Multiplying Multiples of 10
Multiplying Multiples of 10 is a Grade 4 math skill that extends place value reasoning to multiply two-digit multiples of 10 by applying the rule that tens x tens = hundreds and tens x ones = tens. The pattern is: (a x 10) x (b x 10) = (a x b) x 100. So 40 x 20 = 8 x 100 = 800. This skill is covered in Chapter 16: Multiplication of Two-Digit by Two-Digit Numbers in Eureka Math Grade 4 and is the mental math foundation for estimating two-digit by two-digit products before applying the full algorithm.
Key Concepts
To multiply multiples of 10, multiply the non zero digits and then adjust the place value based on the units being multiplied. Tens $\times$ Tens = Hundreds: $(a \times 10) \times (b \times 10) = (a \times b) \times 100$ Tens $\times$ Ones = Tens: $(a \times 10) \times c = (a \times c) \times 10$.
Common Questions
How do I multiply 40 x 20?
Multiply the non-zero digits: 4 x 2 = 8. Then count the total zeros in both numbers: 40 has one zero and 20 has one zero, giving two zeros total. Place two zeros after 8 to get 800. So 40 x 20 = 800.
What rule applies when multiplying tens by tens?
Tens times tens always equals hundreds. (a x 10) x (b x 10) = (a x b) x 100. For example, 3 tens x 5 tens = 15 hundreds = 1,500. The digits multiply and the zeros combine.
How does multiplying multiples of 10 relate to place value?
Each place value is 10 times the one to its right. When you multiply a tens digit by another tens digit, the product lands in the hundreds place because tens x tens = hundreds. This is a direct consequence of the base-ten place value structure.
Why is multiplying multiples of 10 important for two-digit multiplication?
When multiplying two-digit numbers using the standard algorithm or area model, you must multiply the tens digit of one number by the tens digit of the other. Knowing that this partial product lands in the hundreds place is essential for placing digits correctly.
How do I multiply 30 x 50?
30 x 50 = (3 x 10) x (5 x 10) = (3 x 5) x (10 x 10) = 15 x 100 = 1,500. Alternatively, multiply 3 x 5 = 15 and count two zeros (one from 30 and one from 50) to get 1,500.
What chapter covers multiplying multiples of 10 in Eureka Math Grade 4?
Chapter 16: Multiplication of Two-Digit by Two-Digit Numbers in Eureka Math Grade 4 begins with multiplying multiples of 10 as preparation for the full two-digit by two-digit multiplication algorithm.