Adding Fractions with Different Denominators

Show your work for each problem.

1.
What is the LCD (Least Common Denominator) of $\frac{1}{2}$ and $\frac{1}{3}$ ?
1. a)5
2. b)6
3. c)3
4. d)2
Answer: 6
The LCD of 2 and 3 is 6 because 6 is the smallest number that both 2 and 3 divide into evenly (6 ÷ 2 = 3 and 6 ÷ 3 = 2).
2.
What is $\frac{1}{2}$ as an equivalent fraction with denominator 6?
1. a) $\frac{1}{6}$
2. b) $\frac{4}{6}$
3. c) $\frac{2}{6}$
4. d) $\frac{3}{6}$
Answer: $\frac{3}{6}$
$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$ . We multiply both top and bottom by 3 because $2 \times 3 = 6$ .
3.
Calculate: $\frac{1}{2} + \frac{1}{4}$ . Write your answer as a fraction (like 2/5).
Answer: 3/4
$\frac{1}{2} = \frac{2}{4}$ , so $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
4.
What is $\frac{1}{3} + \frac{1}{6}$ in simplest form?
1. a) $\frac{2}{6}$
2. b) $\frac{3}{6}$
3. c) $\frac{2}{9}$
4. d) $\frac{1}{2}$
Answer: $\frac{1}{2}$
$\frac{1}{3} = \frac{2}{6}$ , so $\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$ . $\frac{3}{6}$ has the same value but is not simplified yet.
5.
Which is the first step when adding $\frac{2}{5} + \frac{1}{3}$ ?
1. a)Find a common denominator
2. b)Multiply the fractions
3. c)Simplify both fractions
4. d)Add the numerators
Answer: Find a common denominator
Before adding fractions with unlike denominators, you must find a common denominator so the pieces are the same size.
6.
Add $\frac{1}{2} + \frac{1}{3}$
Answer: 5/6
1. What is the LCD of 2 and 3? 6
2. Convert $\frac{1}{2}$ to sixths: $\frac{1}{2} = \frac{\square}{6}$ . What is the new numerator? 3
3. Convert $\frac{1}{3}$ to sixths: $\frac{1}{3} = \frac{\square}{6}$ . What is the new numerator? 2
4. Add the numerators: $\frac{3}{6} + \frac{2}{6}$ . Enter the final answer. 5/6
7.
Calculate: $\frac{2}{3} + \frac{1}{4}$ . Write your answer as a fraction.
Answer: 11/12
$\frac{2}{3} = \frac{8}{12}$ and $\frac{1}{4} = \frac{3}{12}$ . Sum: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$
8.
What is $\frac{3}{4} + \frac{1}{6}$ ?
1. a) $\frac{11}{12}$
2. b) $\frac{4}{10}$
3. c) $\frac{9}{12}$
4. d) $\frac{5}{6}$
Answer: $\frac{11}{12}$
$\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{6} = \frac{2}{12}$ . Sum: $\frac{9}{12} + \frac{2}{12} = \frac{11}{12}$
9.
Add $\frac{2}{5} + \frac{1}{3}$
Answer: 11/15
1. What is the LCD of 5 and 3? 15
2. Convert $\frac{2}{5}$ to fifteenths: $\frac{2}{5} = \frac{\square}{15}$ . What is the new numerator? 6
3. Convert $\frac{1}{3}$ to fifteenths: $\frac{1}{3} = \frac{\square}{15}$ . What is the new numerator? 5
4. Add the fractions: $\frac{6}{15} + \frac{5}{15}$ 11/15
10.
Calculate: $\frac{3}{8} + \frac{1}{4}$ . Write your answer as a fraction.
Answer: 5/8
$\frac{1}{4} = \frac{2}{8}$ , so $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$
11.
Add $\frac{5}{6} + \frac{1}{4}$ and simplify if needed
Answer: 13/12
1. What is the LCD of 6 and 4? 12
2. Convert $\frac{5}{6}$ to twelfths: $\frac{5}{6} = \frac{\square}{12}$ . What is the new numerator? 10
3. Convert $\frac{1}{4}$ to twelfths: $\frac{1}{4} = \frac{\square}{12}$ . What is the new numerator? 3
4. Add: $\frac{10}{12} + \frac{3}{12}$ 13/12
12.
A recipe calls for $\frac{1}{3}$ cup of oil and $\frac{1}{4}$ cup of vinegar. How much liquid is that in total?
1. a) $\frac{2}{7}$ cup
2. b) $\frac{1}{2}$ cup
3. c) $\frac{7}{12}$ cup
4. d) $\frac{5}{12}$ cup
Answer: $\frac{7}{12}$ cup
$\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$ . Sum: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ cup
13.
Calculate: $\frac{3}{4} + \frac{2}{3}$ . Write as a mixed number (e.g., 2 1/3).
Answer: 1 5/12
$\frac{3}{4} = \frac{9}{12}$ and $\frac{2}{3} = \frac{8}{12}$ . Sum: $\frac{17}{12} = 1\frac{5}{12}$
14.
Add $\frac{5}{8} + \frac{2}{3}$ and write as a mixed number
Answer: 1 7/24
1. What is the LCD of 8 and 3? 24
2. Convert $\frac{5}{8}$ to twenty-fourths: $\frac{5}{8} = \frac{\square}{24}$ . What is the new numerator? 15
3. Convert $\frac{2}{3}$ to twenty-fourths: $\frac{2}{3} = \frac{\square}{24}$ . What is the new numerator? 16
4. Add: $\frac{15}{24} + \frac{16}{24}$ 31/24
5. Convert $\frac{31}{24}$ to a mixed number 1 7/24
15.
Calculate: $\frac{4}{5} + \frac{3}{4}$ . Write as a mixed number.
Answer: 1 11/20
$\frac{4}{5} = \frac{16}{20}$ , $\frac{3}{4} = \frac{15}{20}$ . Sum: $\frac{31}{20} = 1\frac{11}{20}$
16.
Add $\frac{7}{10} + \frac{3}{4}$ and write as a mixed number
Answer: 1 9/20
1. What is the LCD of 10 and 4? 20
2. Convert $\frac{7}{10}$ to twentieths: $\frac{7}{10} = \frac{\square}{20}$ . What is the new numerator? 14
3. Convert $\frac{3}{4}$ to twentieths: $\frac{3}{4} = \frac{\square}{20}$ . What is the new numerator? 15
4. Add: $\frac{14}{20} + \frac{15}{20}$ 29/20
5. Convert to mixed number 1 9/20
17.
You walk $\frac{2}{3}$ km to school and then $\frac{3}{5}$ km to the library. How far did you walk in total?
1. a) $1\frac{4}{15}$ km
2. b) $\frac{17}{15}$ km
3. c) $1\frac{1}{3}$ km
4. d) $\frac{5}{8}$ km
Answer: $1\frac{4}{15}$ km
$\frac{2}{3} = \frac{10}{15}$ , $\frac{3}{5} = \frac{9}{15}$ . Sum: $\frac{19}{15} = 1\frac{4}{15}$ km
18.
Add $\frac{5}{6} + \frac{7}{8}$ and write as a mixed number
Answer: 1 17/24
1. What is the LCD of 6 and 8? 24
2. Convert $\frac{5}{6}$ to twenty-fourths: $\frac{5}{6} = \frac{\square}{24}$ . What is the new numerator? 20
3. Convert $\frac{7}{8}$ to twenty-fourths: $\frac{7}{8} = \frac{\square}{24}$ . What is the new numerator? 21
4. Add: $\frac{20}{24} + \frac{21}{24}$ 41/24
5. Convert to mixed number 1 17/24