. $\frac{x}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$

57. a) $\frac{2}{3}+\frac{1}{6}$ b) $\frac{2}{3}\div \frac{1}{6}$	58. a) $-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}$ b) $-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}\cdot \frac{1}{8}$
59. a) $\frac{5n}{6}\div \frac{8}{15}$ b) $\frac{5n}{6}-\phantom{\rule{0.2em}{0ex}}\frac{8}{15}$	60. a) $\frac{3a}{8}\div \frac{7}{12}$ b) $\frac{3a}{8}-\phantom{\rule{0.2em}{0ex}}\frac{7}{12}$
61. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}\div \left(-\phantom{\rule{0.2em}{0ex}}\frac{3}{10}\right)$	62. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{12}\div \left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{9}\right)$
63. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}+\frac{5}{12}$	64. $-\phantom{\rule{0.2em}{0ex}}\frac{1}{8}+\frac{7}{12}$
65. $\frac{5}{6}-\phantom{\rule{0.2em}{0ex}}\frac{1}{9}$	66. $\frac{5}{9}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$
67. $-\phantom{\rule{0.2em}{0ex}}\frac{7}{15}-\phantom{\rule{0.2em}{0ex}}\frac{y}{4}$	68. $-\phantom{\rule{0.2em}{0ex}}\frac{3}{8}-\phantom{\rule{0.2em}{0ex}}\frac{x}{11}$
69. $\frac{11}{12a}\cdot \frac{9a}{16}$	70. $\frac{10y}{13}\cdot \frac{8}{15y}$

71. $\frac{{2}^{3}+{4}^{2}}{{\left(\frac{2}{3}\right)}^{2}}$	72. $\frac{{3}^{3}-{3}^{2}}{{\left(\frac{3}{4}\right)}^{2}}$
73. $\frac{{\left(\frac{3}{5}\right)}^{2}}{{\left(\frac{3}{7}\right)}^{2}}$	74. $\frac{{\left(\frac{3}{4}\right)}^{2}}{{\left(\frac{5}{8}\right)}^{2}}$
75. $\frac{2}{\frac{1}{3}+\frac{1}{5}}$	76. $\frac{5}{\frac{1}{4}+\frac{1}{3}}$
77. $\frac{\frac{7}{8}-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}}{\frac{1}{2}+\frac{3}{8}}$	78. $\frac{\frac{3}{4}-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}}{\frac{1}{4}+\frac{2}{5}}$
79. $\frac{1}{2}+\frac{2}{3}\cdot \frac{5}{12}$	80. $\frac{1}{3}+\frac{2}{5}\cdot \frac{3}{4}$
81. $1-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}\div \frac{1}{10}$	82. $1-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\div \frac{1}{12}$
83. $\frac{2}{3}+\frac{1}{6}+\frac{3}{4}$	84. $\frac{2}{3}+\frac{1}{4}+\frac{3}{5}$
85. $\frac{3}{8}-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}+\frac{3}{4}$	86. $\frac{2}{5}+\frac{5}{8}-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$
87. $12\left(\frac{9}{20}-\phantom{\rule{0.2em}{0ex}}\frac{4}{15}\right)$	88. $8\left(\frac{15}{16}-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\right)$
89. $\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}$	90. $\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}$
91. $\left(\frac{5}{9}+\frac{1}{6}\right)\div \left(\frac{2}{3}-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}\right)$	92. $\left(\frac{3}{4}+\frac{1}{6}\right)\div \left(\frac{5}{8}-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}\right)$

