Dividing Fractions: 1 1/4 ÷ 1/4
Dividing fractions can seem tricky, but it's actually quite straightforward. Let's break down how to solve 1 1/4 ÷ 1/4.
Step 1: Convert the Mixed Number to a Fraction
First, we need to convert the mixed number 1 1/4 into an improper fraction.
- Multiply the whole number (1) by the denominator of the fraction (4): 1 x 4 = 4
- Add the numerator of the fraction (1): 4 + 1 = 5
- Keep the same denominator (4): 5/4
Now our problem is 5/4 ÷ 1/4.
Step 2: Invert the Divisor and Multiply
The key to dividing fractions is to invert the second fraction (the divisor) and multiply.
- The divisor is 1/4, so its inverse is 4/1.
- Now our problem becomes 5/4 x 4/1.
Step 3: Multiply the Numerators and Denominators
- Multiply the numerators: 5 x 4 = 20
- Multiply the denominators: 4 x 1 = 4
- This gives us 20/4.
Step 4: Simplify the Result
- The fraction 20/4 can be simplified by dividing both numerator and denominator by their greatest common factor (4).
- 20/4 = 5/1
Solution: 1 1/4 ÷ 1/4 = 5/1 or 5
Therefore, 1 1/4 divided by 1/4 is equal to 5.