Divide by Multiples of 10 by Decomposing the Divisor
Divide by Multiples of 10 by Decomposing the Divisor is a Grade 5 math skill in Eureka Math where students rewrite a divisor that is a multiple of 10 as a product of a one-digit number and a power of 10, then divide in two steps to simplify the calculation. This strategy builds on place value understanding and makes large-number division more manageable.
Key Concepts
To divide by a number that is a multiple of a power of ten, you can decompose the divisor into its factors and divide sequentially. This can be expressed as: $$a \div (b \times c) = (a \div b) \div c$$.
Common Questions
How do you divide by a multiple of 10 by decomposing the divisor?
Rewrite the divisor as a one-digit number times a power of 10. For example, 420 divided by 60 becomes 420 divided by 6 divided by 10. First divide 420 by 6 to get 70, then divide 70 by 10 to get 7.
Why is it easier to divide in two steps than all at once?
Dividing by a single-digit number uses basic facts you already know. Then dividing by the power of 10 is a simple place value shift, so the two steps together are simpler than dividing by the full multiple of 10 directly.
What is the mathematical justification for this strategy?
Multiplication and division are related by the associative property. Since 60 = 6 x 10, dividing by 60 is the same as dividing by 6 and then by 10, or in any order.
What are some examples of dividing by multiples of 10 in Grade 5?
Examples include 350 divided by 70, 6,400 divided by 80, and 4,200 divided by 60. All follow the same decompose-and-divide approach using basic division facts.