93. $x+\left(-\phantom{\rule{0.2em}{0ex}}\frac{5}{6}\right)$ when a) $x=\frac{1}{3}$ b) $x=-\phantom{\rule{0.2em}{0ex}}\frac{1}{6}$	94. $x+\left(-\phantom{\rule{0.2em}{0ex}}\frac{11}{12}\right)$ when a) $x=\frac{11}{12}$ b) $x=\frac{3}{4}$
95. $x-\phantom{\rule{0.2em}{0ex}}\frac{2}{5}$ when a) $x=\frac{3}{5}$ b) $x=-\phantom{\rule{0.2em}{0ex}}\frac{3}{5}$	96. $x-\phantom{\rule{0.2em}{0ex}}\frac{1}{3}$ when a) $x=\frac{2}{3}$ b) $x=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}$
97. $\frac{7}{10}-w$ when a) $w=\frac{1}{2}$ b) $w=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$	98. $\frac{5}{12}-w$ when a) $w=\frac{1}{4}$ b) $w=-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$
99. $2{x}^{2}{y}^{3}$ when $x=-\phantom{\rule{0.2em}{0ex}}\frac{2}{3}$ and $y=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$	100. $8{u}^{2}{v}^{3}$ when $u=-\phantom{\rule{0.2em}{0ex}}\frac{3}{4}$ and $v=-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$
101. $\frac{a+b}{a-b}$ when $a=-3,b=8$	102. $\frac{r-s}{r+s}$ when $r=10,s=-5$

1. $\frac{11}{13}$	3. $\frac{x+3}{4}$	5. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{8}$
7. $\frac{7}{17}$	9. $-\phantom{\rule{0.2em}{0ex}}\frac{16}{13}$	11. $\frac{4}{15}$
13. $\frac{1}{2}$	15. $\frac{5}{7}$	17. $\frac{5y-7}{8}$
19. $-\phantom{\rule{0.2em}{0ex}}\frac{38}{u}$	21. $\frac{1}{5}$	23. $-\phantom{\rule{0.2em}{0ex}}\frac{2}{9}$
25. $-\phantom{\rule{0.2em}{0ex}}\frac{1}{4}$	27. $\frac{n-4}{5}$	29. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{24}$
31. $\frac{2}{9}$	33. $\frac{9}{14}$	35. $\frac{4}{9}$
37. $\frac{29}{24}$	39. $\frac{1}{48}$	41. $\frac{7}{24}$
43. $\frac{37}{120}$	45. $\frac{17}{105}$	47. $-\phantom{\rule{0.2em}{0ex}}\frac{53}{40}$
49. $\frac{1}{12}$	51. $\frac{15}{8}$	53. $\frac{4x+3}{12}$
55. $\frac{4y-12}{20}$	57. a) $\frac{5}{6}$ b) 4	59. a) $\frac{25n}{16}$ b) $\frac{25n-16}{30}$
61. $\frac{5}{4}$	63. $\frac{1}{24}$	65. $\frac{13}{18}$
67. $\frac{-28-15y}{60}$	69. $\frac{33}{64}$	71. 54
73. $\frac{49}{25}$	75. $\frac{15}{4}$	77. $\frac{5}{21}$
79. $\frac{7}{9}$	81. $-5$	83. $\frac{19}{12}$
85. $\frac{23}{24}$	87. $\frac{11}{5}$	89. 1
91. $\frac{13}{3}$	93. a) $-\phantom{\rule{0.2em}{0ex}}\frac{1}{2}$ b) $-1$	95. a) $\frac{1}{5}$ b) $-1$
97. a) $\frac{1}{5}$ b) $\frac{6}{5}$	99. $-\phantom{\rule{0.2em}{0ex}}\frac{1}{9}$	101. $-\phantom{\rule{0.2em}{0ex}}\frac{5}{11}$
103. $\frac{7}{8}$ yard	105. Answers may vary



Simplify. $\phantom{\rule{18em}{0ex}}$	0

Add or Subtract Fractions with a Common Denominator

Add or Subtract Fractions with Different Denominators

Use the Order of Operations to Simplify Complex Fractions

Evaluate Variable Expressions with Fractions

Key Concepts

Glossary

Practice Makes Perfect

Add and Subtract Fractions with a Common Denominator

Mixed Practice

Add or Subtract Fractions with Different Denominators

Mixed Practice

Use the Order of Operations to Simplify Complex Fractions

Evaluate Variable Expressions with Fractions

Everyday Math

Writing Exercises

Answers:

Attributions

License

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