Adding mixed numbers with unlike denominators(word Problems ... - Free Printable

Let's solve each problem step by step. These are all addition problems involving mixed numbers (whole numbers and fractions). We'll convert the mixed numbers to improper fractions, find a common denominator, add them, and then simplify if needed.

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Problem 5:

Darcie runs $4\frac{1}{2}$ miles in the morning and $3\frac{3}{8}$ miles in the evening. How many miles does Darcie run in all?

#### Step 1: Convert mixed numbers to improper fractions.
- $4\frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}$
- $3\frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}$

#### Step 2: Find a common denominator.
The least common denominator (LCD) of 2 and 8 is 8.

Convert $\frac{9}{2}$ to eighths:
- $\frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8}$

Now add:
- $\frac{36}{8} + \frac{27}{8} = \frac{63}{8}$

#### Step 3: Convert back to a mixed number.
- $\frac{63}{8} = 7\frac{7}{8}$ (since $8 \times 7 = 56$, and $63 - 56 = 7$)

✔ Answer: $7\frac{7}{8}$ miles

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Problem 6:

A frog jumps $2\frac{1}{4}$ feet. Then the frog jumps $2\frac{1}{6}$ feet. What is the total distance the frog jumped?

#### Step 1: Convert to improper fractions.
- $2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}$
- $2\frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6}$

#### Step 2: Find LCD of 4 and 6 → LCD = 12

Convert:
- $\frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12}$
- $\frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12}$

Add:
- $\frac{27}{12} + \frac{26}{12} = \frac{53}{12}$

#### Step 3: Convert to mixed number.
- $\frac{53}{12} = 4\frac{5}{12}$ (since $12 \times 4 = 48$, $53 - 48 = 5$)

✔ Answer: $4\frac{5}{12}$ feet

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Problem 7:

A plant is $6\frac{1}{2}$ inches tall. After one week, it grows $2\frac{2}{5}$ inches. Now how tall is the plant?

#### Step 1: Convert to improper fractions.
- $6\frac{1}{2} = \frac{6 \times 2 + 1}{2} = \frac{13}{2}$
- $2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$

#### Step 2: LCD of 2 and 5 is 10.

Convert:
- $\frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10}$
- $\frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10}$

Add:
- $\frac{65}{10} + \frac{24}{10} = \frac{89}{10}$

#### Step 3: Convert to mixed number.
- $\frac{89}{10} = 8\frac{9}{10}$

✔ Answer: $8\frac{9}{10}$ inches

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Problem 8:

Clara buys two watermelons. One weighs $6\frac{1}{3}$ pounds, the other $5\frac{5}{12}$ pounds. How much do they weigh together?

#### Step 1: Convert to improper fractions.
- $6\frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{19}{3}$
- $5\frac{5}{12} = \frac{5 \times 12 + 5}{12} = \frac{60 + 5}{12} = \frac{65}{12}$

#### Step 2: LCD of 3 and 12 is 12.

Convert:
- $\frac{19}{3} = \frac{19 \times 4}{3 \times 4} = \frac{76}{12}$

Add:
- $\frac{76}{12} + \frac{65}{12} = \frac{141}{12}$

#### Step 3: Simplify and convert to mixed number.
- $\frac{141}{12} = 11\frac{9}{12}$ → simplify $\frac{9}{12} = \frac{3}{4}$

So: $11\frac{3}{4}$ pounds

✔ Answer: $11\frac{3}{4}$ pounds

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✔ Final Answers:

5. $7\frac{7}{8}$ miles
6. $4\frac{5}{12}$ feet
7. $8\frac{9}{10}$ inches
8. $11\frac{3}{4}$ pounds

Let me know if you'd like these shown with diagrams or visual models!