Find Products by Subtracting from a Larger Fact
Find Products by Subtracting from a Larger Fact is a Grade 3 math skill from Eureka Math using a known easy fact to derive a harder multiplication fact. Specifically, to multiply by 9, use the 10s fact and subtract one group: 9 × n = (10 × n) - (1 × n). For example, 9 × 3 = (10 × 3) - (1 × 3) = 30 - 3 = 27. This strategy lets students derive 9s facts from 10s facts they already know, reducing reliance on pure memorization and illustrating how the Distributive Property enables flexible computation.
Key Concepts
To solve a multiplication fact, you can use a larger, "friendly" fact (like a 10s fact) and then subtract the extra group(s). In unit form: $9$ threes $= 10$ threes $ 1$ threes As a number sentence: $9 \times 3 = (10 \times 3) (1 \times 3)$.
Common Questions
How do you use a larger fact to find a product by subtracting?
Use the 10s fact as the anchor, then subtract one group. For 9 × n: compute 10 × n and subtract 1 × n. For example, 9 × 7 = (10 × 7) - (1 × 7) = 70 - 7 = 63.
Why does the 'subtract one group from a 10s fact' strategy work for multiplying by 9?
Because 9 = 10 - 1. By the Distributive Property: 9 × n = (10 - 1) × n = (10 × n) - (1 × n).
Use this strategy to find 9 × 6.
9 × 6 = (10 × 6) - (1 × 6) = 60 - 6 = 54.
Can this strategy be extended beyond 9s facts?
Yes. You can use any nearby easy fact as an anchor and adjust. For 8 × n, use (10 × n) - (2 × n), or use (5 × n) + (3 × n). The principle is flexible.
In which textbook is Find Products by Subtracting from a Larger Fact taught?
This skill is taught in Eureka Math, Grade 3.