Lesson 2: More Numerical Patterns

Property

When comparing two numerical patterns, a multiplicative relationship exists if each term in one pattern can be found by multiplying the corresponding term in the other pattern by a constant number. If Pattern A has terms $a$ and Pattern B has terms $b$, the relationship is $b = k \times a$ for a constant number $k$.

Examples

• Pattern A: 1, 2, 3, 4
• Pattern B: 4, 8, 12, 16

The relationship is that each term in Pattern B is 4 times the corresponding term in Pattern A. ($B = 4 \times A$)

• Pattern A: Start at 2, add 2 (2, 4, 6, 8)
• Pattern B: Start at 10, add 10 (10, 20, 30, 40)

The relationship is that each term in Pattern B is 5 times the corresponding term in Pattern A. ($B = 5 \times A$)

Explanation

A multiplicative relationship occurs when two patterns are connected by a consistent multiplication rule. To identify this relationship, compare the corresponding terms from each pattern. You can check for this relationship by dividing a term from the second pattern by its corresponding term in the first pattern. If this operation yields the same number for all pairs of terms, you have found the multiplicative rule.