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Let's go through the problems you provided. Here's the breakdown and solution for each one:

### 1. \( 15 \dfrac{2}{3} - 6 \dfrac{3}{4} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 15 \dfrac{2}{3} = \dfrac{47}{3} \) (since \( 15 \times 3 + 2 = 47 \))
- \( 6 \dfrac{3}{4} = \dfrac{27}{4} \) (since \( 6 \times 4 + 3 = 27 \))

Step 2: Find a common denominator (LCM of 3 and 4 is 12).
- \( \dfrac{47}{3} = \dfrac{188}{12} \)
- \( \dfrac{27}{4} = \dfrac{81}{12} \)

Step 3: Subtract the fractions.
- \( \dfrac{188}{12} - \dfrac{81}{12} = \dfrac{107}{12} \)

Step 4: Convert back to a mixed number.
- \( \dfrac{107}{12} = 8 \dfrac{11}{12} \)

So, the result is \( 8 \dfrac{11}{12} \).

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### 2. \( 18 \dfrac{1}{2} - 4 \dfrac{3}{5} \)

Step 1: Convert to improper fractions.
- \( 18 \dfrac{1}{2} = \dfrac{37}{2} \)
- \( 4 \dfrac{3}{5} = \dfrac{23}{5} \)

Step 2: Find a common denominator (LCM of 2 and 5 is 10).
- \( \dfrac{37}{2} = \dfrac{185}{10} \)
- \( \dfrac{23}{5} = \dfrac{46}{10} \)

Step 3: Subtract the fractions.
- \( \dfrac{185}{10} - \dfrac{46}{10} = \dfrac{139}{10} \)

Step 4: Convert to a mixed number.
- \( \dfrac{139}{10} = 13 \dfrac{9}{10} \)

So, the result is \( 13 \dfrac{9}{10} \).

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### 3. \( 9 \dfrac{3}{7} - 5 \dfrac{2}{3} \)

Step 1: Convert to improper fractions.
- \( 9 \dfrac{3}{7} = \dfrac{66}{7} \)
- \( 5 \dfrac{2}{3} = \dfrac{17}{3} \)

Step 2: Find a common denominator (LCM of 7 and 3 is 21).
- \( \dfrac{66}{7} = \dfrac{198}{21} \)
- \( \dfrac{17}{3} = \dfrac{119}{21} \)

Step 3: Subtract the fractions.
- \( \dfrac{198}{21} - \dfrac{119}{21} = \dfrac{79}{21} \)

Step 4: Convert to a mixed number.
- \( \dfrac{79}{21} = 3 \dfrac{16}{21} \)

So, the result is \( 3 \dfrac{16}{21} \).

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Would you like further explanations on any steps?

### Here are 5 related questions for practice:
1. \( 12 \dfrac{5}{6} - 7 \dfrac{1}{2} \)
2. \( 14 \dfrac{3}{5} - 9 \dfrac{4}{7} \)
3. \( 6 \dfrac{2}{9} - 3 \dfrac{5}{8} \)
4. \( 11 \dfrac{7}{10} - 5 \dfrac{9}{12} \)
5. \( 8 \dfrac{4}{11} - 2 \dfrac{1}{3} \)

### Tip:
When dealing with mixed fractions, always convert them to improper fractions first, which makes calculations like addition and subtraction easier!

Subtract the following mixed fractions: 1. 15 2/3 - 6 3/4, 2. 18 1/2 - 4 3/5, 3. 9 3/7 - 5 2/3

Learn how to subtract mixed fractions with examples like 15 2/3 - 6 3/4, 18 1/2 - 4 3/5, and 9 3/7 - 5 2/3. Follow step-by-step solutions involving improper fractions and common denominators. Ideal for students in Grades 5-6.

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