Using Compensation for Subtraction
Using compensation for subtraction is a Grade 5 math skill in enVision Mathematics, Chapter 2: Use Models and Strategies to Add and Subtract Decimals. Students replace the subtrahend with a nearby easy number c, compute a - c, then adjust the result by adding (c - b) to compensate: a - b = (a - c) + (c - b). This mental math strategy simplifies subtraction by working with rounder numbers.
Key Concepts
To mentally calculate a difference like $a b$, you can change the subtrahend ($b$) to a nearby, easier number ($c$). Then, subtract $c$ from $a$ and adjust the result by adding the difference between $c$ and $b$. $$a b = (a c) + (c b)$$.
Common Questions
What is compensation in subtraction?
Compensation means replacing the subtrahend with a nearby round number, subtracting that, then adding back the difference to adjust. For example, 5.4 - 1.9 becomes 5.4 - 2.0 + 0.1 = 3.5.
Why use compensation for subtraction?
Round numbers are easier to subtract mentally. Compensation lets you work with simple numbers first, then make a small adjustment for accuracy.
What is 8.6 - 3.8 using compensation?
Round 3.8 to 4.0: 8.6 - 4.0 = 4.6. Adjust: 4.0 - 3.8 = 0.2, so add 0.2 back: 4.6 + 0.2 = 4.8.
Where is compensation for subtraction taught in enVision Grade 5?
Chapter 2: Use Models and Strategies to Add and Subtract Decimals in enVision Mathematics, Grade 5.
Can compensation be used with whole numbers too?
Yes, compensation works with any numbers. It is a flexible mental math strategy applicable to whole numbers, decimals, and fractions.