Simplify this Problem 1.5 x 1.5
The correct Answer and Explanation is:
To simplify the problem 1.5 × 1.5, we can multiply the two numbers together:
Step-by-step solution:
- 1.5 × 1.5 can be written as:
[
1.5 \times 1.5 = (15 \div 10) \times (15 \div 10)
] - Multiply the numerators: ( 15 \times 15 = 225 ).
- Multiply the denominators: ( 10 \times 10 = 100 ).
- Now we divide:
[
\frac{225}{100} = 2.25
]
So, the simplified answer is 2.25.
Explanation:
Multiplication of decimal numbers follows the same rules as multiplying whole numbers, but with an additional step to account for the decimal places.
1. Converting to Whole Numbers:
One way to approach multiplying decimal numbers like 1.5 × 1.5 is to convert them into whole numbers first. By recognizing that 1.5 is the same as 15 divided by 10 (or ( \frac{15}{10} )), the multiplication becomes a simple fraction operation. Multiply the numerators (15 × 15 = 225) and the denominators (10 × 10 = 100). This gives ( \frac{225}{100} ), which simplifies to 2.25.
2. Decimal Placement:
Another way to consider this is to multiply the numbers as if there were no decimal points:
1.5 × 1.5 = 15 × 15 = 225.
Then, count the decimal places. Since each number has one decimal place, the result must have two decimal places. Therefore, 225 becomes 2.25.
3. Real-world Application:
This multiplication might be used in practical situations like calculating the area of a square with sides of 1.5 units. The area of the square is the length of one side squared, which would be 2.25 square units.
Thus, 1.5 multiplied by 1.5 equals 2.25, a straightforward application of basic multiplication principles.