Multiplying Mixed Numbers: A Step-by-Step Guide
Multiplying mixed numbers can seem intimidating, but it's actually quite simple. Let's break down how to multiply 1 1/2 x 3 1/2 and get the answer in its simplest form.
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) / 2 = 3/2
- 3 1/2: Multiply the whole number (3) by the denominator (2) and add the numerator (1). Keep the same denominator. (3 * 2 + 1) / 2 = 7/2
Now our problem looks like this: (3/2) x (7/2)
Step 2: Multiply the Numerators and Denominators
- Multiply the numerators: 3 x 7 = 21
- Multiply the denominators: 2 x 2 = 4
We now have 21/4.
Step 3: Simplify the Fraction
- 21/4 is an improper fraction (the numerator is larger than the denominator). To simplify, we convert it to a mixed number.
- Divide the numerator (21) by the denominator (4): 21 / 4 = 5 with a remainder of 1.
- The quotient (5) becomes the whole number, and the remainder (1) becomes the numerator. The denominator stays the same.
- 21/4 simplifies to 5 1/4
Final Answer:
Therefore, 1 1/2 x 3 1/2 = 5 1/4