DECOMPOSE

Decompose

Definition Of Decompose

Decompose is the process of separating numbers into their components (to divide a number into smaller parts).

Example of Decompose

456 can be decomposed as 456 = 400 + 50 + 6

Video Examples: Function Decomposition

Solved Example onDecompose

Ques: What will we get when we decompose 25,368?

Choices:

A. 2 ten thousands, 5 thousands, 3 hundreds, 6 tens, and 8 ones
B. 2 ten thousands, 5 thousands, 3 hundreds, 6 tens, and 6 ones
C. 2 thousands, 5 ten thousands, 3 hundreds, 6 tens, and 8 ones
D. 2 thousands, 5 hundreds, 3 tens, and 68 ones
Correct Answer: A

Solution:

Step 1: 21,368 = 20,000 + 5,000 + 300 + 60 + 8
Step 2: = (2 × 10,000) + (5 × 1,000) + (3 × 100) + (6 × 10) + (8 × 1)
Step 3: So, when we decompose 25,368, we will get '2 ten thousands, 5 thousands, 3 hundreds, 6 tens, and 8 ones'.

Quick Summary

Decomposition breaks down a number into its individual place values.
It helps in understanding the value of each digit in a number.
It is useful in performing arithmetic operations more easily.

\[ N = a_n * 10^n + a_{n-1} * 10^{n-1} + ... + a_1 * 10^1 + a_0 * 10^0 \]

⚠️ Common Mistakes

Mixing up place values (e.g., confusing tens and hundreds).
Incorrectly assigning values to digits during decomposition.
Forgetting to include zero as a placeholder.

🌍 Real-World Uses

Breaking down a grocery bill into categories like produce, dairy, and snacks to track spending.
Decomposing a complex project into smaller, manageable tasks with individual deadlines to improve workflow.
Analyzing the population of a city by decomposing it into age groups, genders, and ethnicities for urban planning.

📋 Standards Alignment

CCSS.MATH.CONTENT.1.NBT.B.2
CCSS.MATH.CONTENT.2.NBT.A.1

🍎 Teacher Insights

Use visual aids like base-ten blocks to illustrate the concept of place value and decomposition. Encourage students to practice with different numbers and different representations (e.g., expanded form, word form).

🎓 Prerequisites

Place Value
Addition
Understanding of Digits

Check Your Knowledge

Q1: What is the correct decomposition of 372?

A. 3 + 7 + 2 B. 30 + 70 + 2 C. 300 + 70 + 2 D. 300 + 7 + 2

Q2: Which of the following represents 500 + 20 + 9?

A. 52 B. 529 C. 592 D. 5029

Frequently Asked Questions

Q: Why do we decompose numbers?
A: Decomposing numbers helps us understand the value of each digit and makes it easier to perform addition, subtraction, and other arithmetic operations.

Q: Is there only one way to decompose a number?
A: While the most common method involves breaking down by place value, numbers can be decomposed in different ways depending on the context (e.g., using factors).