ding Mixed Numb nowe Skill : Adding mixed numbers Narm Up d the sum. $$ \frac{9}{12}+6 \frac{1}{4} $$ $$ =\frac{5}{6} $$ the sum. $$ 1 \frac{1}{10}+1 \frac{2}{3}=2 \frac{3}{13} $$ 2) Find the sum. $$ 2 \frac{1}{5}+4 \frac{3}{4}= $$ 4) Find the sum. $$ 3 \frac{1}{2}+\frac{4}{5} $$ sum. $$ 1 \frac{1}{6}+3 \frac{3}{4} $$ 6) Find the sum. $$ 2 \frac{1}{3}+8 \frac{1}{8} $$

Question

UpStudy AI · Accepted Answer

Let's solve each of the mixed number addition problems step by step.

### Problem 1: 
$$
\frac{9}{12} + 6 \frac{1}{4}
$$

1. **Convert the mixed number to an improper fraction**:
   $$
   6 \frac{1}{4} = 6 \times 4 + 1 = 24 + 1 = 25 \quad \text{(improper fraction: } \frac{25}{4}\text{)}
   $$

2. **Find a common denominator**:
   The denominators are 12 and 4. The least common multiple (LCM) of 12 and 4 is 12.

3. **Convert $$\frac{25}{4}$$ to have a denominator of 12**:
   $$
   \frac{25}{4} = \frac{25 \times 3}{4 \times 3} = \frac{75}{12}
   $$

4. **Add the fractions**:
   $$
   \frac{9}{12} + \frac{75}{12} = \frac{9 + 75}{12} = \frac{84}{12} = 7
   $$

### Problem 2:
$$
1 \frac{1}{10} + 1 \frac{2}{3}
$$

1. **Convert to improper fractions**:
   $$
   1 \frac{1}{10} = \frac{1 \times 10 + 1}{10} = \frac{11}{10}
   $$
   $$
   1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}
   $$

2. **Find a common denominator**:
   The LCM of 10 and 3 is 30.

3. **Convert both fractions**:
   $$
   \frac{11}{10} = \frac{11 \times 3}{10 \times 3} = \frac{33}{30}
   $$
   $$
   \frac{5}{3} = \frac{5 \times 10}{3 \times 10} = \frac{50}{30}
   $$

4. **Add the fractions**:
   $$
   \frac{33}{30} + \frac{50}{30} = \frac{33 + 50}{30} = \frac{83}{30} = 2 \frac{23}{30}
   $$

### Problem 3:
$$
2 \frac{1}{5} + 4 \frac{3}{4}
$$

1. **Convert to improper fractions**:
   $$
   2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}
   $$
   $$
   4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}
   $$

2. **Find a common denominator**:
   The LCM of 5 and 4 is 20.

3. **Convert both fractions**:
   $$
   \frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20}
   $$
   $$
   \frac{19}{4} = \frac{19 \times 5}{4 \times 5} = \frac{95}{20}
   $$

4. **Add the fractions**:
   $$
   \frac{44}{20} + \frac{95}{20} = \frac{44 + 95}{20} = \frac{139}{20} = 6 \frac{19}{20}
   $$

### Problem 4:
$$
3 \frac{1}{2} + \frac{4}{5}
$$

1. **Convert to improper fractions**:
   $$
   3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}
   $$

2. **Find a common denominator**:
   The LCM of 2 and 5 is 10.

3. **Convert both fractions**:
   $$
   \frac{7}{2} = \frac{7 \times 5}{2 \times 5} = \frac{35}{10}
   $$
   $$
   \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
   $$

4. **Add the fractions**:
   $$
   \frac{35}{10} + \frac{8}{10} = \frac{35 + 8}{10} = \frac{43}{10} = 4 \frac{3}{10}
   $$

### Problem 5:
$$
1 \frac{1}{6} + 3 \frac{3}{4}
$$

1. **Convert to improper fractions**:
   $$
   1 \frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6}
   $$
   $$
   3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4}
   $$

2. **Find a common denominator**:
   The LCM of 6 and 4 is 12.

3. **Convert both fractions**:
   $$
   \frac{7}{6} = \frac{7 \times 2}{6 \times 2} = \frac{14}{12}
   $$
   $$
   \frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}
   $$

4. **Add the fractions**:
   $$
   \frac{14}{12} + \frac{45}{12} = \frac{14 + 45}{12} = \frac{59}{12} = 4 \frac{11}{12}
   $$

### Problem 6:
$$
2 \frac{1}{3} + 8 \frac{1}{8}
$$

1. **Convert to improper fractions**:
   $$
   2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}
   $$
   $$
   8 \frac{1}{8} = \frac{8 \times 8 + 1}{8} = \frac{65}{8}
   $$

2. **Find a common denominator**:
   The LCM of 3 and 8 is 24.

3. **Convert both fractions**:
   \[
   \frac{7}{3} = \frac{
Here are the sums of the mixed numbers: 1. $$ \frac{9}{12} + 6 \frac{1}{4} = 7 $$ 2. $$ 1 \frac{1}{10} + 1 \frac{2}{3} = 2 \frac{23}{30} $$ 3. $$ 2 \frac{1}{5} + 4 \frac{3}{4} = 6 \frac{19}{20} $$ 4. $$ 3 \frac{1}{2} + \frac{4}{5} = 4 \frac{3}{10} $$ 5. $$ 1 \frac{1}{6} + 3 \frac{3}{4} = 4 \frac{11}{12} $$ 6. $$ 2 \frac{1}{3} + 8 \frac{1}{8} = 10 \frac{11}{24} $$

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions