Using the Partial Differences Method
Using the partial differences method for subtraction is a Grade 5 math skill in enVision Mathematics, Chapter 2: Use Models and Strategies to Add and Subtract Decimals. Students decompose the subtrahend into its place value parts and subtract each part from the minuend one at a time, making each step simpler. For example, 5.85 - 2.41 = (5.85 - 2) - 0.4 - 0.01 = 3.44.
Key Concepts
To subtract using partial differences, break the second number into its place value parts (e.g., ones, tenths, hundredths). Then, subtract each part one at a time from the first number. For a problem like $5.85 2.41$, the process is: $$(5.85 2) 0.4 0.01$$.
Common Questions
What is the partial differences method for subtraction?
Break the subtrahend into its place value parts and subtract each part from the minuend one step at a time. Each step reduces the minuend until all parts are subtracted.
How do you solve 7.63 - 3.24 using partial differences?
7.63 - 3 = 4.63; 4.63 - 0.2 = 4.43; 4.43 - 0.04 = 4.39. Answer: 4.39.
Why is the partial differences method useful?
It breaks a complex subtraction into smaller, easier steps that can be done mentally, reducing errors from borrowing across multiple decimal places.
Where is the partial differences method taught in enVision Grade 5?
Chapter 2: Use Models and Strategies to Add and Subtract Decimals in enVision Mathematics, Grade 5.
Is partial differences similar to partial sums for addition?
Yes. Just as partial sums adds place value parts separately, partial differences subtracts them one piece at a time.