1. Find each sum or difference. a. $$ 381 \frac{1}{10}-214 \frac{43}{100} $$ b. $$ 32 \frac{3}{4}-12 \frac{1}{2} $$ c. $$ 517 \frac{37}{50}+312 \frac{3}{100} $$ d. $$ 632 \frac{16}{25}+32 \frac{3}{10} $$ e. $$ 421 \frac{3}{50}-212 \frac{9}{10} $$

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Let's solve each of the given problems step by step.

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### **Problem 1a**
$$ 381 \frac{1}{10} - 214 \frac{43}{100} $$

**Step 1:** Convert the mixed numbers to improper fractions with a common denominator.

- $$ 381 \frac{1}{10} = \frac{381 \times 10 + 1}{10} = \frac{3811}{10} $$
- $$ 214 \frac{43}{100} = \frac{214 \times 100 + 43}{100} = \frac{21443}{100} $$

**Step 2:** Convert both fractions to have the same denominator (100).

- $$ \frac{3811}{10} = \frac{3811 \times 10}{10 \times 10} = \frac{38110}{100} $$

**Step 3:** Subtract the fractions.

$$ \frac{38110}{100} - \frac{21443}{100} = \frac{38110 - 21443}{100} = \frac{16667}{100} $$

**Step 4:** Convert the improper fraction back to a mixed number.

$$ \frac{16667}{100} = 166 \frac{67}{100} $$

**Answer:**  
$$ 381 \frac{1}{10} - 214 \frac{43}{100} = 166 \frac{67}{100} $$

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### **Problem 1b**
$$ 32 \frac{3}{4} - 12 \frac{1}{2} $$

**Step 1:** Find a common denominator for the fractions. The least common denominator (LCD) of 4 and 2 is 4.

- $$ \frac{1}{2} = \frac{2}{4} $$

**Step 2:** Subtract the fractions.

$$ \frac{3}{4} - \frac{2}{4} = \frac{1}{4} $$

**Step 3:** Subtract the whole numbers.

$$ 32 - 12 = 20 $$

**Step 4:** Combine the results.

$$ 20 + \frac{1}{4} = 20 \frac{1}{4} $$

**Answer:**  
$$ 32 \frac{3}{4} - 12 \frac{1}{2} = 20 \frac{1}{4} $$

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### **Problem 1c**
$$ 517 \frac{37}{50} + 312 \frac{3}{100} $$

**Step 1:** Convert the fractions to have the same denominator (100).

- $$ \frac{37}{50} = \frac{74}{100} $$

**Step 2:** Add the fractions.

$$ \frac{74}{100} + \frac{3}{100} = \frac{77}{100} $$

**Step 3:** Add the whole numbers.

$$ 517 + 312 = 829 $$

**Step 4:** Combine the results.

$$ 829 + \frac{77}{100} = 829 \frac{77}{100} $$

**Answer:**  
$$ 517 \frac{37}{50} + 312 \frac{3}{100} = 829 \frac{77}{100} $$

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### **Problem 1d**
$$ 632 \frac{16}{25} + 32 \frac{3}{10} $$

**Step 1:** Convert the fractions to have the same denominator (50).

- $$ \frac{16}{25} = \frac{32}{50} $$
- $$ \frac{3}{10} = \frac{15}{50} $$

**Step 2:** Add the fractions.

$$ \frac{32}{50} + \frac{15}{50} = \frac{47}{50} $$

**Step 3:** Add the whole numbers.

$$ 632 + 32 = 664 $$

**Step 4:** Combine the results.

$$ 664 + \frac{47}{50} = 664 \frac{47}{50} $$

**Answer:**  
$$ 632 \frac{16}{25} + 32 \frac{3}{10} = 664 \frac{47}{50} $$

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### **Problem 1e**
$$ 421 \frac{3}{50} - 212 \frac{9}{10} $$

**Step 1:** Convert the fractions to have the same denominator (50).

- $$ \frac{9}{10} = \frac{45}{50} $$

**Step 2:** Subtract the fractions.

$$ \frac{3}{50} - \frac{45}{50} = \frac{-42}{50} = -\frac{21}{25} $$

**Step 3:** Subtract the whole numbers.

$$ 421 - 212 = 209 $$

**Step 4:** Combine the results.

$$ 209 - \frac{21}{25} = 208 \frac{4}{25} $$

**Answer:**  
$$ 421 \frac{3}{50} - 212 \frac{9}{10} = 208 \frac{4}{25} $$

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### **Summary of Answers:**
a. $$ 166 \frac{67}{100} $$  
b. $$ 20 \frac{1}{4} $$  
c. $$ 829 \frac{77}{100} $$  
d. $$ 664 \frac{47}{50} $$  
e. $$ 208 \frac{4}{25} $$
a. $$ 166 \frac{67}{100} $$ b. $$ 20 \frac{1}{4} $$ c. $$ 829 \frac{77}{100} $$ d. $$ 664 \frac{47}{50} $$ e. $$ 208 \frac{4}{25} $$

1. Find each sum or difference. a. \( 381 \frac{1}{10}-214 \frac{43}{100} \) b. \( 32 \frac{3}{4}-12 \frac{1}{2} \) c. \( 517 \frac{37}{50}+312 \frac{3}{100} \) d. \( 632 \frac{16}{25}+32 \frac{3}{10} \) e. \( 421 \frac{3}{50}-212 \frac{9}{10} \)

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