To solve the division of mixed numbers [tex]\(6 \frac{2}{5}\)[/tex] and [tex]\(3 \frac{2}{10}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(6 \frac{2}{5}\)[/tex]:
- Multiply the whole number part (6) by the denominator (5) and add the numerator (2).
- This gives: [tex]\(6 \cdot 5 + 2 = 30 + 2 = 32\)[/tex].
- Therefore, [tex]\(6 \frac{2}{5}\)[/tex] becomes [tex]\(\frac{32}{5}\)[/tex].
- For [tex]\(3 \frac{2}{10}\)[/tex]:
- Multiply the whole number part (3) by the denominator (10) and add the numerator (2).
- This gives: [tex]\(3 \cdot 10 + 2 = 30 + 2 = 32\)[/tex].
- Therefore, [tex]\(3 \frac{2}{10}\)[/tex] becomes [tex]\(\frac{32}{10}\)[/tex].
2. Divide the fractions:
- Dividing by a fraction [tex]\(\frac{a}{b}\)[/tex] is equivalent to multiplying by its reciprocal [tex]\(\frac{b}{a}\)[/tex].
- So, we need to perform the division: [tex]\(\frac{32}{5} \div \frac{32}{10}\)[/tex].
- This is the same as: [tex]\(\frac{32}{5} \times \frac{10}{32}\)[/tex].
3. Multiply the fractions:
- Multiply the numerators and the denominators:
- Numerator: [tex]\(32 \times 10 = 320\)[/tex].
- Denominator: [tex]\(5 \times 32 = 160\)[/tex].
- So, [tex]\(\frac{32}{5} \times \frac{10}{32} = \frac{320}{160}\)[/tex].
4. Simplify the resulting fraction:
- Find the greatest common divisor (GCD) of 320 and 160 to simplify the fraction.
- The GCD of 320 and 160 is 160.
- Divide both the numerator and the denominator by their GCD:
- Numerator: [tex]\(320 \div 160 = 2\)[/tex].
- Denominator: [tex]\(160 \div 160 = 1\)[/tex].
- So, [tex]\(\frac{320}{160} = \frac{2}{1} = 2\)[/tex].
Thus, the result of [tex]\(6 \frac{2}{5} \div 3 \frac{2}{10} = 2\)[/tex].
