Multiplying Three or More Factors
Multiplying three or more factors in Grade 4 math is done by multiplying any two factors first, taking the result, and multiplying by the next factor—repeating until all factors are used. For example, 2 × 5 × 7 = (2 × 5) × 7 = 10 × 7 = 70. Covered in Chapter 7 of Saxon Math Intermediate 4, students apply the Associative Property of Multiplication, which guarantees the order of grouping does not affect the final product, allowing them to choose the easiest grouping.
Key Concepts
To find the product of three or more numbers, multiply any two factors first, then multiply that result by the next factor. Continue this process until all factors are used. The order in which you multiply does not change the final product, thanks to the awesome Associative Property of Multiplication we learned about earlier.
$2 \times 5 \times 7 = (2 \times 5) \times 7 = 10 \times 7 = 70$ $4 \times 6 \times 5 = 4 \times (6 \times 5) = 4 \times 30 = 120$ $3 \times 2 \times 5 \times 10 = (3 \times 2) \times (5 \times 10) = 6 \times 50 = 300$.
Think of it as a multiplication party! You can't dance with everyone at once, so you pick a partner, then the next, and so on. The best part? It doesn't matter who you multiply first. You can group numbers to make it easier, like finding a 10, to get the same answer.
Common Questions
How do you multiply three or more numbers together?
Multiply any two factors first, then multiply the result by the next factor. Repeat until all factors are used. For 3 × 4 × 5: (3 × 4) × 5 = 12 × 5 = 60.
Does the order of grouping matter when multiplying three numbers?
No. The Associative Property of Multiplication says (a × b) × c = a × (b × c). You can group any two factors first and get the same product.
What strategy makes multiplying three factors easier?
Look for a pair of factors that multiply to give a 'nice' number like 10 or 100. In 4 × 5 × 7: multiply 4 × 5 = 20 first, then 20 × 7 = 140.
When do Grade 4 students learn to multiply three or more factors?
Multiplying three or more factors is covered in Chapter 7 of Saxon Math Intermediate 4, after students have mastered two-factor multiplication.
How does multiplying three factors connect to the Distributive Property?
While the Associative Property governs grouping, the Distributive Property can sometimes simplify one factor before multiplying. Both strategies lead to the same product.
What is a real-world example of multiplying three factors?
A classroom has 4 rows of desks, each row has 6 desks, and there are 3 classrooms: 4 × 6 × 3 = 72 total desks. Or group as (4 × 3) × 6 = 12 × 6 = 72.