Subtracting With Fractions, Whole Numbers, & Mixed Numbers | Math ... - Free Printable

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

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Problem 1:

$$
4\frac{5}{8} - 3\frac{1}{4}
$$

#### Step 1: Convert mixed numbers to improper fractions.
- $4\frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{32 + 5}{8} = \frac{37}{8}$
- $3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$

#### Step 2: Find a common denominator.
The denominators are 8 and 4. The least common denominator (LCD) is 8.

Convert $\frac{13}{4}$ to eighths:
$$
\frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8}
$$

#### Step 3: Subtract the fractions.
$$
\frac{37}{8} - \frac{26}{8} = \frac{11}{8}
$$

#### Step 4: Convert back to a mixed number.
$$
\frac{11}{8} = 1\frac{3}{8}
$$

✔ Answer for Problem 1:
$$
\boxed{1\frac{3}{8}}
$$

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Problem 2:

$$
9\frac{1}{2} - 8\frac{3}{5}
$$

#### Step 1: Convert mixed numbers to improper fractions.
- $9\frac{1}{2} = \frac{9 \times 2 + 1}{2} = \frac{18 + 1}{2} = \frac{19}{2}$
- $8\frac{3}{5} = \frac{8 \times 5 + 3}{5} = \frac{40 + 3}{5} = \frac{43}{5}$

#### Step 2: Find a common denominator.
Denominators: 2 and 5 → LCD is 10

Convert both fractions:
- $\frac{19}{2} = \frac{19 \times 5}{2 \times 5} = \frac{95}{10}$
- $\frac{43}{5} = \frac{43 \times 2}{5 \times 2} = \frac{86}{10}$

#### Step 3: Subtract the fractions.
$$
\frac{95}{10} - \frac{86}{10} = \frac{9}{10}
$$

✔ Answer for Problem 2:
$$
\boxed{\frac{9}{10}}
$$

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✔ Final Answers:

1) $ \boxed{1\frac{3}{8}} $
2) $ \boxed{\frac{9}{10}} $

Let me know if you'd like a visual explanation or extra practice!