Adding Fractions with the Same Denominator

Show your work for each problem.

1.
What is $\frac{1}{5} + \frac{2}{5}$ ?
1. a) $\frac{3}{5}$
2. b) $\frac{1}{5}$
3. c) $\frac{3}{10}$
4. d) $\frac{2}{5}$
Answer: $\frac{3}{5}$
Add the numerators: $1 + 2 = 3$ . Keep the denominator 5. Answer: $\frac{3}{5}$
2.
What is $\frac{2}{8} + \frac{4}{8}$ ?
1. a) $\frac{8}{8}$
2. b) $\frac{5}{8}$
3. c) $\frac{3}{4}$
4. d) $\frac{6}{16}$
Answer: $\frac{3}{4}$
$2 + 4 = 6$ , so $\frac{6}{8}$ . Simplified: $\frac{6}{8} = \frac{3}{4}$
3.
Calculate $\frac{3}{7} + \frac{2}{7}$ . Write your answer as a fraction (like 2/9).
Answer: 5/7
$3 + 2 = 5$ . The denominator stays 7. Answer: $\frac{5}{7}$
4.
In simplest form, $\frac{1}{4} + \frac{1}{4} = \frac{1}{\square}$ . What number goes in the box?
Answer: 2
$1 + 1 = 2$ , giving $\frac{2}{4}$ . Simplified: $\frac{2}{4} = \frac{1}{2}$ , so the box holds 2.
5.
Solve $\frac{2}{6} + \frac{3}{6}$ step by step.
Answer: 5/6
1. What is the denominator of both fractions? 6
2. Add the numerators: 2 + 3 = ? 5
3. Write the sum as a fraction over 6. 5/6
6.
A recipe needs $\frac{3}{8}$ cup of flour and $\frac{2}{8}$ cup of sugar. How much total?
1. a) $\frac{6}{8}$ cup
2. b) $\frac{5}{8}$ cup
3. c) $\frac{1}{8}$ cup
4. d) $\frac{5}{16}$ cup
Answer: $\frac{5}{8}$ cup
$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$ cup total
7.
What is $\frac{5}{6} + \frac{4}{6}$ ?
1. a) $1\frac{1}{3}$
2. b) $1\frac{1}{2}$
3. c) $\frac{9}{12}$
4. d) $\frac{2}{3}$
Answer: $1\frac{1}{2}$
$\frac{9}{6} = 1\frac{3}{6} = 1\frac{1}{2}$ (simplified)
8.
Calculate $\frac{4}{10} + \frac{5}{10}$ . Write your answer as a fraction (like 2/3).
Answer: 9/10
$4 + 5 = 9$ . Answer: $\frac{9}{10}$ (already in simplest form)
9.
What is $\frac{5}{9} + \frac{7}{9}$ ? Write it as a mixed number in simplest form, like 2 1/4.
Answer: 1 1/3
$\frac{12}{9} = 1\frac{3}{9} = 1\frac{1}{3}$ (simplified)
10.
Solve $\frac{3}{8} + \frac{5}{8}$ step by step. Give the simplified answer.
Answer: 1
1. Add the numerators: 3 + 5 = ? 8
2. Write the fraction: 8 over 8 = ? 8/8
3. What does 8/8 equal? 1
11.
Emma ate $\frac{2}{8}$ of a cake. Her brother ate $\frac{3}{8}$ . How much did they eat together?
Answer: 5/8
1. What fraction did Emma eat? 2/8
2. What fraction did her brother eat? 3/8
3. Add: 2/8 + 3/8 = ? 5/8
12.
Calculate $\frac{7}{12} + \frac{8}{12}$ . Write your answer as a mixed number in simplest form, like 2 1/3.
Answer: 1 1/4
$\frac{15}{12} = 1\frac{3}{12} = 1\frac{1}{4}$
13.
The sum $\frac{5}{16} + \frac{7}{16} + \frac{4}{16}$ is a whole number. Which whole number?
Answer: 1
$5 + 7 + 4 = 16$ , so $\frac{16}{16} = 1$
14.
Leo walked $\frac{7}{10}$ km in the morning and $\frac{6}{10}$ km in the afternoon. How far did he walk?
1. a) $1\frac{1}{5}$ km
2. b) $\frac{1}{10}$ km
3. c) $\frac{13}{20}$ km
4. d) $1\frac{3}{10}$ km
Answer: $1\frac{3}{10}$ km
$\frac{7}{10} + \frac{6}{10} = \frac{13}{10} = 1\frac{3}{10}$ km
15.
Add $\frac{11}{15} + \frac{9}{15}$ and write the result as a mixed number in simplest form.
Answer: 1 1/3
1. Add the numerators: 11 + 9 = ? 20
2. Write the sum 20/15 as a mixed number (do not simplify yet). 1 5/15
3. Divide the numerator and the denominator of 5/15 by 5. What is the new denominator? 3
4. Final answer as a mixed number in simplest form? 1 1/3
16.
A water tank is $\frac{3}{20}$ full. Then another $\frac{9}{20}$ of the tank is filled with water. What fraction of the tank is full now, in simplest form?
Answer: 3/5
1. How full was the tank at the start? 3/20
2. What fraction of the tank was added? 9/20
3. Add: 3/20 + 9/20 = ? 12/20
4. Divide the numerator and the denominator of 12/20 by 4. What is the new denominator? 5
17.
Add $\frac{2}{9} + \frac{5}{9} + \frac{4}{9}$ . What is the answer as a mixed number (like 2 1/3)?
Answer: 1 2/9
1. Add all numerators: 2 + 5 + 4 = ? 11
2. Write the fraction over 9. 11/9
3. Convert 11/9 to a mixed number. 1 2/9
18.
Maria read $\frac{5}{12}$ of a book on Monday and $\frac{4}{12}$ on Tuesday. What fraction of the book has she read, in simplest form?
1. a) $\frac{2}{3}$
2. b) $\frac{9}{24}$
3. c) $\frac{9}{12}$
4. d) $\frac{3}{4}$
Answer: $\frac{3}{4}$
$\frac{5}{12} + \frac{4}{12} = \frac{9}{12}$ . Dividing both by 3 gives $\frac{3}{4}$ . $\frac{9}{12}$ is the same amount but not in simplest form, and $\frac{9}{24}$ comes from wrongly adding the denominators.