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

Of course! Let's solve each problem step by step, showing all the work.

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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?

We need to add:
$4 \frac{1}{2} + 3 \frac{3}{8}$

Step 1: Convert mixed numbers to improper fractions (optional, but helpful for adding).

- $4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}$
- $3 \frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{27}{8}$

Step 2: Find a common denominator.

The denominators are 2 and 8. The least common denominator 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.

$\frac{63}{8} = 7 \frac{7}{8}$ (because 8 × 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?

Add:
$2 \frac{1}{4} + 2 \frac{1}{6}$

Step 1: Add the whole numbers first.

$2 + 2 = 4$

Step 2: Add the fractions: $\frac{1}{4} + \frac{1}{6}$

Find the least common denominator of 4 and 6 → 12.

Convert:
- $\frac{1}{4} = \frac{3}{12}$
- $\frac{1}{6} = \frac{2}{12}$

Add: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

Step 3: Combine whole number and fraction.

$4 + \frac{5}{12} = 4 \frac{5}{12}$

✔ Answer: $4 \frac{5}{12}$ feet

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Problem 7:
A plant is $6 \frac{1}{2}$ inches tall. After one week, the plant grows $2 \frac{2}{5}$ inches. Now how tall is the plant?

Add:
$6 \frac{1}{2} + 2 \frac{2}{5}$

Step 1: Add whole numbers.

$6 + 2 = 8$

Step 2: Add fractions: $\frac{1}{2} + \frac{2}{5}$

Common denominator of 2 and 5 is 10.

Convert:
- $\frac{1}{2} = \frac{5}{10}$
- $\frac{2}{5} = \frac{4}{10}$

Add: $\frac{5}{10} + \frac{4}{10} = \frac{9}{10}$

Step 3: Combine.

$8 + \frac{9}{10} = 8 \frac{9}{10}$

✔ Answer: $8 \frac{9}{10}$ inches

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Problem 8:
Clara buys two watermelons. One weighs $6 \frac{1}{3}$ pounds. The second weighs $5 \frac{5}{12}$ pounds. How much do they weigh together?

Add:
$6 \frac{1}{3} + 5 \frac{5}{12}$

Step 1: Add whole numbers.

$6 + 5 = 11$

Step 2: Add fractions: $\frac{1}{3} + \frac{5}{12}$

Common denominator of 3 and 12 is 12.

Convert:
- $\frac{1}{3} = \frac{4}{12}$
- $\frac{5}{12}$ stays the same.

Add: $\frac{4}{12} + \frac{5}{12} = \frac{9}{12}$

Simplify $\frac{9}{12}$ → divide numerator and denominator by 3 → $\frac{3}{4}$

Step 3: Combine.

$11 + \frac{3}{4} = 11 \frac{3}{4}$

✔ 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