To solve the expression \( 4 \dfrac{2}{3} \div 7 \), let's follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \( 4 \dfrac{2}{3} \) can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator:

\[
4 \dfrac{2}{3} = \dfrac{4 \times 3 + 2}{3} = \dfrac{12 + 2}{3} = \dfrac{14}{3}
\]

### Step 2: Division of fractions.
Dividing by 7 is equivalent to multiplying by the reciprocal of 7 (which is \( \dfrac{1}{7} \)):

\[
\dfrac{14}{3} \div 7 = \dfrac{14}{3} \times \dfrac{1}{7}
\]

### Step 3: Multiply the fractions.
Now, multiply the numerators and denominators:

\[
\dfrac{14 \times 1}{3 \times 7} = \dfrac{14}{21}
\]

### Step 4: Simplify the fraction.
Simplify \( \dfrac{14}{21} \) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 7:

\[
\dfrac{14 \div 7}{21 \div 7} = \dfrac{2}{3}
\]

Thus, the solution is:

\[
4 \dfrac{2}{3} \div 7 = \dfrac{2}{3}
\]

Would you like more details or have any questions? 

Here are 5 related questions to expand your knowledge:
1. How do you multiply two mixed numbers?
2. How do you divide two improper fractions?
3. What are the steps to simplify a complex fraction?
4. How can you convert a decimal to a fraction?
5. What is the reciprocal of a fraction, and how is it used in division?

**Tip:** When dividing by a number, you can always multiply by its reciprocal to simplify the process.

Learn how to divide the mixed number 4 2/3 by 7 using fractions and simplification techniques. This step-by-step guide covers converting mixed numbers to improper fractions, multiplying by the reciprocal, and simplifying. Suitable for Grades 5-7.

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