What is 2 divided by 1 1/5 simplified
The correct answer and explanation is:
To solve:
2 ÷ 1 1/5,
first convert the mixed number 1 1/5 to an improper fraction.
Step 1: Convert Mixed Number to Improper Fraction
1 1/5 = (1 × 5 + 1)/5 = 6/5
Step 2: Change the Division to Multiplication
When dividing by a fraction, multiply by the reciprocal (flip the fraction).
So:
2 ÷ 6/5 = 2 × 5/6
Step 3: Multiply the Fractions
Write 2 as a fraction:
2 = 2/1
Now multiply:
(2/1) × (5/6) = (2 × 5) / (1 × 6) = 10/6
Step 4: Simplify the Result
10/6 can be simplified by dividing both the numerator and denominator by 2:
10 ÷ 2 = 5
6 ÷ 2 = 3
So:
10/6 = 5/3
Step 5: Convert to Mixed Number (Optional)
5/3 = 1 2/3
✅ Final Answer: 5/3 or 1 2/3
✏️ Explanation (300 words)
When solving a problem like 2 ÷ 1 1/5, it’s important to remember how to handle mixed numbers and division with fractions. A mixed number like 1 1/5 consists of a whole number (1) and a fraction (1/5). To work with it in a division problem, we must convert it into an improper fraction. This step makes arithmetic easier because it removes the mix of whole and fractional parts.
To convert 1 1/5, multiply the whole number (1) by the denominator (5), which gives 5. Then add the numerator (1), resulting in 6. This makes 1 1/5 equal to 6/5.
Next, divide 2 by this fraction. Division by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 6/5 is 5/6, so we multiply 2 by 5/6 instead of dividing. Before multiplying, we rewrite 2 as a fraction: 2/1. Now we multiply the numerators and denominators:
2 × 5 = 10, and 1 × 6 = 6, giving us 10/6.
We then simplify 10/6. Both 10 and 6 can be divided by 2, so the fraction reduces to 5/3. As an improper fraction, 5/3 means 1 whole and 2/3 left over, or 1 2/3 as a mixed number.
This process shows the importance of understanding fraction operations. Being comfortable with converting between mixed and improper fractions, and knowing how to divide by a fraction, helps avoid common mistakes.