Decomposition Examples for 5th Grade: Real-World Problems

📚 Quick Study Guide

• 🔍 Decomposition: Breaking down a number into smaller parts. For example, $15$ can be decomposed into $10 + 5$ or $7 + 8$.
• ➕ Addition Decomposition: Splitting numbers to make addition easier. For example, $27 + 15$ can become $27 + (10 + 5) = (27 + 10) + 5 = 37 + 5 = 42$.
• ➖ Subtraction Decomposition: Splitting numbers to make subtraction easier. For example, $43 - 16$ can become $43 - (10 + 6) = (43 - 10) - 6 = 33 - 6 = 27$.
• ✖️ Multiplication Decomposition: Breaking numbers to make multiplication simpler. For example, $6 \times 7$ can become $6 \times (5 + 2) = (6 \times 5) + (6 \times 2) = 30 + 12 = 42$. This uses the distributive property.
• ➗ Division Decomposition: This is a bit trickier, but you can break the dividend (the number being divided) into parts that are easily divisible by the divisor.
• 💡 Tip: Practice makes perfect! The more you decompose numbers, the easier it becomes.
• 📝 Remember: The goal is to make math easier, not harder! Choose decompositions that simplify the problem.

Practice Quiz

1. What is one way to decompose the number 36 to help you solve a problem?
   1. A. 30 + 6
   2. B. 18 + 12
   3. C. 20 + 16
   4. D. All of the above
2. Emily has 52 stickers. She gives 25 to her friend. How can she decompose 25 to make the subtraction easier?
   1. A. 20 + 5
   2. B. 10 + 15
   3. C. 30 - 5
   4. D. 24 + 1
3. John wants to multiply 8 x 7. Which decomposition of 7 would make the problem easier?
   1. A. 4 + 3
   2. B. 5 + 2
   3. C. 6 + 1
   4. D. All of the above
4. A baker has 48 cookies to pack into boxes. If each box holds 6 cookies, what decomposition can help find how many boxes are needed?
   1. A. Breaking 48 into 40 + 8
   2. B. Dividing 48 by 2 and then by 3
   3. C. Thinking of 48 as 6 x 8
   4. D. All of the above
5. Sarah needs to add 19 + 33. How can she decompose the numbers to make it simpler?
   1. A. (10 + 9) + (30 + 3)
   2. B. 20 + 32
   3. C. 15 + 37
   4. D. 10 + 42
6. A farmer has 63 apples and wants to divide them into 7 bags. What decomposition helps determine how many apples per bag?
   1. A. Dividing 63 by 3 and then by 4
   2. B. Recognizing 63 as 7 x 9
   3. C. Breaking 63 into 60 + 3
   4. D. All of the above
7. What is the main goal of decomposing numbers in math problems?
   1. A. To make the problem look harder
   2. B. To confuse your teacher
   3. C. To make the problem easier to solve
   4. D. To use more paper