Dividing Mixed Numbers: 1 1/2 Divided by 2 1/4
Dividing mixed numbers can seem daunting, but it's actually quite simple once you understand the process. Let's break down how to solve 1 1/2 divided by 2 1/4 as a fraction.
Step 1: Convert Mixed Numbers to Improper Fractions
- 1 1/2: Multiply the whole number (1) by the denominator (2) and add the numerator (1). Keep the same denominator: (1 * 2) + 1 = 3/2
- 2 1/4: Multiply the whole number (2) by the denominator (4) and add the numerator (1). Keep the same denominator: (2 * 4) + 1 = 9/4
Step 2: Flip the Second Fraction (Reciprocal)
The reciprocal of 9/4 is 4/9.
Step 3: Multiply the First Fraction by the Reciprocal
Now we have: (3/2) * (4/9)
Step 4: Simplify the Multiplication
- Multiply the numerators: 3 * 4 = 12
- Multiply the denominators: 2 * 9 = 18
- This gives us 12/18
Step 5: Simplify to Lowest Terms
Both 12 and 18 are divisible by 6: 12/6 = 2 and 18/6 = 3
Therefore, 1 1/2 divided by 2 1/4 equals 2/3.