Divide Decimals by Multiples of 10
Divide Decimals by Multiples of 10 is a Grade 5 math skill from Eureka Math that teaches students to divide decimal numbers by 10, 20, 30, and other multiples of 10. Students decompose the divisor into its factors and apply place value thinking to find quotients efficiently. This skill extends understanding of division to the decimal domain and supports fluency with decimal operations.
Key Concepts
Property To divide a decimal by a multiple of 10, you can use a two step process. First, divide the decimal by the single digit factor of the divisor. Then, divide the resulting quotient by 10. $$a.b \div (c \times 10) = (a.b \div c) \div 10$$.
Examples $5.4 \div 60 = (5.4 \div 6) \div 10 = 0.9 \div 10 = 0.09$ $4.8 \div 40 = (4.8 \div 4) \div 10 = 1.2 \div 10 = 0.12$ $0.72 \div 90 = (0.72 \div 9) \div 10 = 0.08 \div 10 = 0.008$.
Explanation This skill extends division by multiples of 10 to decimal dividends. You can simplify the problem by breaking the divisor into its factors (e.g., 60 becomes 6 and 10). First, perform the standard division with the single digit factor, and then shift the decimal point one place to the left to divide by 10. This method connects basic division facts to the rules of place value for an efficient strategy.
Common Questions
How do you divide a decimal by a multiple of 10?
Decompose the multiple of 10 into its factors. For example, dividing by 20 is the same as dividing by 2 and then by 10. Apply each operation in sequence using place value reasoning.
What does it mean to divide decimals by multiples of 10?
It means dividing a decimal number by values like 20, 30, or 40. You can use the fact that 20 = 2 x 10 to break the problem into simpler steps.
How is dividing by 20 different from dividing by 10?
Dividing by 20 = dividing by 2 x 10: first divide by 2 (or by 10), then divide by the remaining factor. The result is half the size of dividing by 10.
What Eureka Math Grade 5 chapter covers dividing decimals by multiples of 10?
Eureka Math Grade 5 covers dividing decimals by multiples of 10 in the decimal division chapters, building on students knowledge of dividing by single powers of 10.
How does decomposing divisors help with decimal division?
Breaking a divisor like 40 into 4 x 10 lets students apply two simpler operations rather than one harder one, leveraging existing knowledge of basic facts and place value.