Multiply Decimals Using Compensation
Multiply Decimals Using Compensation is a Grade 5 math skill from Eureka Math that teaches students to multiply decimals more easily by adjusting one factor to a simpler value, then compensating for the adjustment. For example, to compute 0.99 x 6, multiply 1 x 6 = 6 and then subtract 0.01 x 6 = 0.06, giving 5.94. This mental math strategy reduces computational burden and builds number sense.
Key Concepts
To multiply a decimal by a whole number, you can multiply the decimal by a power of 10 to make it a whole number, perform the multiplication, and then divide the product by the same power of 10. This compensation strategy keeps the overall value the same. $$a \times b = (a \times 10^n) \times b \div 10^n$$.
Common Questions
What is the compensation strategy for decimal multiplication?
Round one factor to a simpler value, perform the multiplication, then adjust the result to account for the difference between the original and rounded factor.
How do you use compensation to multiply 4.9 x 8?
Round 4.9 to 5: 5 x 8 = 40. The difference is 0.1, and 0.1 x 8 = 0.8. Since you rounded up, subtract: 40 - 0.8 = 39.2. So 4.9 x 8 = 39.2.
Why is compensation useful for decimal multiplication in Grade 5?
Many decimals like 0.99, 1.01, 4.9, and 5.1 are near round numbers. The compensation strategy makes these problems much faster to compute mentally than using the full standard algorithm.
What Eureka Math Grade 5 chapter covers decimal multiplication with compensation?
Eureka Math Grade 5 covers multiplying decimals using compensation in its decimal multiplication chapters as a mental math strategy alongside the standard algorithm.
How does compensation for decimals relate to compensation for whole numbers?
It is the same strategy: adjust a difficult number to a round number, compute, then add or subtract the adjustment. The strategy extends naturally from whole numbers to decimals.