x(-2)x-9.jpeg "(-3 5)x(-2)x 9")
Multiplying Integers: A Step-by-Step Guide
This article will guide you through the process of multiplying the integers (-3 5) x (-2) x 9.
Understanding the Problem
We have three integers to multiply:
- (-3 5): This is a mixed number, representing -3 and 5/1.
- (-2): A negative integer.
- 9: A positive integer.
Step 1: Convert the mixed number to an improper fraction
To simplify the multiplication, we first need to convert the mixed number (-3 5) into an improper fraction.
- Multiply the whole number (-3) by the denominator (1): -3 x 1 = -3
- Add the numerator (5) to the result: -3 + 5 = 2
- Keep the same denominator (1): The improper fraction is 2/1.
Step 2: Multiply the fractions
Now we have: (2/1) x (-2) x 9.
- Multiply the numerators: 2 x (-2) x 9 = -36
- Multiply the denominators: 1 x 1 x 1 = 1
Step 3: Simplify the result
The product of the three integers is -36/1, which simplifies to -36.
Key takeaways
- Sign rules: When multiplying integers, the product is positive if both numbers have the same sign (both positive or both negative). The product is negative if the numbers have different signs (one positive and one negative).
- Mixed numbers: Convert mixed numbers to improper fractions for easier multiplication.
By following these steps, you can easily multiply integers, even those involving mixed numbers.