Dividing Fractions: 1 1/4 Divided by 2/3
Dividing fractions can seem tricky, but it's actually a straightforward process. Here's how to solve 1 1/4 divided by 2/3.
Step 1: Convert Mixed Number to a Fraction
First, convert the mixed number 1 1/4 to an improper fraction.
- Multiply the whole number (1) by the denominator (4): 1 * 4 = 4
- Add the numerator (1): 4 + 1 = 5
- Keep the same denominator: 5/4
Now our problem is 5/4 divided by 2/3.
Step 2: Invert the Second Fraction and Multiply
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2.
So, our problem becomes 5/4 multiplied by 3/2.
Step 3: Multiply the Numerators and Denominators
- Numerators: 5 * 3 = 15
- Denominators: 4 * 2 = 8
This gives us 15/8.
Step 4: Simplify the Fraction
15/8 is an improper fraction (the numerator is greater than the denominator). We can convert this to a mixed number:
- Divide the numerator (15) by the denominator (8): 15 ÷ 8 = 1 with a remainder of 7.
- The quotient (1) becomes the whole number.
- The remainder (7) becomes the numerator.
- The denominator stays the same (8).
Therefore, 1 1/4 divided by 2/3 equals 1 7/8.