What is 1 1/2 x 3 1/2 x 2 1/2?
This equation represents the multiplication of three mixed numbers: 1 1/2, 3 1/2, and 2 1/2. Let's break down how to solve this:
Understanding Mixed Numbers
Mixed numbers combine a whole number and a fraction. To multiply mixed numbers, you need to convert them into improper fractions.
Here's how to convert each mixed number:
- 1 1/2: Multiply the whole number (1) by the denominator (2) and add the numerator (1), keeping the same denominator. (1 x 2) + 1 = 3. So, 1 1/2 is equivalent to 3/2.
- 3 1/2: (3 x 2) + 1 = 7. So, 3 1/2 is equivalent to 7/2.
- 2 1/2: (2 x 2) + 1 = 5. So, 2 1/2 is equivalent to 5/2.
Multiplying Improper Fractions
Now we have: 3/2 x 7/2 x 5/2
To multiply fractions, simply multiply the numerators (top numbers) and the denominators (bottom numbers):
- Numerator: 3 x 7 x 5 = 105
- Denominator: 2 x 2 x 2 = 8
This gives us 105/8.
Converting Back to a Mixed Number
To express the answer as a mixed number, divide the numerator (105) by the denominator (8):
- 105 divided by 8 equals 13 with a remainder of 1.
Therefore, 105/8 is equivalent to 13 1/8.
In conclusion, 1 1/2 x 3 1/2 x 2 1/2 = 13 1/8.