Multiplying Mixed Numbers: 1 3/4 x 2 1/4 x 3/4 as a Fraction
In this article, we will explore how to multiply mixed numbers and simplify the result as a fraction. Specifically, we will multiply 1 3/4, 2 1/4, and 3/4, and express the result as a fraction.
Step 1: Convert Mixed Numbers to Improper Fractions
To multiply mixed numbers, we need to convert them to improper fractions first. Here are the conversions:
- 1 3/4 = (4 + 3) / 4 = 7/4
- 2 1/4 = (8 + 1) / 4 = 9/4
- 3/4 (no conversion needed)
Step 2: Multiply the Fractions
Now, let's multiply the fractions:
(7/4) × (9/4) × (3/4) = ?
To multiply fractions, we multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom), then simplify the result:
(7 × 9 × 3) / (4 × 4 × 4) = 189 / 64
Step 3: Simplify the Result
The result of the multiplication is an improper fraction, 189/64. To simplify it, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 189 and 64 is 1, so the simplified result is:
189/64
Therefore, the result of multiplying 1 3/4, 2 1/4, and 3/4 is 189/64.
