Multiply Multiples of 10 by Decomposing Factors
Multiply Multiples of 10 by Decomposing Factors is a Grade 4 math skill that uses the associative property to break down multiplication of two-digit multiples of 10. The key insight is that tens times tens equals hundreds: (a x 10) x (b x 10) = (a x b) x 100. So 30 x 20 becomes (3 x 2) x 100 = 600. This approach is taught in Chapter 10: Multiplication by 10, 100, and 1,000 in Eureka Math Grade 4 and builds fluency with large-number mental math, which is essential for multi-digit multiplication in later chapters.
Key Concepts
To multiply two digit multiples of 10, you can decompose each number, then use the associative property to regroup the factors. $$(a \times 10) \times (b \times 10) = (a \times b) \times (10 \times 10)$$ This is the same as multiplying the units: $a \text{ tens} \times b \text{ tens} = (a \times b) \text{ hundreds}$.
Common Questions
How do I multiply multiples of 10 together?
Decompose each multiple of 10 into its non-zero digit and a factor of 10. Multiply the digits together, then multiply the powers of 10. For example, 30 x 20 = (3 x 10) x (2 x 10) = 6 x 100 = 600.
What is the associative property and how does it help with multiples of 10?
The associative property says you can regroup factors without changing the product. For multiples of 10, regrouping lets you multiply the non-zero digits first, then handle the zeros separately: (3 x 10) x (2 x 10) = (3 x 2) x (10 x 10) = 6 x 100.
What does tens times tens equal in place value?
Tens times tens equals hundreds. For example, 3 tens times 2 tens equals 6 hundreds, because (3 x 10) x (2 x 10) = 6 x 100. This place value pattern is why multiplying multiples of 10 always ends in at least two zeros.
How do I multiply 50 x 40?
Decompose: 50 x 40 = (5 x 10) x (4 x 10) = (5 x 4) x (10 x 10) = 20 x 100 = 2,000. Alternatively, multiply 5 x 4 = 20, then count the zeros in both numbers (two total), so the answer is 2,000.
What chapter in Eureka Math Grade 4 covers multiplying multiples of 10?
Chapter 10: Multiplication by 10, 100, and 1,000 in Eureka Math Grade 4 covers multiplying single digits and multiples of 10 by powers of ten using place value reasoning and the associative property.
Why is multiplying multiples of 10 an important skill?
Fluency with multiples of 10 is the foundation for estimating products, solving multi-digit multiplication problems, and understanding place value shifts. It helps students solve problems mentally and check whether calculated answers are reasonable.