Multiply Using the Distributive Property
This Grade 4 Eureka Math skill teaches students to multiply two-digit by two-digit numbers using the distributive property, breaking one factor into its tens and ones and multiplying each part separately. For example, 50 times 31 = 50 times (30 + 1) = (50 times 30) + (50 times 1) = 1,500 + 50 = 1,550. Similarly, 74 times 6 can be rewritten as (70 + 4) times 6 = 420 + 24 = 444. This decomposition strategy from Chapter 16 of Eureka Math Grade 4 lays the groundwork for the area model and the standard two-digit multiplication algorithm.
Key Concepts
The distributive property of multiplication states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products. $$a \times (b + c) = (a \times b) + (a \times c)$$.
Common Questions
What is the distributive property of multiplication?
a times (b + c) = (a times b) + (a times c). Multiplying a number by a sum equals the sum of multiplying that number by each addend separately.
How do you use the distributive property to solve 50 times 31?
Break 31 into 30 + 1. Multiply: 50 times 30 = 1,500 and 50 times 1 = 50. Add: 1,500 + 50 = 1,550.
How do you use distributive property for 30 times 42?
Break 42 into 40 + 2. Multiply: 30 times 40 = 1,200 and 30 times 2 = 60. Add: 1,200 + 60 = 1,260.
Can you break up either factor when using the distributive property?
Yes. You can break up either factor into expanded form. For 74 times 6, break 74 into 70 + 4: (70 times 6) + (4 times 6) = 420 + 24 = 444.
Why is the distributive property useful for multiplication?
It turns one difficult multiplication into two easier ones. By breaking a factor into tens and ones, you only need to multiply by single-digit or round numbers, which is more manageable.