Dividing Fractions: A Step-by-Step Guide to 1 1/2 ÷ 2/5
Dividing fractions can seem intimidating, but with the right approach, it becomes a breeze! Let's break down how to solve 1 1/2 ÷ 2/5 in a step-by-step manner.
1. Convert Mixed Number to an Improper Fraction
Firstly, let's transform the mixed number 1 1/2 into an improper fraction.
- Multiply the whole number (1) by the denominator of the fraction (2): 1 * 2 = 2
- Add the numerator (1) to the result: 2 + 1 = 3
- Keep the same denominator (2): 3/2
Now our problem becomes 3/2 ÷ 2/5.
2. The "Flip and Multiply" Rule
The key to dividing fractions is to flip the second fraction (the divisor) and multiply. This means we'll change 2/5 to 5/2.
3. Multiplication
We now have: 3/2 × 5/2
To multiply fractions, simply multiply the numerators and the denominators:
- 3 × 5 = 15
- 2 × 2 = 4
This gives us a final answer of 15/4.
4. Simplification (Optional)
The fraction 15/4 can be simplified into a mixed number if desired.
- Divide the numerator (15) by the denominator (4): 15 ÷ 4 = 3 with a remainder of 3
- The quotient (3) becomes the whole number part of the mixed number.
- The remainder (3) becomes the numerator of the fraction.
- Keep the same denominator (4): 3 3/4
Therefore, 1 1/2 ÷ 2/5 equals 15/4 or 3 3/4.